Physics 7B Discussion/Lab Manual - Waifer XPhysics 7B Discussion/Lab Manual "D" cell Multimeter used...

Physics 7BDiscussion/Lab Manual

"D" cell

Multimeter used to measure current flow through circuit (don't move!)

Multimeter used to measure ∆V between two locations (touch wire leads at various places)

COM

200m

DCA

VΩA blue

blue

blue

COM

20DCV

VΩA

redblack

2 3 4 5 61 7

0 8

milliAmpsVolts

Fall Quarter 2002 ArchivesUniversity of California, Davis

©Dr. Patrick M. Len, Ph.D

03.03.17

Dedicated to my wonderful wife, H. M.

A "Waifer X® Industries, Inc. Book"™

Copyright © 2003 by Patrick M. Len([email protected]). This material may bedistributed only subject to the terms andconditions set forth in the Open PublicationLicense v1.0 without options A or B(http://www.opencontent.org/openpub/).

Physics 7B Fall 2002: Discussion/Lab Manual 1

03.03.18

Physics 7B Discussion/Lab ManualFall Quarter 2002Constants and Conversion Factors 2Block 6 Discussion/Lab Activities 3

DLM 01 3DLM 02 11DLM 03 16

Block 7 Discussion/Lab Activities 25DLM 04 25DLM 05 30DLM 06 35DLM 07 42


Block 9 Discussion/Lab Activities 64DLM 12 64DLM 13 68DLM 14 74


Fall 2002 Quiz Archives 89Quiz 11 90Quiz 12 91Quiz 13 92Quiz 14 94

2 Physics 7B Fall 2002: Discussion/Lab Manual

03.03.18

Constants and Conversion FactorsConstants

G gravitational constant 6.67 ×10−11 N ⋅ m2 / kg2

k electric force constant 9 ×109 N ⋅ m2 / Coul2

c velocity of light 3.00 ×108 m/sme mass of the electron 9.11×10−31 kgmp mass of the proton 1.67 ×10−27 kgmn mass of the neutron 1.67 ×10−27 kge fundamental charge 1.602 ×10−19 Coul

Solar SystemgE gravitational field magnitude9.8 N / kg or m / s2

(acceleration) at or near Earth's surfaceME mass of the Earth 5.98 ×1024 kgRE radius of the Earth 6.37 ×106 mrE Earth-sun distance (mean) 1.50 ×1011 mMM mass of the moon 7.36 ×1022 kgrm Earth-moon distance 3.84 ×108 m

Conversion factorsEnergy1 eV = 1.602 ×10−19 J1 BTU = 1,055 J1 cal = 4.186 J1 kcal ("food Calorie") = 4,186 J

Length1 m = 39.4 in = 3.28 ft1 km = 0.621 mile1 Å (angstrom) = 10−10 m

Speed1 m/s = 3.28 fps (ft/s) = 2.24 mph (miles/hr) = 3.60 kph (km/hr)

Force1 N = 0.225 lb

Pressure1 Pa = 1 N / m2 = 0.000145 psi (lbs / in2 )1 Atm = 1.01×105 Pa = 14.7 psi

Mass1 kg = 0.0685 slugs

Angular measure2π radians = 360° = 400 gradients = 1 revolution


03.03.18

DLM 00 Exit handout (the first one!)

AnnouncementsThere are two items that you must purchase for Physics 7B, and both are available from Navin's CopyShop (231 Third Street; 758-2311) for a nominal fee.• Physics 7B Course Notes (W. H. Potter, 2002, J. Wiley Custom Services, ISBN 0-471-23044-8).• Physics 7B Student Packet, Fall 2002 (P. M. Len, 2002).

The first day of lecture will be on Tuesday, October 1, in Roessler 66. Discussion/labs willstart later that day as well. Quiz 6 will be given during lecture on Tuesday, October 15, and will cover the material inBlock 6. Bring a pen or pencil, calculator, and prepare to show your UC-Davis student ID card (orsimilar photo ID) upon entering, and/or during the quiz.


03.03.18

FNT ("For Next Time")1. Read the Block 6 Glossary in the Physics 7B Student Packet, Fall 2002, and familiarize

yourself with the following terms that will be used extensively in DLM 01.

Bernoulli's EquationContinuity Equationcurrent Idensity ρ fluid

frictionless flowgravity headkinetic head

laminar flowpressure Presistance Rsteady statestreamlinetotal hydraulic head

2. Analyze the five situations below, using the models developed in Block 5 of Physics 7A(Bernoulli's Equation, Continuity Equation), comparing points [1] and [2] for each situation forsteady-state frictionless fluid flow. Note that we are using "head" to refer to energy densities.

∆(total head)(+, –, or 0)

∆(pressure head)(+, –, or 0)

∆(gravity head)(+, –, or 0)

∆(velocity head)(+, –, or 0)

(a)(b)(c)(d)(e)

(a)

1 2

flow

1

2flow

2

flow

1

2

1

flow

1 2

(b) (c)

(d) (e)


03.03.18

Activity Cycle 6.1.1: Analyzing steady-state frictionless flow

Learning goals:• Identify energy density systems for steady-state frictionless fluid flow.• Proper use of energy density conservation for initial-final points in steady-state fluid flow.• Proper use of fluid conservation ("continuity") for initial-final points in steady-state fluid flow.

A. Review the approach for analyzing steady-state fluid flow without friction. Discussthese situations (a)-(e) in your group, and then put your group's answers up on theboard. This one is a quick fill-in chart; go on to (B) on the next page.

1. Analyze the five situations below, using the models developed in Block 5 of Physics 7A(Bernoulli's Equation, Continuity Equation), comparing points [1] and [2] for eachsituation. Note that we are using "head" to refer to energy densities.

∆(total head)(+, –, or 0)

∆(pressure head)(+, –, or 0)

∆(gravity head)(+, –, or 0)

∆(velocity head)(+, –, or 0)

(a)(b)(c)(d)(e)

(a)

1 2

flow

1

2flow

2

flow

1

2

1

flow

1 2

(b) (c)

(d) (e)

This activity concludes on the other side of this page. Your TA may elect to have a whole-classdiscussion here before moving on to the rest of this activity, in order to move every group along atthe same pace, and to clear up board space.


03.03.18

Activity Cycle 6.1.1: Analyzing steady-state frictionless flow(continued)

B. A more open-ended case to consider. Discuss these situations (a)-(c) in your group,and then put your group's answers up on the board. This one requires more thoughtand justification than (1).

Consider the frictionless steady-state fluid flow situation below, where at [1] the pipe has alarger cross-sectional area A1 and a higher height h1; at [2] the pipe has a smaller cross-sectional area A2 and a lower height h2.

12

2. Explain under what circumstances would each of the following situations (a)-(c) bepossible. Use the models developed in Block 5 of Physics 7A (Bernoulli's Equation,Continuity Equation), comparing points [1] and [2] for each situation by drawing energydensity diagrams, equations, etc. (Come up with a quantitative statement regardingrelative changes in kinetic and gravity heads for each situation(a)-(c)).(a) P1 > P2.(b) P1 = P2.(c) P1 < P2.

C. Challenge questions. Discuss these questions in your group, but unless instructed bythe TA, you do not have to put these up on the board.

3. In the most general sense, why are the situations in (2) so much more difficult to analyzethan in (1)?

4. Did you have to assume a direction for fluid flow in (2)? Would you have to change anyof your answers if the fluid flow was in the opposite direction? Explain why or why not.


03.03.18

Activity Cycle 6.2.1: Analyzing steady-state flow with friction

Learning goals:• Identify energy density systems for steady-state fluid flow with friction.• Proper use of energy density conservation for initial-final points in steady-state fluid flow.• Proper use of fluid conservation ("continuity") for initial-final points in steady-state fluid flow.

A. Extend your models to include friction. Discuss (1)-(3) in your group, and then putyour answers up on the board.

Consider the steady-state fluid flow situation at right, where at [1] the pipe has a larger cross-sectional area A1 and a higher height h1; at [2] the pipe has a smaller cross-sectional area A2

and a lower height h2, but now there is considerable frictional flow through this pipe frompoint [1] to point [2].

12

1. Explain how one of the two conservation laws (Bernoulli's Equation and the ContinuityEquation) must be modified in order to include the effect of friction, and explain why theother law does not have to be modified when there is friction.

2. Write out the appropriate conservation law that incorporates friction, and then explicitlyidentify how each term in that law is affected by the presence of friction, or does not differcompared to the frictionless flow case in activity cycle 6.1.1. (Put up an equation with"same as frictionless" or "different" for each term, and explain.)

3. For the two fluid flow parameters—pressure P2, and velocity v2—at point [2] in thisspecific situation, identify whether they are less than, equal to, or more compared to thefrictionless flow case in activity cycle 6.1.1. (Solve for P2, then set R = 0 or not.)

B. Practical things to consider when we apply this model in the next activity. Discuss(4)-(5) in your group, and then put your answers up on the board.

4. At point [2], either a pressure meter or a vertical column isattached. Explain how the vertical column could be used tocalculate the pressure at that point.

5. Draw streamlines (steady-state flow paths for fluidparticles) through the tube above from [1] to [2]. Now drawstreamlines for the tube with the pressure gauge, and for thetube with the vertical column at right. Does the vertical columnadversely affect the steady-state streamlines as it "measures"pressure, compared to a pressure meter?

pressure meter

2

vertical column(top is open to

atmosphere)

2


03.03.18

Activity Cycle 6.2.2: Steady-state flow with friction in a circuit

Learning goals:• Identify energy density systems for steady-state fluid flow with friction.• Proper use of energy density conservation for initial-final points in steady-state fluid flow.• Proper use of fluid conservation ("continuity") for initial-final points in steady-state fluid flow.

A. Understanding a physical fluid flow circuit. Discuss (1) in your group, do not putanything up the board, but be prepared to be called on individually in the whole-classdiscussion.

Consider a schematic of your flow tube experiment (make sure the valve is completely open).

(and back around again)

2 3 4

7

5 610

valve

pump

flow

no appreciable friction in thelarge section

segments

0

8 9

considerable friction in the small section segments

? ? ? ? ?

1. "Walk through" the schematic drawing above and on the actual flow tube experiment,from point [1] to point [2], and understand which terms in Bernoulli's Equation changes(increase? decrease?) or remain constant. Keep going, from [2] to [3], [3] to [4], etc.Make sure you understand what is going on for each segment of this circuit enough toanswer questions in the whole-class discussion.

B. Applying conservation laws to physical fluid flow circuit. Discuss (2)-(4) in yourgroup, and then put your answers up on the board.

2. Write out both conservation laws for point [2] to point [3].(a) Cross out energy density ("head") terms that simplify to zero, and explain why they

did. (Use R2 3→ = resistance of [2]-[3] pipe segment, etc.)(b) Identify each (remaining) variable with a physical "thing" on the flow tube

experiment.

3. Repeat 2(a), but change the valve setting such that the flow is a third of what is was before.Write out both conservation laws for point [2] to point [3] again, and now identify whichquantities increased, remained the same, or decreased compared to when the valve was allthe way open before.

4. Repeat 2(a), but for the valve completely shut, such that there is no flow at all. Write outboth conservation laws for point [2] to point [3] again, and now identify which quantitiesincreased, remained the same, or decreased compared to when the valve was all the wayopen before.


03.03.18

DLM 01 Exit handout

AnnouncementsThere are two items that you must purchase for Physics 7B, and both are available from Navin's CopyShop (231 Third Street; 758-2311) for a nominal fee.• Physics 7B Course Notes (W. H. Potter, 2002, J. Wiley Custom Services, ISBN 0-471-23044-8).• Physics 7B Student Packet, Fall 2002 (P. M. Len, 2002).

Quiz 6 will be given during lecture on Tuesday, October 15, and will cover the material inBlock 6. Bring a pen or pencil, calculator, and prepare to show your UC-Davis student ID card (orsimilar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1. A frictionless fluid enters a horizontal section of pipe (with the

same cross-sectional area throughout) from the left with avelocity v1 , and exits to the right. Explain whether eachstatement is true or false, using the appropriate conservationlaw(s).(a) P1 = P2 .(b) I1 = I2 .(c) v1 = v2 .

2. Repeat 1(a)-(c), but for fluid flow with friction.

3. A frictionless fluid enters a horizontal section of pipe (with thesame cross-sectional area throughout) from the left with avelocity v1 , and exits to the right, after going through a pump.Explain whether each statement is true or false, using theappropriate conservation law(s).(a) P P1 2< .(b) I I1 2< .(c) v v1 2< .


1 2

v1

pipe

pipe

1 2

v1

pump


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5. Consider the schematic of the flow tube experiment (the valve is open, but not all the way).


2 3 4

7

5 610

valve

pump

flow

no appreciable friction in the

large pipe segments

0

8 9

considerable friction in the small pipe segments

? ? ? ? ?

For each [ ]→[ ] listed below, write out both conservation laws; cross out energy density("head") terms that simplify to zero, and explain why they did so.(a) [1]→[2] (as already done in activity 6.2.2).(b) [6]→[7] (the valve itself has it own resistance value Rvalve ).(c) [8]→[9].(d) [9]→[0].(e) [7] all the way through back to [0].(f) Use your result in (e) to prove (very generally) that the drop in total hydraulic head from

[0] to [7] (due to resistance) must be equal to the gain in total hydraulic head (due to thepump) from [7] back to [0].

6. In this side view of a portion of a steady-state system, fluid at a pressure P0 enters a "wye" (Y)connection, and exits horizontally either through hose 1 (with a large cross-sectional area A1), orexits through hose 2 (with a small cross-sectional area A2). Explain which set of quantities canbe related to each other via a fluid conservation law (or laws), and then write out the appropriateconservation law (or laws). If a set of quantities cannot be related to each other via a fluidconservation law, then briefly explain why. (Hint: consider the streamlines!)(a) P0, P1.(b) P0, P2.(c) P1, P2.(d) I0, I1.(e) I0, I2.(f) I1, I2.(g) I0, I1, and I2.

7. Read the Block 6 Glossary in the Physics 7B Student Packet, Fall 2002, and familiarizeyourself with the following terms that will be introduced and used extensively in DLM 02.

laminar flowpower Ppump

2

01

I 0

I 1

I 2


03.03.18

Activity Cycle 6.2.3: Fluid flow conservation laws, wrap-up

Learning goals:• Identify energy density systems for steady-state fluid flow.• Proper use of energy density conservation for initial-final points in steady-state fluid flow.• Proper use of fluid conservation ("continuity") for initial-final points in steady-state fluid flow.

A. Summarizing FNT results. Discuss (1)-(4) in your group, and then put your group'sanswers up on the board, along with a brief explanations for your 12 differentanswers.

1. A frictionless fluid enters a horizontal section of pipe(with the same cross-sectional area throughout) from theleft with a velocity v1 , and exits to the right. Explainwhether each statement is true or false, using theappropriate conservation law(s).(a) P1 = P2 .(b) I1 = I2 .(c) v1 = v2 .


3. A frictionless fluid enters a horizontal section of pipe(with the same cross-sectional area throughout) from theleft with a velocity v1 , and exits to the right, after goingthrough a pump. Explain whether each statement is trueor false, using the appropriate conservation law(s).(a) P P1 2< .(b) I I1 2< .(c) v v1 2< .


B. Which conservation laws to use, and when? Review your group's answers for(1)-(4), and then discuss (5) in your group, and then put your group's answers up onthe board.

5. Which conservation law is "different" whether there is frictionless flow or flow withfriction? Which conservation law does not matter whether there is frictionless flow orflow with friction?

1 2

v1

pipe

pipe

1 2

v1

pump


03.03.18

Activity Cycle 6.3.1: Analyzing realistic friction flow situations

Learning goals:• Proper use of energy density conservation for initial-final points in steady-state fluid flow.• Proper use of fluid conservation ("continuity") for initial-final points in steady-state fluid flow.

A. Summarizing FNT results. Discuss (4)-(5) in your group, and then put your group'sanswers up on the board, along with a brief explanations for your answers.

4. Consider the schematic of the flow tube experiment (the valve is open, but not all the way).For each [ ]→[ ] listed below, write out both conservation laws; cross out energy density("head") terms that simplify to zero, and explain why they did so.(a) [1]→[2] (as already done in activity 6.2.2).(b) [6]→[7] (the valve itself has it own resistance value Rvalve ).(c) [8]→[9].(d) [9]→[0].(e) [7] all the way through back to [0].(f) Use your result in (e) to prove (very generally) that the drop in total hydraulic head

from [0] to [7] (due to resistance) must be equal to the gain in total hydraulic head(due to the pump) from [7] back to [0].

5. In this side view, fluid at a pressure P0 enters a "wye" (Y) connection, and exitshorizontally either through hose 1 (with a large cross-sectional area A1), or exits throughhose 2 (with a small cross-sectional area A2). Explain which set of quantities can berelated to each other via a fluid conservation law (or laws), and then write out theappropriate conservation law (or laws). If a set of quantities cannot be related to eachother via a fluid conservation law, then briefly explain why. (Hint: consider thestreamlines!)(a) P0, P1.(b) P0, P2.(c) P1, P2.(d) I0, I1.(e) I0, I2.(f) I1, I2.(g) I0, I1, and I2.

B. How are streamlines important in applying fluid flow conservation laws? Discuss (6)in your group, and then put your group's answers up on the board.

6. Draw a bunch of streamlines starting from point [0], with some going to point [1], andsome going to point [2].(a) Explain why you can't use the Continuity Equation here for comparing point [1]

with point [2]. Does a streamline have to "connect" the two points used in theContinuity Equation? Do all streamlines have to "connect" these two points?

(b) Explain why you can't use Bernoulli's Equation here for comparing point [1] withpoint [2]. Does a streamline have to "connect" the two points used in the Bernoulli'sEquation? Do all streamlines have to "connect" these two points?

2

01

I 0

I 1

I 2


03.03.18

Activity Cycle 6.3.2: Analyzing a real friction flow situation

Learning goals:• Proper use of conservation laws for initial-final points in steady-state fluid flow with friction.• Power converted to thermal systems for steady-state fluid flow with friction.


2 3 4

7

5 610

valve

pump

flow

no appreciable friction in the

large pipe segments

0

8 9

considerable friction in the small pipe segments

? ? ? ? ?

A. This is an open-ended activity in the sense that you are given a list of things tocalculate, but are not given an explicit experimental procedure of quantities tomeasure. Put your results up on the board as you work, in order that your TA cangauge your progress.

Consider the flow tube experiment, with the valve is only a third of the way open (such that theheight of the water in column [6] is non-zero).

1. Determine the numerical value of the resistance for any small pipe section of the flowtube, between adjacent columns (it will have peculiar units of J·s/m6). Make whatevermeasurements you need to with a ruler, graduated cylinder, and the second hand of a clockor watch. Then determine the amount of power (in J/s) converted to thermal systems inthis small pipe section. (Hint: first define your points [ ] and [ ] to be used in theappropriate conservation law equation(s), write out the conservationequation(s), and then determine what quantities to be calculated or measured!Don't forget to calculate the power loss.)

B. Challenge question. Put this one up on the board, but the same level of explanation asin (1) is not required.2. Repeat (1), but for the valve/spigot (from [6] to [7]). Take into account the 90° bend of

the spigot, down to where the water flows out of the spigot into the atmosphere. Makewhatever measurements you need to with a ruler, graduated cylinder, and the second handof a clock or watch.

Constants:g = 9.8 N/kg.

1 Atm = 101,000 Pa = 101,000 J

m3 .

ρwater = 1,000 kgm3 .

1 m3 = 1,000 L.1 L = 1,000 mL = 1,000 "cc".


03.03.18

DLM 02 Exit handout

AnnouncementsThere are two items that you must have already purchased for Physics 7B from Navin's Copy Shop(231 Third Street; 758-2311):• Physics 7B Course Notes (W. H. Potter, 2002, J. Wiley Custom Services, ISBN 0-471-23044-8).• Physics 7B Student Packet, Fall 2002 (P. M. Len, 2002).

Quiz 6 will be given during lecture on Tuesday, October 15, and will cover the material inBlock 6. Bring a pen or pencil, calculator, and prepare to show your UC-Davis student ID card (orsimilar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1-8. You must have two AA batteries and three holiday light bulbs with attached pigtail leads in

order to do this assignment. The plastic insulation needs to be stripped back about 1 cm to2 cm on the end of each wire before you leave this DL, using the wire stripper.(a) For each electrical circuit set-up (1)-(8) shown on the next page, make a simple physical

picture of the batteries, bulbs and wires showing how they are arranged.(b) Actually wire together the batteries and bulbs as you have drawn them in (a). Using an

extra pair of hands usually works, but also consider laying the batteries flat along thecrease of an open book, and/or with twisting wires together, especially if you are doingthis assignment alone.

(c) Indicate the observed brightness of each bulb in each diagram in (a). (You may want todo this in the dark!) For example, if you have a set-up with three bulbs and one is brightand two are dim, you might put the words "bright" by the bright one and "dim" by each ofthe dim ones. Only compare between different light bulbs in the same electrical circuit);you are not comparing between different light bulbs in different electrical circuits.

9. Read the Block 6 Glossary in the Physics 7B Student Packet, Fall 2002, and familiarizeyourself with the following terms that will be used extensively in DLM 03.

batteryContinuity Equationcurrent Ielectric potentialelectromotive force (emf) E

power Presistance RresistorTransport Equationvoltage V

Challenge FNT10. We will go over this as an activity in DLM 03, but you may want to start getting practice with

electric charge flow circuits. Write out the Transport Equation for each circuit set-up (1)-(8),starting at the upper left-hand corner of a circuit, and then going all the way around until comingback to the upper left-hand corner. You should begin to see a pattern in the way the TransportEquation is written out for many of these circuits.


03.03.18

2.

+–

+– +– +–6.

5.1. +– +– +– +–

3.

+ –

+– +– + –7.

4. +– +– +– +–8.


03.03.18

Activity Cycle 6.4.1: Analogies between fluid and charge flow

Learning goals:• Identify energy density systems for steady-state charge flow.• Proper use of energy density conservation for initial-final points in steady-state charge flow.

A. This is an open-ended activity in thesense that you aregiven a list of thingsto calculate, but arenot given an explicitprocedure. Fill inthe chart on the nextpage up on theboard as you work,in order that yourTA can gauge yourprogress.

1. For each [ ] to [ ]listed on the next page, decide whether that portion of the electric circuit is best describedby one of the following fluid flow analogy choices below.(Be prepared to explain your justification for these choices when called uponduring a whole-class discussion.)(i) Wide fluid pipe with very little resistance.(ii) Narrow fluid pipe with significant resistance.(iii) Very narrow fluid pipe with large amounts of resistance.(iv) Fluid pump.

2. Measure I (in milliAmps) and ∆ V (in Volts) for each and every [ ] to [ ] section.(Hint: you should not have to move the multimeter used to measure current if you use aconservation law!)

3. Write out the transport equation using the [ ] and [ ] as your initial and final points, anddetermine the electrical resistance R (in Ω or Ohms) of that section of the circuit.

B. Focus in on more abstract analogies between fluid and charge flow.

4. What is the physical object/fluid flow analog for the following charge flow concepts?(a) I.(b) ∆ V .(c) Ammeter.(d) Voltmeter.

"D" cell

Multimeter used to measure current flow through circuit (don't move!)

Multimeter used to measure ∆V between two locations (touch wire leads at various places)

COM

200m

DCA

VΩA blue

blue

blueCOM

20DCV

VΩA

redblack

2 3 4 5 61 7

0 8

milliAmpsVolts


03.03.18

Activity Cycle 6.4.1: Analogies between fluid and charge flow

[8]→[0]

[7]→[8]

[6]→[7]

[5]→[6]

[4]→[5]

[3]→[4]

[2]→[3]

[1]→[2]

[0]→[1]

Current I

[milliA

mps]

Change in

electric potential("voltage") ∆

V[V

olts]T

ransport Equation, solving for resistance

R [O

hm

s]F

luid flowanalog(i)-(iv)


03.03.18

Activity Cycle 6.4.2: Charge flow conservation laws

Learning goals:• Proper use of energy density conservation for initial-final points in steady-state charge flow.• Proper use of fluid conservation ("continuity") for initial-final points in steady-state charge flow.

A. Summarizing FNT results. Your TA will assign one or two of the FNT circuits(1)-(8) for your group to discuss, put up on the board, and present to the whole class.

1. Write out the Transport Equation for your entire circuit, starting at the upper left-handcorner of a circuit, and then going all the way around until coming back to the upper left-hand corner. Drop subscripts on terms that are equal to other terms, be carefulwhat you set ∆ V equal to, and watch ± signs!

2. Of the three types of charge flow quantities ( E , I, R) in your Transport Equation, identifywhich are given constants (i.e., will have the same value no matter which circuit it is in),and which quantities are unknown (i.e., its value must be calculated for each differentcircuit).

3. Determine the power used by each light bulb in your assigned circuit (label them as P 1,

P 2, etc.). Make sure your power expressions depend only on given constants!Explicitly show how you used the Transport Equation again, and which twolocations were used for each light bulb ∆ V .

B. Analyzing the analysis process. Work at the board in your groups; you may find iteasier to "fill-in" steps in your outline as you go along.

4. Write out a generalized procedure for determining the power transferred to thermal energysystems of a given charge flow circuit element (such as a light bulb), as used here. (Don'tfixate on this procedure from start-to-finish; later we will often "go backwards" or "startin the middle!" The idea here is to keep track of "good practice" in analyzing chargeflow circuits.) Explicitly show how you used the Transport Equation again, andwhich two locations were used for each light bulb ∆ V .• Write out the Transport Equation for the entire circuit.

• Set ∆ V = 0. (Why?)• Watch for ± terms in E and IR terms. (How do you know which ± to use?)

• Solve for ..., etc., etc.


03.03.18

Activity Cycle 6.4.2: Charge flow conservation laws (continued)

2.

+–

+– +– +–6.

5.1. +– +– +– +–

3.

+ –

+– +– + –7.

4. +– +– +– +–8.


03.03.18

Activity Cycle 6.4.3: Analyzing realistic charge flow situations

Learning goals:• Proper use of energy density conservation for initial-final points in steady-state charge flow.• Proper use of fluid conservation ("continuity") for initial-final points in steady-state charge flow.

A. This is an open-ended activity in the sense that you are given a list of things tocalculate, but are not given an explicit procedure. Put your results up on the board asyou work, in order that your TA can gauge your progress. Show your steps here; youwill need the Continuity Equation in addition to multiple Transport Equations!

1.

+– +–

bulb (b)

bulb (c)

bulb (a)

2.

bulb (b)

bulb (a)

bulb (c)

+–+–

Do the following separately for each circuit (1) and (2). Express everything in terms of thegiven quantities E and R (each battery has the same emf value; each light bulb has the samevalue of resistance). You may use "symmetry" arguments in your explanations.

1. Draw a circuit diagram, using proper symbols. (Note that there can be more than oneunique way of drawing a diagram for a given circuit.)

2. Rank the amount of current (Ia, Ib, Ic ) passing through each and every light bulb, fromgreatest to least. If some light bulbs have the same amount of current flowing throughthem, make sure you say so.

3. Rank the amount of electric potential ( ÆV a , ÆV b , ÆV c) used by each and every light bulb,from greatest to least. If some light bulbs use the same amount of electric potential, makesure you say so.

4. Rank the power ( P a , P b , P c) used by each and every light bulb, from brightest todimmest. If some light bulbs use the same amount of power, make sure you say so.(You can also wire the circuit together to check your answer!)

B. Challenge question. Put this one up on the board.

X. Write out in words a short explanation for each light bulb as to why it is bright or dimwith respect to the others in its respective circuit (Lots of current? Lots of electricpotential drop? Both? Only one?)


03.03.18

DLM 03 Exit handout

Announcements Quiz 6 will be given during lecture on Tuesday, October 15, and will cover the material inBlock 6. Bring a pen or pencil, calculator, and prepare to show your UC-Davis student ID card (orsimilar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")DLM 04 is a problem-solving session that will consolidate the material covered in Block 6. Thefollowing six problems represent actual or sample quiz or final exam questions given in previousquarters.

Keep in mind that your Quiz 6 grade will explicitly depend on the methodical application ofthe analytical tools developed in Block 6, and being able to demonstrate this understanding in wordsand equations. Generous partial credit will be given for starting the correct approach in aconscientious manner, much less partial credit will be given for blind plugging-and-chugging.

These question/problems were completely new situations that were never seen before by thestudents who took these quizzes in the past. Similarly, you should expect completely new situationson Quiz 6 that you have never seen before as well. However, no matter how strange and differentyour Quiz 6 will appear to you at first, you must learn to rely on the analytical tools developed inBlock 6. Don't fixate on a "solving-problems-like-these" mentality, you should concentrate on aformulating a "general-approach-to-any-problem" strategy when doing these question/problemsand when studying for Quiz 6.

(Quiz 6, Spring 2002)1. Water flows with friction

through a horizontalsection of pipe ofchanging cross-sectionalarea as shown. This pipeis a segment of a largercomplete fluid circuit,which has reached asteady state. Thepressure at each end ofthe pipe is indicated on the diagram. Determine the direction of flow for the water in the pipe,and explain your choice of direction. Credit is assigned for the completeness and clarity ofyour justification, not necessarily for finding the correct direction of flow.

(A) It is only possible that water flows from [1]→[2].(B) It is only possible that water flows from [2]→[1].(C) It is possible that water flows from [1]→[2] or from [2]→[1].(D) It is not possible that water flows from [1]→[2] nor from [2]→[1].

1

2

pressure meter

pressure meter

P = 113,000 Pa1 P = 120,000 Pa2


03.03.18

(Final Exam, Winter 2001)2. Water flows through a section of horizontal pipe that is a

portion of a complete steady-state system, similar to thepipe in DL. Water flows into this particular pipe section(from somewhere else) at point [1], then leaves this pipesection (to continue onwards to somewhere else) at point[3]. The height of the water in each vertical column, incm, is shown at right.

Now suppose that the radius of the pipe is made wider(while it still has its original length), thus decreasing itsresistance by a factor of 5×. The pressure at point [1] isthe same as before, and the amount of current flowingthrough this new wider pipe is somehow made identicalto the amount of current flowing through the narrowsection of pipe above. Fill in the water level in thevertical columns [2] and [3] in the diagram at right. Beclear and accurate in drawing the water level, and explainyour reasoning. Credit is assigned for the completenessand clarity of your justification, not necessarily forfinding the correct water level.

(Quiz 6, Spring 2000)3. When the walls of a section of an artery lose their

elasticity, the flow through the section will rapidlyfluctuate. The artery rapidly collapses and expands inthe constricted region, producing vascular flutter.The pressure outside the artery, Poutside , remainsconstant throughout this entire process, and P1 alsoremains constant. Explain (a) why the artery wouldclose off momentarily in the narrowed region as shownat right, stopping the flow of blood, and (b) why itwould subsequently open back up again. Credit isassigned for the completeness and clarity of yourjustification.

1

flow

3

5 cm

10 cm

15 cm

2

1

flow

3

5 cm

10 cm

15 cm

2

21

flow

21

flow

outside

outside


03.03.18

(Quiz 6, Spring 2002)4. A 1.5 Volt battery (battery 1) and a 2.0 Volt battery

(battery 2) are hooked up to three identical light bulbs,each of the same resistance "R" (light bulbs 1, 2 and 3),as shown at right. Credit is assigned for thecompleteness and clarity of your justification, notnecessarily for finding the correct rankings.(a) Rank the five circuit elements, from highest to

lowest amount of current flowing through them.If some circuit elements have the same amount ofcurrent flowing through them, make sure you sayso.

(b) Rank the five circuit elements, from highest tolowest amount of voltage change ( ∆V only, don'tworry about the ± signs or whether it is a voltagedrop or increase). If some circuit elements have thesame amount of voltage change, make sure you say so.

(Quiz 6, Winter 2001)5. An ideal battery of E = 20 Volts is connected to three light

bulbs, as shown in the circuit at right. Credit is assigned forthe completeness and clarity of your justification.(a) Determine the three resistances R1 , R2 , R3 (in Ω) of

the three light bulbs, if all three light bulbs have thesame brightness, dissipating 40 Watts each.

(b) Originally, all three light bulbs have the samebrightness (40 Watts each). Suppose now that theresistance of R2 (light bulb 2) is now increased by afactor of two. By what factor would the brightness oflight bulb 1 increase, decrease, (or experience nochange)? Explain your answer and show yourreasoning.

(Block 6 assignment, Winter 2001)6. Consider a non-ideal battery, with an emf E battery = 1.5 Volts, and an

internal resistance rbattery . This battery is hooked up to a light bulb ofresistance R. As the battery grows older, its internal resistance rbattery

increases, as the chemical products inside do not conduct electric currentas well as the reactants in a "fresh" battery. However, the emf E battery

from the reactant chemicals inside is still a constant 1.5 Volts, no matterhow little reactants are left in the battery. Calculate the numerical factorthat the in the power dissipated in the light bulb decreases by, after theinternal resistance rbattery increased from zero to the same value as R.Credit is assigned for the completeness andclarity of your justification.

+-

E

R 1

R 2R 3

battery 2 = 2.0 V

battery 1 = 1.5 V

+ –

light bulb 2

light bulb 3

2

E

+–

light bulb 1

E

1

+-

rE

R


03.03.18

7. Read the Block 7 Glossary in the Physics 7B Student Packet, Fall 2002, and familiarizeyourself with the following terms that will be introduced in DLM 05, and used extensivelyDLM 06.

force (definition)net force F∑Newton's First LawNewton's Second Lawtail-to-head additionvector

vector addition(superposition)

vector multiplicationvector subtractionvelocity

rv

8. Subtract these velocity vectors graphically using the"tail-to-head" method. Label the resultant change invelocity vector for each case below, on a separate pieceof graph paper.(a) ∆ = −→v v v1 2 2 1.(b) ∆ = −→v v v1 3 3 1.(c) ∆ = −→v v v1 4 4 1.(d) ∆ = −→v v v2 3 3 2 .(e) ∆ = −→v v v2 4 4 2 .(f) ∆ = −→v v v3 4 4 3 .

unit length

1v 2v

3v

4v


03.03.18

2v8

4

Activity Cycle 7.1.1: Net forces and changes in velocity

Learning goals:• Apply Newton's Laws to determine motion (constant or changing) of the object of interest.• Apply Newton's Laws to determine direction of net force acting on object of interest.• Understand vector subtraction properties of velocities.

A. Summarizing FNT results. Your TA will assign to your group one of the (a)-(f)change in velocity vectors (∆∆∆∆v) to put up on the board. Once your TA has checked offyour work and understanding of velocity vector subtraction, go onto the next activitybelow.

1. Subtract these velocity vectors graphicallyusing the "tail-to-head" method. On theboard, label the length of the rectilinearcomponents of your vectors (since there isno board grid) as shown below.(a) ∆ = −→v v v1 2 2 1.(b) ∆ = −→v v v1 3 3 1.(c) ∆ = −→v v v1 4 4 1.(d) ∆ = −→v v v2 3 3 2 .(e) ∆ = −→v v v2 4 4 2 .(f) ∆ = −→v v v3 4 4 3 .

B. Relate velocity (changing or constant) to direction of net force. Work at the board inyour groups; you may find it easier to fill in a big chart on the board as you go along,such that your TA can gauge your group's progress.

2. For each object (a)-(j) listed below, draw its initial velocity vector vinitial and its finalvelocity vector v final , as seen from the side.

3. For each object (a)-(j) listed below, draw its change in velocity vector ∆v.4. For each object (a)-(j) listed below, state whether the net force F∑ is zero; or if it is non-

zero, indicate the direction of F∑ . State whether its motion is described by Newton'sFirst Law or Newton's Second Law.(a) A basketball stationary on the ground.(b) A basketball rolling horizontally on the ground, at constant speed, to the right.(c) A basketball rolling horizontally on the ground, that bounces off of a wall

(initial = just before hitting the wall; final = just after hitting the wall).(d) A basketball rolling horizontally on the ground, at constant speed, to the left.(e) A basketball rolling horizontally on the ground, to the right, but slowing down.(f) A basketball that is falling down vertically.(g) A basketball, after being thrown upwards, and still moving upwards (initial = just

after leaving hand; final = still moving upwards, but at slower speed).(h) A basketball, at the very topmost peak of its vertical arc (initial = just before the

peak; final = just after the peak).(i) A stationary basketball on a tabletop, with you pressing down on it.(j) A basketball resting stationary, atop the palm of your hand.

unit length

1v 2v

3v

4v


03.03.18

Activity Cycle 7.1.1: Net forces and changes in velocity (continued)

initial velocity vectorvinitial

final velocity vectorv final

change in velocity∆v

F∑ = 0, or

F∑ direction

(N1 or N2?)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)


03.03.18

Activity Cycle 6.4.4: Analyzing fluid or charge flow systems

Learning goals:• Identify energy density systems for steady-state charge and fluid flow.• Proper use of energy density conservation for initial-final points in steady-state charge/fluid flow.

A. (50 minutes.) Summarizing FNT results. Your TA will assign one of the sample quizquestion/problems (1)-(6) for your group to discuss, put up on the board, and presentto the whole class.

When working on your assigned question/problem:• Make sure you clearly show the following!

I. List and circle the (relevant) given information you used.II. List and circle the assumptions/laws/equations you used.III. State what you were asked to solve for.IV. Write your solution to the question/problem on the board. In order to conserve space,

do not show every math step (e.g., show the equation; solve it in terms of everythingelse; then show the numerical answer).

B. (40 minutes.) Presenting FNT results. Your TA will call on one or a number ofpeople at random in your group to present your group's solution to your assignedquestion/problem (1)-(6).

When presenting your assigned question/problem:• Make sure everyone in your group is able to explain your question/problem when called

upon! Your TA will either call on a person at random from your group; or may call oneveryone in turn to present your group's question/problem.

• After your question/problem is on the board, and you are ready to present your solution, thenyou can compare your individual work to the question/problems assigned to the other groups.


03.03.18

DLM 04 Exit handout


FNT ("For Next Time")1. Add these force vectors graphically using the "tail-to-

head" method. Label the resultant force vector foreach case below, on a separate piece of graph paper.

(a) F∑ = F1 + F2.

(b) F∑ = F2 + F1.

(c) F∑ = F2 + F1 + F3.

(d) F∑ = F1 + F3 + F2.

2. Forces F1, F2, andF3 are all exerted on an object,adding together to form a net force vector F∑ , asshown at right. However, only forces F1, F2, and

F∑ are known. On a separate piece of graph paper,use the properties of vector addition to graphicallydetermine the vector for force F3.

3. Forces F1, F2, F3, and F4 are all exerted on anobject, adding together to form a net force vector

F∑ = 0, as shown at right. However, only forcesF1, F2, and F∑ (which is zero) are known. It isknown that F3 is completely vertical, and F4 iscompletely horizontal. On a separate piece of graphpaper, use the properties of vector addition tographically determine the magnitudes of the verticalforce F3 vector, and the horizontal force vector F4.

unit length

1F

2F

F∑ = F1 + F2 + F3

object

unit length

1F

2F

F = 0∑

object

unit length

1F2F

3F


03.03.18


component-by-componentaddition

force diagramforce, contactforce, gravity

force, rope/string (tension)force, spring (elastic)rectilinear components

(no trigonometry)


03.03.18

Activity Cycle 7.1.2: Introduction to force diagrams

Force diagram conventions:• Draw the object acted upon as a dot. Do not "draw" the object—idealize the object as just a dot.• One force diagram per object (i.e., one dot per object). Label your object dot.• Only forces exerted on that object are shown on the force diagram.• Each force vector is drawn as an arrow acting on the object dot.

• Direction represents its direction of its push or pull.• Magnitude (length) represents the amount of push or pull (in N). Use a proportional scale (say,

so many cm or inches on a ruler for each N of force) to draw the lengths of your force vectors.Label the length of the force vector in N, as well.

• Each force vector must be labeled as such: F type of force of exerting object on object of interest( ) ( ) ( ).• All the force vectors acting on an object must add up into the net force

rF∑ . Separately, draw the

net force vector rF∑ beside the object dot as a double line vector .

A. (30 minutes.) Making simple force diagrams. Put up the force diagrams for (1)-(2)up on the board as you go along, so your TA can check your progress.

1. Consider a 1.0 kg mass hanging from a string.(a) List all the types of interactions that involve this object.(b) Explicitly write out these interactions as forces labeled as

" F type of force of exerting object on object of interest( ) ( ) ( )."(c) Draw the object acted upon as a dot. Do not "draw" the object—idealize it as a dot.

Label your dot.(d) Draw these force vectors acting on the object dot. Properly scale the magnitudes of

these vectors (in N). Use g = 9.8 N/kg in your calculations, and a scale of 1"↔↔↔↔ 1 N to draw the vectors on the board.

(e) Off to the side of the diagram, show

rF∑ , the result of adding all these force

vectors together.(f) Is the velocity vector of this object constant, or is it changing? Briefly explain using

Newton's Laws.

2. Repeat steps (a)-(f) above, but for a penny taped onto a coffee filter (10 g total mass),falling downwards with a constant speed. Use g = 9.8 N/kg in your calculations, anda scale of 10" ↔↔↔↔ 1 N to draw the vectors on the board.


03.03.18

Activity Cycle 7.1.3: More force diagrams

Learning goals:• Apply Newton's Laws to determine motion (constant or changing) of the object of interest.• Apply Newton's Laws to determine magnitude and direction of force(s) acting on object of interest.• Understand vector properties of forces and velocities.• Model behavior of objects subject to specific types of forces.

A. Making more force diagrams. Put up the force diagrams for (1)-(5) up on the board asyou go along, so your TA can check your progress. Your TA may elect to assign onlyone force diagram to each group, if time remaining in today's DL is an issue.

For each properly labeled and scaled force diagram:(a) List all the types of interactions that involve this object.(b) Explicitly write out these interactions as forces labeled as

" F type of force of exerting object on object of interest( ) ( ) ( )."(c) Draw the object acted upon as a dot. Do not "draw" the object—idealize it as a dot.

Label your dot.(d) Draw these force vectors acting on the object dot. Properly scale the magnitudes of

these vectors (in N). Use g = 9.8 N/kg in your calculations, and a scale of 1"↔↔↔↔ 1 N to draw the vectors on the board.

(e) Off to the side of the diagram, show

rF∑ , the result of adding all these force

vectors together. Label and scale the length of the net force vector, in N.(f) Is the velocity vector of this object constant, or is it changing? Briefly explain using

Newton's Laws.

1. A 0.5 kg basketball held in the palm of a hand;(i) raised with constant speed.(ii) after being released, while falling.

2. A hand pushing 10 N down on a 0.5 kg basketball on a table.

3. A 1.0 kg mass hanging from a string, with a hand pulling down on a string attached to itwith 10 N.

4. A 1.0 kg mass hanging from a string, with a 0.5 kg mass hanging from it.

5. A 1.0 kg mass hanging from a string, with a hand pushing 5 N up on it.


03.03.18

Activity Cycle 7.2.1: Analysis of forces using force diagrams

Learning goals:(Cf. activity cycle 7.1.3.)

A. Summarizing FNT results. Your TA will assign to your group one of the tail-to-headvector addition problems 1(a), 1(b), 1(c), 1(d), (2) or (3) to put up on the board.Once your TA has checked off your work and understanding of tail-to-head vectoraddition, go onto the activity on the other side of this page.

1. (a) F∑ = F1 + F2.

(b) F∑ = F2 + F1.

(c) F∑ = F2 + F1 + F3.

(d) F∑ = F1 + F3 + F2.

On the board, label the lengths of the rectilinearcomponents of F∑ , since there is no whiteboardgrid.

2. Determine the vector for force F3.

3. Determine the magnitudes of F3 and F4.

This activity concludes on the other side of this page.Your TA may elect to have a whole-class discussion herebefore moving on to the rest of this activity, in order tomove every group along a the same pace, and to clear upboard space.

unit length

1F2F

3F

unit length

1F

2F

F∑ = F1 + F2 + F3

object

unit length

1F

2F

F = 0∑

object


03.03.18

Activity Cycle 7.2.1: Analysis of forces using force diagrams(continued)

B. This is an open-ended activity in the sense that you are given objectives, but are notgiven an explicit procedure.

4. Use just one spring scale torecord the amount of horizontalforce (in N) exerted to hold thering stationary, as shown at right.Do everything in front of theboard, so you can also trace thedirection of the string onto theboard. How much force youpull horizontally is up to you, butwhatever it is, write it down!(Don't forget that the pull scale isyours to keep!)

5. Use a scaled force diagram and a separate scaled tail-to-head vector addition diagram forthe massless ring in order to determine the magnitude (in N) of the string tension force.Don't fixate too much on the "proper" labels for the forces, concentrate here on gettingthe magnitudes and directions and vector addition as accurate as possible without usingtrigonometry! Use g = 9.8 N/kg in your calculations, and a scale of 1" ↔↔↔↔ 1 N todraw the vectors on the board.

C. Challenge question. Put this one up on the board if time allows.

6. Explain using Newton's Laws, a force diagram and/ora tail-to-head vector addition diagram to explainwhether the new situation shown at below right(where the pull scale, ring, and masses are all in avertical line) is possible or not.

diagonal string

(trace direction on board)

"massless" ring

2 kg total mass

pull scale

diagonal string

"massless" ring

2 kg total mass

pull

scal

e


03.03.18

DLM 05 Exit handout


FNT ("For Next Time")1. Consider a 7 kg bowling ball on the floor. Draw a properly labeled and scaled force diagram for

the 7 kg b.b. for each of the following cases (a)-(f). Off to the side of each diagram, show F∑ .Label and scale the length of the each force and net force vector, in N. Use g = 9.8 N/kg in yourcalculations.

(a) 7 kg bowling ball resting on the floor.(b) 7 kg b.b. on the floor with you pulling up (say, with an attached rope) with a force of

10 N.(c) 7 kg b.b. on the floor with you pulling up with a force of 65 N.(d) 7 kg b.b. on the floor with you pushing down with a force of 10 N.(e) 7 kg b.b. on the floor with you pushing down with a force of 65 N.(f) 7 kg b.b. with you pulling up with a force of 70 N.


force, contactforce, friction (" |||||||| contact")force, normal (" ⊥⊥⊥⊥ contact")Newton's Third Law"Third Law pair"

(The question below will be collected at the start of DLM 06. Write your answer on a separate pieceof paper with your name on it, and turn it in to your TA as you enter DLM 06.)

3. Consider that when 1 kg is hangingfrom a scale, it reads "1 kg" (duh).What will this scale read when it is"double-pulled?"(A) The scale will read "0.0 kg."(B) The scale will read "0.5 kg."(C) The scale will read "1.0 kg."(D) The scale will read "2.0 kg."(E) The scale will read something other than the above choices.

1 kg mass

pull

scal

e re

ads

"1 k

g"

1 kgmass

1 kgmass

table

pull scale reads "???"


03.03.18

Activity Cycle 7.2.2: Analysis of ⊥ contact forces

Learning goals:• Apply Newton's Laws to determine magnitude and direction of force(s) acting on object of interest.• Understand vector properties of forces.• Model behavior of specific types of forces.

A. Summarizing FNT results. Your TA will assign to your group one of the force diagrams(a)-(f) to put up on the board. Once your TA has checked off your work, go ontoquestions (2)-(4) below.

1. Consider a 7 kg bowling ball on the floor. Draw a properly labeled and scaled forcediagram for the 7 kg b.b. for each of the following cases (a)-(f). Use a scale of 0.5 cm ↔↔↔↔10 N (but also write down the magnitude of each force, in N). Off to the side of eachdiagram, show F∑ . Label and scale the length of these net force vectors, in N. Use g =9.8 N/kg in your calculations.

(a) 7 kg bowling ball resting on the floor.(b) 7 kg b.b. on the floor with you pulling up (say, with an attached rope) with a force

of 10 N.(c) 7 kg b.b. on the floor with you pulling up with a force of 65 N.(d) 7 kg b.b. on the floor with you pushing down with a force of 10 N.(e) 7 kg b.b. on the floor with you pushing down with a force of 65 N.(f) 7 kg b.b. with you pulling up with a force of 70 N.

B. Analysis of the ⊥⊥⊥⊥ contact force. Discuss (2)-(4) in your group, and then put yourgroup's answer up on the board.

2. Draw a Physics 7A model of the atoms in a floor, with connecting springs between theatoms. How will the positions of the floor atoms change if a bowling ball is placed atop it?Write a brief explanation using this picture and Newton's Law of how the floor seems to"know" how much ⊥ contact force to push up on any object placed atop it.

Look at all the force diagrams (a)-(f). Put up brief explanations for your answers to thesemultiple choice questions. There can be more than one possible answer.

3. The magnitude of the ⊥ contact force can be

less than

equal to

more than

to the weight of an object.

4. The ⊥ contact force always points in the direction directly opposite of .

to the surface.

Fgravity

⊥

.


03.03.18

Activity Cycle 7.2.3: Analysis of || contact forces


A. Making force diagrams of different situations involving || contact forces. Actuallyperform and measure all forces involved for 1(a)-(f). Then put up the following sixscaled and labeled force diagrams up on the board. You should be able to give actualvalues for all the force vectors in each force diagram.

1. Your group should have a box of weights on a floor, with a rope attached to its side. Youshould use a yellow pull-scale, and there should also be a bathroom scale somewhere in theroom (which measures in pounds; weight of 2.2 lbs = force of 9.8 N). Perform andexperimentally measure all the forces involved for the following cases (a)-(f).

Draw a properly labeled and scaled force diagram up on the board for the box for each ofthe following cases (a)-(f). For each of your six force diagrams, use a scale of 0.5 cm↔↔↔↔ 10 N (but also write down the magnitude of each force, in N). Indicate the F∑net force vector separately on the side, for each case.(a) The box is stationary (no pulling).(b) The box has 1 N of force pulling sideways on it.(c) The box has a maximum amount of force pulling sideways on it, such that it is still

stationary.(d) The box has enough force pulling sideways on it to barely get it starting to move

sideways.(e) The box is being pulled sideways, with constant speed.(f) While the box is coming to a stop, after releasing the rope.

Note that in this activity, the difference between static and kinetic frictional forces may benearly negligible. In this case, it is okay to make the approximation that µkinetic ≈ µstatic .



03.03.18

Activity Cycle 7.2.3: Analysis of || contact forces (continued)

B. Analysis of the || contact force. Discuss (2)-(5) in your group, and then put your group'sanswer up on the board.

2. What is the coefficient µ for wood on linoleum?

Put up brief explanations for your answers to these multiple choice questions.

3. When an object in contact with a surface is stationary, then the amount of frictional

contact force exerted on it has a minimum value of

0

F

Fgravity

contact⊥

and a given maximum value

of

∞

⊥

.

.

.

some coefficient times


F

Fgravity

contact

4. When an object in contact with a surface is moving (whether its speed is constant orchanging), then the frictional contact force on it is always (approximately) at its given

maximum value of

∞

⊥

.

.

.



F

Fgravity

contact

5. The frictional contact force always points in the direction⊥⊥

⊥

to .

to (parallel to the surface).

F

Fgravity

contact


03.03.18

Activity Cycle 7.3.1: Newton's Third Law and "Third Law pairs"

Learning goals:• Apply Newton's Laws to determine magnitude and direction of force(s) acting on object of interest.• Distinguish between forces related by Newton's First Law, and forces related by Newton's Third Law.

A. Your TA will collect your homework, then survey your predictions for the "double-pulled" scale as a class, before actually demonstrating it.

(i) 1 kg mass

pull

scal

e re

ads

"1 k

g"

(ii) 1 kgmass

1 kgmass

table

pull scale reads "???"

B. Making force diagrams to model the behavior of the "single-pulled" and "double-pulled" scales. Put up the following five scaled and labeled force diagrams up on theboard.

1. Draw two separate properly labeled and scaled force diagrams for the pull scale and the1 kg mass, for situation (i). (Assume ideal massless ropes, scales, pulleys, etc.) Use ascale of 1" ↔↔↔↔ 1 N (but also write down the magnitude of each force, in N).

2. Draw three separate properly labeled and scaled force diagrams for the pull scale, the left1 kg mass, and the right 1 kg mass, for the "double-pulled" situation (ii). Use a scale of1" ↔↔↔↔ 1 N (but also write down the magnitude of each force, in N).

3. Group together forces associated together by Newton's First Law with a "1."

4. Pair off forces associated together by Newton's Third Law with a "3."

5. Why does the scale read "___ kg" when it is "double-pulled?"


03.03.18

DLM 06 Exit handout


FNT ("For Next Time")DLM 07 is a problem-solving session that will consolidate the material covered in Block 7. Thefollowing six problems represent actual or sample quiz or final exam questions given in previousquarters.

(Quiz 7, Spring 2002)1. Two bowling balls, each with a weight of 300 N, are placed on the floor. Bowling ball A has a

hand pressing down on it with 50 N of force. Bowling ball B has a cable attached to its top, anda hand pulls upward on this cable with 50 N of force. As a result, both bowling balls A and Bstill remain at rest on the floor. (You may elect to answer questions (a) and (b) separately, ortogether in one discussion.) Credit is assigned for the completeness and clarity of yourdiscussion using Newton's Laws and the properties of vector addition/subtraction, and notnecessarily for your multiple-choice answers below.(a) Consider the magnitude of the ⊥ contact force on either bowling ball. Choose the

statement below that is true, and justify your answer using force diagrams, Newton'sLaws, and the properties of vectors.(I) F⊥ contact of floor on bowling ball A magnitude > F⊥ contact of floor on bowling ball B magnitude.(II) F⊥ contact of floor on bowling ball A magnitude < F⊥ contact of floor on bowling ball B magnitude.(III) F⊥ contact of floor on bowling ball A magnitude = F⊥ contact of floor on bowling ball B magnitude.

(b) Consider the direction of the ⊥ contact force on either bowling ball. Choose the statementbelow that is true, and justify your answer using force diagrams, Newton's Laws, and theproperties of vectors.(I) F⊥ contact of floor on bowling ball A and F⊥ contact of floor on bowling ball B have the same direction.(II) F⊥ contact of floor on bowling ball A and F⊥ contact of floor on bowling ball B have the opposite direction

(Quiz 7, Spring 2002)2. A person who weighs 500 N is trying to move a refrigerator that weighs 1,200 N, but without

success. The person pushes on the refrigerator with a horizontal force of 900 N and neither therefrigerator nor the person move at all. Justify your answers using force diagrams, Newton'sLaws, and the properties of vectors. Credit is assigned for the completeness and clarity of yourdiscussion using Newton's Laws and the properties of vector addition/subtraction.(a) Make a properly labeled and scaled force diagram for the person and another separate

diagram for the refrigerator. Indicate clearly (by circling) any Third Law force pairs.(b) Draw on graph paper a properly scaled tail-to-head vector addition diagram for the

person. Use a scale of 1 square = 50 N.

(Quiz 7, Winter 20001)


03.03.18

3. Three stationary boxes are stacked on top of a scale that measures weightin pounds. The top box weighs 4.0 pounds, and the lowest box weighs5.0 pounds, but the weight of the middle box is unknown. However, it isknown that a force with a magnitude of 6.0 pounds is exerted by thebottom box on the middle box. (You can leave the magnitudes of allforces in pounds, as that is the English system measurement of force. Or2.2 lbs = 9.8 N, for you metricphiles.) Credit is assigned for thecompleteness and clarity of your discussion using Newton's Laws andthe properties of vector addition/subtraction.(a) Make a properly labeled and scaled force diagram of the forces on

the bottom box on graph paper.(b) What reading does the scale have in pounds?

(Quiz 7, Winter 20001)4. A box of unknown mass is initially held stationary on an inclined slope that has friction. After

the box is let go, it begins to slide down the slope. The velocity of the box as it slides down theslope is not constant; its speed gradually increases. An incomplete force diagram for the box asit begins to slide down this slope is shown below, as seen from the side. (Count squarescarefully—one square = 1.0 N.) Credit is assigned for the completeness and clarity of yourdiscussion using Newton's Laws and the properties of vector addition/subtraction.(a) As the box begins to slide down the slope, in which direction does the net force F∑

vector point? Describe this direction in words as explicitly as possible, and support anddefend your answer in words.

(b) Make a tail-to-head vector addition diagram of the forces on the box, using graph paper.(c) What is the mass (in kg) of this box?

box is b

eginning to

slide down sl

ope

Physical picture Incomplete force diagram

F ⊥ contact (norm

al)

of slope on box

F || contact

(fricti

on)

of slope on box

box

4 poundbox

?

5 poundbox

weight scale


03.03.18

(Block 7 assignment, Winter 2001)5. Consider an ideal, massless bathroom scale that "weighs" objects placed atop of it. Use graph

paper to draw two properly labeled and scaled force diagrams (for the person and for thebathroom scale itself) for each situation (a)-(b) below, for a total of four separate forcediagrams. Pair off forces using Newton's First Law and Newton's Third Law. Credit isassigned for the completeness and clarity of your discussion using Newton's Laws and theproperties of vector addition/subtraction.(a) A 50 kg person stands on top of the (ideal, massless) bathroom scale.(b) Same as (a); but now the bathroom scale itself has a mass of 2 kg. The bathroom scale

here reads the same as in (a); come up with a plausible explanation of how and what thescale "reads."

(New Block 7 assignment, Fall 2002)6. A metal cylinder is hung from a vertically mounted k = 80 N/m spring. A string is attached to

the bottom of the cylinder, such that a person pulling with a force of 10 N on the string is ablepull the mass 0.2 m below the equilibrium position of the spring, and holds it stationary there.Credit is assigned for the completeness and clarity of your discussion using Newton's Lawsand the properties of vector addition/subtraction.(a) Make a properly labeled and scaled force diagram of the cylinder on graph paper.(b) What is the mass (in kg) of the cylinder?(c) What is the magnitude and direction of the net force F∑ on the cylinder, at the moment

in time just after the person lets go of the string?


03.03.18

Activity Cycle 7.3.2: Newton's Third Law and Third Law pairs


A. A new situation involving multiple interacting objects. Discuss and quickly put yourgroup's answers up on the board.

1. Three boxes are stacked on a table. The bottom box weighs 7 lbs, themiddle box 3 lbs, and the top block 5 lbs. (You can leave themagnitudes of all forces in pounds, as that is the English systemmeasurement of force. Or 2.2 lbs = 9.8 N, for you metricphiles.)(a) List all the forces that will come into play in an analysis of this

situation, using the form "F(type of force) of (exerting object ) on (object acted upon)"for each force you list. (You should have eight different forces in your list!Have your TA check this list before moving on.)

(b) Draw three separate force diagrams for this situation.(c) Use Newton's Laws and your force diagrams to determine the magnitude (in lbs) of

the upward ⊥ contact force on the middle box by the bottom box. Explain yourreasoning. (Pair off as many forces as you can using Newton's Third Law;group together forces that are related by Newton's First Law.)

B. Analysis of Third Law pairs, and forces related by Newton's First Law. Discuss(2)-(4) in your group, and then put your group's answers up on the board.

Look at your force diagrams in (1). Put up brief explanations for your answers to these multiplechoice questions, using your force diagrams as examples.

2. Forces related by Newton's First Law have switched " on ," " on " labels.

all share "__ on " labels.

A B B A

A

3. Forces related by Newton's Third Law have switched " on ," " on " labels.

all share "__ on " labels.

A B B A

A

4.Only two forces

Many forces

can be related by Newton's First Law, all exerted on

different objects.

the same object.

5.Only two forces

Many forces

can be related by Newton's Third Law, all exerted on

different objects.

the same object.

5lbs

3lbs

7lbs


03.03.18

Activity Cycle 7.2.4: Analysis of forces on objects

Learning goals:• Apply Newton's Laws to determine magnitude and direction of force(s) acting on object of interest.










03.03.18

DLM 07 Exit handout


FNT ("For Next Time")1. Take a hike! In order to "normalize" everyone's data, make one-second strides (count off

seconds as "one-Mississippi, two-Mississippi, etc.," and walk in such a way that the your rightfoot always repeats itself every second.(a) Measure the length of your right-foot-to-right-foot stride, in cm. (1" = 2.54 cm.)(b) Which one of the horizontal velocity versus time v(t) graphs below best depicts the

horizontal motion of your belly button as you smoothly walk in the forward direction?(c) Which one of the horizontal velocity versus time v(t) graphs below best depicts the

horizontal motion of your right heel as you smoothly walk in the forward direction?

t

v

t

v

t

v

t

v

t

v(A)

t

v(B) (C) (D)

t

v(E)

t

v(F) (G) (H)


acceleration ra

areaderivativeintegral"method of Oresme"

Newton's Second Lawposition (

rx,

ry)

slopespeedvelocity

rv


03.03.18

Activity Cycle 8.1.1: Integration in the method of Oresme

Learning goals:• Apply integral calculus relations between kinematic variables to analyze motion.

A. Summarizing FNT results. Quickly put your group's results up on the board,selecting one person's set of measurements. Also practice walking like each graph.

1. Make one-second strides (count off seconds as "one-Mississippi, two-Mississippi, etc.,"and walk in such a way that the your right foot always repeats itself every second.(a) Measure the length of your right-foot-to-right-foot stride, in cm. (1" = 2.54 cm.)(b) Act out each of the horizontal velocity v(t) graphs below, and discuss which

must be eliminated as being impossible depictions of the motion of your bellybutton while walking.

(c) Act out each of the horizontal velocity v(t) graphs below, and discuss whichmust be eliminated as being impossible depictions of the motion of your rightheel while walking.

t

v

t

v

t

v

t

v

t

v(A)

t

v(B) (C) (D)

t

v(E)

t

v(F) (G) (H)

B. Analysis of walking motion. This is an open-ended activity in the sense that you aregiven an objective, but are not given an explicit procedure.

2. Model the motion of your right heel with graph (G), where the stride time interval is onesecond1. Knowing that the area contained under the v(t) graph for one stride is thedistance covered by your foot in one stride, determine the maximum horizontal velocity(in cm/s) of your right foot. (FYI: 1 cm/s = 2.23694× −10 2 mph.)

velo

city

v [m

/s]

0

?

0.5 1.0–

+

time t [s]

1 Can you draw a new v(t) graph that would better describe the motion of your right heel?


03.03.18

Activity Cycle 8.1.2: Differentiation in the method of Oresme

Learning goals:• Apply integral calculus relations between kinematic variables to analyze motion.• Apply differential calculus relations between kinematic variables to analyze motion.• Connect forces with kinematic variables via Newton's Laws.

A. Making v(t) graphs. Discuss the given information below in your group, and put yourvelocity versus time graph for the basketball up on the board. You will later scale thisgraph in the following activity (2) below.

1. Consider the horizontal motion of an m = 0.5 kg basketball as described below. Sketchone v(t) graph that consecutively shows all three motions, and explain physically whichdirection you have (arbitrarily) chosen to be the positive velocity direction. Assume thatthe velocity graph consists of three line segments. (Also assume that the basketball haslong since left the hand of the person throwing it, and neglect any effect of air resistanceor friction throughout its motion.)• From t = 0 seconds to t = 0.80 seconds, it rolls at a constant speed of 1.2 m/s towards a

wall.• From t = 0.80 seconds to 0.82 seconds, it is momentarily in contact with ("bouncing off

of") the wall.• From t = 0.82 seconds to 2.42 seconds, it rolls back at a constant speed to where it

started from.

B. Quantitative analysis of the v(t) graphs. This is an open-ended activity in the sensethat you are given an objective, but are not given an explicit procedure. Discuss andscale the vertical axis of your group's v(t) graph up on the board.

2. Scale the vertical ± velocity values for your v(t) graph. In your analysis, you shoulddetermine somehow the distance between the initial position of the basketball att = 0 seconds, and the wall. Show your work and explain your reasoning.

C. Connection with Newton's Laws. Discuss and put up your group's three forcediagrams up on the board.

3. Make three separate force diagrams, as seen from the side, for the basketball for the threemotions described above in (1). Properly label each force vector. Use a scale of 1 cm ↔1 N, but also write down the magnitude of each force, in N. Use g = 9.8 N/kg. Indicatethe F∑ net force vector (magnitude and direction) separately on the side, for each case,and whether you used Newton's First Law or Newton's Second Law to deduce the detailsof each force diagram.


03.03.18

Activity Cycle 8.2.1: Method of Oresme: freefall with no drag

Learning goals:• Apply the method of Oresme describe the motion of and quantify the forces acting upon an object.

A. This is an open-ended activity in the sense that you are given several objectives, butare not given an explicit procedure. You may need to work this problem using severaldifferent approaches, and in the end make everything consistent with each other.

Consider the vertical motion of an m = 0.5 kg basketball as described below.[0] At t = 0 seconds, it is moving straight upwards with a speed of 2.0 m/s. (Assume that it has

long since left the hand of the person throwing it, and neglect any effect of air resistancethroughout its motion.)

[1] At some unknown time, it reaches it maximum height.[2] At some unknown time, it is moving downwards with a speed of 2.0 m/s, past the point at

which it started its motion at t = 0 seconds.

1. Draw a v(t) graph for the basketball, and scale the vertical v and horizontal t axes. Whattime did the basketball reach its highest height? Hint: what must the slope of your v(t)graph be?

2. Determine the maximum height of the basketball, above the point at which it started itsmotion at t = 0 seconds. (Although it is possible to do so, do not use the initial-finalenergy conservation approach developed in Physics 7A to answer this question.Concentrate on using the method of Oresme instead!)

3. Make three separate force diagrams, as seen from the side, for the basketball for the threeinstances in time described above. Properly label each force vector. Use a scale of1 cm ↔ 1 N, but also write down the magnitude of each force, in N. g = 9.8 N/kg.Indicate the F∑ net force vector (magnitude and direction) separately on the side, foreach case.

B. Ensuring that everything is self-consistent. Revise your work above as necessary,when going through the consistency checks below.

4. What is the slope of your v(t) graph at each of the instances in time described above?Show that these v(t) slopes are consistent with the magnitude and direction of your F∑net force vectors. Is the ± sign of your slope consistent with the direction of your netforce vector?

5. What is the total area bounded by your v(t) graph from t = 0 seconds to when thebasketball reaches it maximum height? What is the total area bounded by your v(t) graphfrom t = 0 seconds to when the basketball falls downwards past its starting point?

6. On the same v(t) graph that you have drawn on the board, show the motion of a basketballthat just after released from rest, and allowed to fall downwards towards the floor.


03.03.18

DLM 08 Exit handout


FNT ("For Next Time")Consider the vertical motion of an m = 0.5 kg basketball as described by the graph below.• At t = 0 seconds, its center of mass originally starts at some unknown height above the floor.• It falls straight downwards, bounces off of the floor, and then moves upwards to an unknown

shorter maximum height. Throughout this problem, neglect the effect of air resistance on thebasketball!

velo

city

v [m

/s]

0

+10.0

0.5 1.0

–10.0

v = +5.05 m/st = 0.58 s

v = –5.24 m/st = 0.53 s

time t [s]

2

3

1

0

v = 0.00 m/st = 0.00 s

v = 0.00 m/st = ____ s

1. Determine the maximum height of the (center of mass of the) basketball above the floor att = 0 seconds (time [0]), and the maximum height above the floor at time [3]. (Although it ispossible to do so, do not use the initial-final energy conservation approach developed inPhysics 7A to answer this question. Concentrate on using the method of Oresme instead!)

2. Determine the time (in seconds) for [3].

3. Make three separate force diagrams, as seen from the side, for the basketball for the three timeintervals [0]→[1]. [1]→[2], and [2]→[3]. Properly label each force vector, but also write downthe magnitude of each force, in N. Use g = 9.8 N/kg. Indicate the F∑ net force vector(magnitude and direction) separately on the side, for each case.


03.03.18

4. Take a ride—in the Physics/Geology building elevators! Sit in the silver chair (don't fret—itwill push down as you sit on it), which records your weight (in lbs). This may require twopeople; one to sit in the chair, the other to read off your weight as measured by the chair.• Record values of your weight (in lbs) while going up—first at rest; speeding up; upwards at

constant speed; slowing down; at rest at top floor, for a total of five measurements. Convert tothis weight to the gravitational force of the Earth on you, in N (2.2 lbs = 9.8 N).

• Now do this again, estimating how much time (to the nearest half-second) it takes for theelevator to speed up, to move at constant speed, and then to slow down, for a total of three timeintervals. Use a watch, or count off seconds.

Draw properly labeled and scaled force diagrams for you (the elevator passenger) for the fivedifferent situations for going up. (Note that the F⊥ contact of you on chair (what the chair scale "reads")is the Third Law pair of F⊥ contact of chair on you .) Draw the net force F∑ vector next to each ofyour five force diagrams, and indicate its magnitude (in N) and direction for each case.

5. Read the Block 8 Glossary in the Physics 7B Student Packet, Fall 2002, and familiarizeyourself with the following term that will be introduced in DLM 09.

force, drag


03.03.18

Activity Cycle 8.2.2: Method of Oresme: freefall/bounce w/no drag


A. Summarizing FNT results. Quickly put your group's results up on the board.

Consider the vertical motion of an m = 0.5 kg basketball as described by the graph below.• At t = 0 seconds, its center of mass originally starts at some unknown height above the floor.• It falls straight downwards, bounces off of the floor, and then moves upwards to an unknown

shorter maximum height. Throughout this problem, neglect the effect of air resistance on thebasketball!

velo

city

v [m

/s]

0

+10.0

0.5 1.0

–10.0

v = +5.05 m/st = 0.58 s

v = –5.24 m/st = 0.53 s

time t [s]

2

3

1

0

v = 0.00 m/st = 0.00 s

v = 0.00 m/st = ____ s

1. Determine the maximum height of the (center of mass of the) basketball above the floor att = 0 seconds (time [0]), and the maximum height above the floor at time [3].

2. Determine the time (in seconds) for [3].

3. Make three separate force diagrams, as seen from the side, for the basketball for the threetime intervals [0]→[1]. [1]→[2], and [2]→[3]. Properly label each force vector. Use ascale of 1 cm ↔ 1 N, but also write down the magnitude of each force, in N. Useg = 9.8 N/kg. Indicate the F∑ net force vector (magnitude and direction) separately onthe side, for each case.

B. Challenge question—analysis of the results. Discuss (4) in your group and then putyour answers up on the board.

4. Why is magnitude of the ⊥ contact force of the floor so much greater than the force ofgravity during the bounce? What would happen to the basketball after the bounce if themagnitude of the ⊥ contact force of the floor during the bounce was say, only 80 N?What would happen to the basketball after the bounce if the magnitude of the ⊥ contactforce of the floor during the bounce was only 4.9 N?


03.03.18

Activity Cycle 8.2.3: Method of Oresme: freefall with drag


A. Making force diagrams. Discuss the given information below in your group, and putyour group's four force diagrams up on the board.

Consider the vertical motion of a ping-pong ball (m = 2.5 g) and a golf ball (m = 45.5 g).(1,000 g = 1 kg.) Drop these balls and convince yourselves of the observations below.• At t = 0 seconds, they are both released 2.0 m above the floor.• The ping-pong ball speeds up, but at about 1.5 m above the floor falls with a constant speed

until it hits the floor.• The golf ball speeds up, and keeps on speeding up until it hits the floor.• The golf ball hits the floor well before the ping-pong ball does.

1. Make two separate force diagrams, as seen from the side, for the ping-pong ball and forthe golf ball, just after the moment they are released from rest. Properly label each forcevector. Use a scale of 1 mm ↔ 1 N, but also write down the magnitude of each force, inN. g = 9.8 N/kg. Indicate the F∑ net force vector (magnitude and direction) separatelyon the side, for each diagram. Put up your two force diagrams.

2. Repeat (1) for the ping-pong ball and for the golf ball, at their respective moments in timejust as they are 1 cm above the floor. (Hint: the ping-pong ball has reached "terminalvelocity." Simplify things by making the drag force on the golf ball 1.5× more than as onthe ping-pong ball. You should be able to explain why the drag force on the golf ballmust be greater than on the ping-pong ball, after both fall 2.0 m downwards!) Put upyour two force diagrams.

B. Analysis of v(t) graphs. Discuss (3) in your group and put yourgroup's answers up on the board. This is an open-ended activity.

3. Shown at left are the v(t) graphs for the ping-pong ball and the golfball (which is which? Is up or down defined to be the positive direction? What does thedashed line represent?). Make whatever additional experimental observations,measurements, and approximations necessary to answer the following quantitativequestions below. Explain your reasoning.(a) What is the slope (approximately) of the golf ball v(t) graph, just before it hits the floor?

(Hint: use your force diagram.) What is the % difference from g = 9.8 N/kg?(b) What is the terminal velocity (in m/s) for the ping-pong ball?

C. Challenge questions. Discuss and put these up on the board.

4. How would the golf ball v(t) graph eventually continue, if it were allowed to drop "forever?"

5. Sketch the v(t) graph of a ping-pong ball, thrown downwards at t = 0 at an initial speed oftwice its terminal velocity on the same v(t) graph above. Explain what happens to itsvelocity as time goes on, and why, using a force diagram and Newton's Laws.

t

v


03.03.18

Activity Cycle 8.2.4: Method of Oresme: elevator riding



Take a ride—in the Physics/Geology building elevators! Sit in the silver chair (don't fret—itwill push down as you sit on it), which records your weight (in lbs). This may require twopeople; one to sit in the chair, the other to read off your weight as measured by the chair.• Record values of your weight (in lbs) while going up—first at rest; speeding up; upwards at

constant speed; slowing down; at rest at top floor, for a total of five measurements. Convert tothis weight to the gravitational force of the Earth on you, in N (2.2 lbs = 9.8 N).

• Now do this again, estimating how much time (to the nearest half-second) it takes for theelevator to speed up, to move at constant speed, and then to slow down, for a total of three timeintervals. Use a watch, or count off seconds.

1. Draw properly labeled and scaled force diagrams for you (the elevator passenger) for thefive different situations for going up. (Note that the F⊥ contact of you on chair (what the chairscale "reads") is the Third Law pair of F⊥ contact of chair on you .) Draw the net force F∑ vectornext to each of your five force diagrams, and indicate its magnitude (in N) and directionfor each case. Draw the net force F∑ vector next to each of your force diagrams, andindicate its magnitude (in N) for each case. Use a scale of 0.5 mm ↔↔↔↔ 1 N to scale theforce vectors for your five force diagrams and net forces.

B. Analysis of v(t) graphs. Discuss (2) in your group and put your group's answers upon the board. This is an open-ended activity.

2. Draw a v(t) graph for the passenger in the elevator. Scale the vertical (v) and horizontal (t)axes. Determine from this graph the height of the fifth floor above the basement floor ofthe Physics/Geology building. If your results don't seem very plausible—that's okay, aslong as your results directly follow from your (crude) measurements. (1 m = 3.28 ft.)


03.03.18

DLM 09 Exit handout

Announcements Quiz 8 will be given during lecture on Tuesday, November 12, and will cover the material inBlock 8. Bring a pen or pencil, calculator, and prepare to show your UC-Davis student ID card (orsimilar photo ID) upon entering, and/or during the quiz.

FNT ("For Next Time")1. Draw properly labeled and scaled force diagrams

for the three different situations of a m = 2 gpenny described below. Ignore air resistance.Draw the net force F∑ vector next to each ofyour force diagrams, and indicate its magnitude (inN) for each case. For the purposes of FNTs (1)-(2), approximate g ≈≈≈≈ 10 N/kg instead of themore exact value of 9.8 N/kg.(a) Penny [A], which initially starts off from

rest, just after it loses contact with the ruler,as it falls down towards the floor.

(b) Penny [B], which starts off with no initialvertical velocity, but with an initialhorizontal velocity of 1.0 m/s, just after it loses contact with the ruler and the table, as itfalls down towards the floor.

(c) Penny [C] (not shown here), which starts off with no initial vertical velocity, but starts offwith an initial horizontal velocity of 2.0 m/s, just after it loses contact with the ruler andthe table, as it falls down towards the floor.

2. Draw a vertical vy (t) velocity graph for penny [A], which initially starts from rest at y = +1.4 mat t = 0 seconds, and falls down to the y = 0 m floor at t = ___ seconds (when?). Use themethod of Oresme; remember to use the approximate value g = 10 N/kg.

3. Read the Block 9 Glossary in the Physics 7B Student Packet, Fall 2002, and familiarizeyourself with the following term that will be introduced and used extensively in DLM 10.

"method of Newton"

penny [A]nudged from off of the top of ruler; nearly zero horizontal velocity

penny [B]has horizontal

velocity

a sh

ort t

ap

hold ruler so it pivots here


03.03.18

Activity Cycle 8.2.5: Method of Oresme: two penny trick

Learning goals:• Apply the method of Oresme describe the motion of and quantify the forces acting upon an object.• Understand the orthogonality of x and y directions, as applied to method of Oresme.

A. The two penny trick (you are actually comparing three pennies, but only two penniesat a time). Hit two pennies off of the table, as shown in the figure below. Observewhich penny hits the ground first (listen carefully!). Do this again, but give one of thepennies even more horizontal velocity, while still making the other penny fall straightdown. (If you are broke, use the 50 g circular disks instead.)

B. Summarizing FNT results—analysis of the two penny trick, using the method ofOresme. Quickly put your group's results for (1)-(2) up on the board.

1. Draw properly labeled and scaled forcediagrams for the three different situationsof a m = 2 g penny described below.Ignore air resistance. Draw the net force

F∑ vector next to each of your forcediagrams, and indicate its magnitude (in N)for each case. Approximate g ≈≈≈≈ 10 N/kginstead of the more exact value of9.8 N/kg.(a) Penny [A], which initially starts off

from rest, just after it loses contactwith the ruler, as it falls downtowards the floor.

(b) Penny [B], which starts off with no initial vertical velocity, but with an initialhorizontal velocity of 1.0 m/s, just after it loses contact with the ruler and the table,as it falls down towards the floor.

(c) Penny [C] (not shown here), which starts off with no initial vertical velocity, butstarts off with an initial horizontal velocity of 2.0 m/s, just after it loses contact withthe ruler and the table, as it falls down towards the floor.

2. On the same vertical vy (t) velocity graph, draw the motion for pennies [A], [B], and [C],which all initially start at y = +1.4 m at t = 0 seconds, and each falls down to the y = 0 mfloor at t = ___ seconds (when?).

3. On the same horizontal vx (t) velocity graph, draw the motion for pennies [A], [B], and[C], which all initially start at x = 0.0 m at t = 0 seconds, and each falls down to they = 0 m floor at x = ___ (how far?), and t = ___ seconds (when?).

C. Challenge question. Discuss this and put this up on the board.

4. What did you notice about the force diagrams in (1) for the three pennies? Are their vy (t)graphs same or different? Why? Are their vx (t) graphs same or different? Why?

penny [A]nudged from off of the top of ruler; nearly zero horizontal velocity

penny [B]has horizontal

velocity

a sh

ort t

ap

hold ruler so it pivots here


03.03.18

Activity Cycle 8.3.1: Method of Newton: the two penny trick

Learning goals:• Apply the method of Newton describe the motion of and quantify the forces acting upon an object.• Understand the orthogonality of x and y directions, as applied to method of Newton.• Compare and contrast the different methods of analyzing motion (Oresme and Newton).

A. Using the method of Newton. No need to put this work on the board; but check youranswers within your group.

1. On the back of this sheet are the initial steps in the method of Newton for pennies [A],[B], and [C]. Complete the method of Newton for all three pennies on the back of sheet,up to v5, at which time all three pennies hit the ground.

B. Analysis of the two penny trick, using the method of Newton. Discuss and put yourgroup's results for (2)-(4) up on the board.

2. Determine the scale factors for this implementation of the method of Newton.(a) Noting how many graph units there are for the v1 vectors for pennies [B] and [C],

how many m/s does one graph unit represent on this scale?(b) Using ∆ = ∆v a t , what is the time step ∆t (in seconds) used here? (Don't forget that

g ≈ 10 N/kg here.)

3. (Approximately) at what time does the method of Newton show the pennies hitting theground?

4. Count the horizontal graph units that pennies [B] and [C] traveled in their respectivetrajectories. Multiply the number of graph units by the (m/s per graph unit) scale factor,and the ∆t time step, to get the horizontal distance (in m) each penny landed from the tablefrom the method of Newton:

∆ ∆ = ⋅

⋅ ∆( )x or y N t

m/s stepo o

.


03.03.18

∆x ≈ 0.45 m

∆x ≈ 1.00 m

∆v = a∆t

∆v

∆∆∆∆v = a∆t

v1

v2

v3

v4

v5

∆v

∆v

v1

v2

v3

v4

v5

∆v

∆v

∆v

∆v

∆v = a∆tv2

v3

v4

v5

table y = 0.00 m

floor y = –1.40 m

1 unit ≡ 0.5 m/s∆t ≡ 0.1 s

∆v

∆v

v = 01


03.03.18

Activity Cycle 8.3.2: Comparing both methods

Learning goals:• Understand the orthogonality of x and y directions.• Compare and contrast the different methods of analyzing motion (Oresme and Newton).

A. Orthogonality. Discuss (1)-(4) and then put your group's answer up on the board.

Put up brief explanations for your answers to these multiple choice questions, especiallydescribing what gets affected on a v(t) graph or method of Newton velocity vectors, and how.

1. A net force along the y direction affects the horizontal

vertical

v t

v tx

y

( )( )

graph of an object.

2. An initial horizontal velocity affects the horizontal

vertical

v t

v tx

y

( )( )

graph of an object.

3. A net force along the y direction affects the horizontal

vertical

component of the ∆v vector in

the method of Newton.

4. An initial horizontal velocity of an object affects the horizontal

vertical

component of the initial

v1 velocity vector in the method of Newton?

B. Challenge questions—comparing the different methods. Discuss (5)-(7) and put themup on the board.

5. Would "doing finer steps" (smaller ∆t intervals, and smaller graph scale units) or "doingcoarser steps" result in more accurate answers in using the method of Newton in(3)-(4)? What would be the drawback of trying to make the method of Newton veryprecise?

6. Which method (Oresme or Newton, or both) is possible to obtain the following results?Briefly explain your answers. (Remember that g ≈ 10 N/kg is used today.)(a) Showing the x and y location of penny [C] at t = 0.3 seconds, a specific instant in

time. Show your work using results from the method of Oresme and/or fromthe method of Newton.

(b) The magnitude of the velocity (in m/s) of penny [C], just as it hits the ground att = 0.53 s (approximately given by the "v5" vector in the method of Newton).Show your work using results from the method of Oresme and/or from themethod of Newton.

(c) The trajectory of an object through space.

7. Repeat (6) above, but decide which method (either Oresme or Newton) should be used inpractice to obtain the most precise results (assuming that g = 9.8 N/kg is used for bothmethods).


03.03.18

DLM 10 Exit handout


FNT ("For Next Time")DLM 11 is a problem-solving session that will consolidate the material covered in Block 8. Thefollowing six problems represent actual or sample quiz or final exam questions given in previousquarters. (Unless explicitly told otherwise, use gEarth = 9.8 N/kg throughout.)

(Quiz 8, Spring 2002)1. A 7.0 kg bowling ball is suspended above the

ground by a cable. This cable is pulled upwardssuch that the bowling ball moves with a verticalvelocity given by the graph at right. Neglect airresistance. Credit is assigned for thecompleteness and clarity of your justificationusing the appropriate method(s).(a) Determine the magnitude (in N) and direction of Fcable tension of ceiling on bowling ball at

t = 2.5 seconds, and the magnitude (in N) and direction of Fcable tension of ceiling on bowling ball att = 5.0 seconds.

(b) What vertical distance (in m) did the bowling ball move in the time interval fromt = 3 seconds to t = 4 seconds? Explain whether this is an upwards or downwardsdistance traveled, and why.

(c) If the bowling ball was at y = 0.0 m at t = 0 seconds, where is it located at t = 8 seconds?

(Block 8 assignment, Winter 2000)2. The velocity graph of a 1.0 g coffee filter released from rest is shown below. Note the break in

the time axis, and approximate its motion using the superimposed straight line segments.Credit is assigned for the completeness and clarity of your justification using the appropriatemethod(s).

0.00.05 0.10 4.90 4.95

time t [sec]

5.00

+0.2

–0.4

–0.2

velo

city

v [m

/s]

0.15

1

0

2 3

4

[0]→[1] negligible drag forces[1]→[2] increasing drag forces[2]→[3] falling with constant speed[3] first hits floor [4] comes to rest on floor

0.0

+2.0

velo

city

v [m

/s]

time t [sec]2.0 4.0 6.0 8.0


03.03.18

(a) Determine the magnitude (in N) and direction of Fdrag of air on filter at t = 0.05 s. Explainwhether this magnitude is greater than, less than, or equal to its value in the time interval0.00 s ≤ t ≤ 0.02 s, and why.

(b) How high above the floor (in m) was the coffee filter released from rest?(c) Determine the magnitude (in N) and direction of F⊥ contact of floor on filter during

4.99 s ≤ t ≤ 5.00 s. Explain whether this magnitude is greater than, less than, or equal tothe magnitude of Fgravity of Earth on filter , and why.

(Final Exam, Spring 1998)3. Ice-skater Nicole Bobek (m = 55 kg) is coasting to the right with a velocity of 4 m/s at t = 0 s.

However, there is a slight, constant frictional contact force of 5.50 N on her from the ice. Att = 10 s, Nicole suddenly turns her skates such that the constant frictional contact force on heris now 82.5 N, and as a result she comes to a complete stop a short time later. Neglect airresistance. Credit is assigned for the completeness and clarity of your justification using theappropriate method(s).(a) Draw two separate force diagrams for Nicole, one diagram for 0 s ≤ t ≤ 10 s, and another

for 10 s < t < "stopped." Indicate the direction and magnitude (in N) of the F∑ netforce vector in each case.

(b) Draw the horizontal v(t) velocity graph for Nicole. Use the method of Oresme to calculatethe values of Nicole's velocity and position at t = 0 s, t = 10 s, and calculate the totaldistance traveled by the time Nicole comes to a complete stop.

(Quiz 8, Spring 1998)4. A 2,000 kg rocket car accelerates by expelling gases (Fgas on rocket car = 10,000 N) behind it, while

rolling on a dry lake bed that exerts a constant frictional force on it( F contact of road on rocket car|| = 1,000 N). The rocket car is sufficiently streamlined such that airresistance is negligible. The rocket car starts at from rest at t = 0 seconds when the rocketengine ignites at x = 0 m, and the rocket engine shuts off at t = 30 seconds. Afterwards, therocket car coasts (until it eventually comes to a complete stop). Credit is assigned for thecompleteness and clarity of your justification using the appropriate method(s).(a) Draw two separate force diagrams for the rocket car, one diagram for 0 s ≤ t ≤ 30 s, and

another for 30 s < t < "stopped." Indicate the direction and magnitude (in N) of the F∑net force vector in each case.

(b) Draw the horizontal v(t) velocity graph for the rocket car. Use the method of Oresme todetermine how far the rocket will be at t = 60 seconds, from its initial position att = 0 seconds. (Will the rocket car still be moving at t = 60 seconds?)


03.03.18

(Quiz 8, Winter 2001)5. Róisín kicks a 2.0 kg iceball at a downwards 45° angle off the edge of a

cliff, with an initial speed of 5.66 m/s. The iceball finally splashes in thesea after spending a total of 2.0 seconds in the air. Neglect air resistance.(a) Draw two separate velocity versus time graphs: a vx t( ) graph for the

horizontal motion of the iceball, and a vy t( ) graph for the verticalmotion of the ball. Accurately scale your graphs! Note that up is the+y direction; and to the right is the +x direction.

(b) How far away from the base of the cliff did the iceball splash into thesea? How high is the cliff? (Part (c) is on the following page.)

+5.0

–5.0

0.0

+5.0

–5.0

0.0

horiz

onta

l vel

ocity

v

(t)

[m/s

]x

+10.0

+15.0

+20.0

+25.0

–25.0

–20.0

–15.0

–10.0

verti

cal v

eloc

ity

v (t

) [m

/s]

y

+10.0

+15.0

+20.0

+25.0

–25.0

–20.0

–15.0

–10.0

time t [sec]

0.5 1.0 1.5 2.00.5 1.0 1.5 2.0

time t [sec]R

óisí

n

iceball

sea

yx


03.03.18

(c) Now consider if Róisín kicks another 2.0 kg iceball off the edge of this same cliff, withthe same downwards 45° angle, but now with a faster initial speed. Will this iceball landcloser to; the same distance as; or farther away from the bottom edge of the cliff asbefore? Be sure to carefully justify your answer explicitly using either the method ofOresme or Newton.

(Based on Quiz 8, Winter 2000)6. Eoín kicks a soccer ball diagonally upwards, such that it reaches its maximum height, then

comes back down to hit a wall 0.95 seconds after leaving Eoín's foot. A diagram showing themethod of Newton is shown at right below. Neglect air resistance.(a) What is the

magnitude(in m/s) anddirection(angle withrespect tothehorizontal)of the initialvelocity v1

of thesoccer ball?

(b) Using thismethod ofNewton,what is theheight ∆yand distance∆x awayfrom Eoínfor thesoccer ball,when it hitsthe wall?

(c) Use themethod ofOresme, andg = 9.8 m/s2

to moreaccurately determine the height ∆y and distance ∆x away from Eoín for the soccer ball,when it hits the wall.

(d) If Eoín kicks the ball with the same amount of initial vertical speed, but with a fasterhorizontal speed such that it reaches the wall 0.6 seconds after leaving Eoín's foot,determine (explicitly using either the method of Oresme or Newton) whether the ball willhit the wall before it would have reached its maximum height, or whether the ball will hitthe wall after it already reached its highest height.

wal

l

floor

Eoín

0.5 m/s∆t = 0.1 s

∆v = a∆tv1

v2


03.03.18

Activity Cycle 8.3.3: Analysis of the motion of objects

Learning goals:• Apply the method of Oresme describe the motion of and quantify the forces acting upon an object.• Apply the method of Newton describe the motion of and quantify the forces acting upon an object.










03.03.18

DLM 11 Exit handout


FNT ("For Next Time")1. Identify in words three factors that help quantify the "rotational effectiveness" of force on a

wrench.2. Show these three variables on a simplified diagram of a wrench.3. Combine these three variables into a single mathematical expression for torque.4. Identify the single one factor that affects the torque exerted on the wrench, separately for each

case (a)-(c).

F F

F

F

(a) F

F

F

(b)

F

F

(c)


center of mass center of gravity C.G.extended force

(extended body) diagramextended objectlever arm l"moment of inertia"net torque

τ∑

Newton's First Law,rotational

Newton's Second Law,rotational

pivot point P.P.rotation axis R.A.rotational inertia/mass Isymmetry axistorque

rτ

vector, rotationalvelocity, rotational

rω

6. Bring your yellow pull scales to DLM 12!


03.03.18

Activity Cycle 9.1.1: Introducing the torque concept

Learning goals:• Understanding "torque" as a "rotational effectiveness" of a force.• Mathematical description of torque.


1. Identify in words three factors that help quantify the "rotational effectiveness" of force ona wrench.

2. Show these three variables on a simplified diagram of a wrench.

3. Combine these three variables into a single mathematical expression for torque.

B. Application of the mathematical description of torque. Discuss (4) in your group(there is an actual wrench and bolt for you to use if you like), and then put youranswers up on the board.

4. Identify the single one factor that affects the torque exerted on the wrench, for each case(a)-(c).

F F

F

F

(a) F

F

F

(b)

F

F

(c)


03.03.18

Activity Cycle 9.1.2: Introduction to extended force diagramsExtended force diagram conventions:• Draw the extended object acted upon as a rod or disk. Label your object.• Only forces exerted on that object are shown on the extended force diagram.• Each force vector is drawn as an arrow acting on a specific point on the extended object.• Each force vector must have a lever arm l , as measured from the pivot point PP.• A torque must be calculated separately for each force vector: τ θ= Flsin .

• Like forces, torques have "directions" (sort of). Torques can either turn anextended object clockwise or counterclockwise ("cw" or "ccw").

• All the torques acting on an object must add up into the net torque

rτ∑ ,

whose direction is specified as "cw/ccw" or ±.

A. Rotational form of Newton's First Law. Discuss (1)-(2) in your group, and then putyour answers up on the board.

1. Write out in words, and then in brief equation form the "translational" form of Newton'sFirst Law, as used in Block 7 and in Block 8.

2. Write out in words, and then in brief equation form the rotational form of Newton's FirstLaw. Identify the corresponding variables/concepts in either form of Newton's First Law.

B. Applying the rotational form of Newton's First Law. Record your data in (3), andthen work on (4)-(5) on the board.

3. Use your yellow springscale to pull on the end ofthe horizontal rod to makeit constantly rotate. Adjustthe clamp such that there isenough friction toconstantly rotate the rodaround-and-around bypulling the spring scale.Record the spring scaleforce (in N), and measureall distances you need tomake.

4. Make an extended force diagram of your experiment in (3), as seen from above. Simplifythe horizontal rod! Identify your pivot point, and show all lever arms (in m) and forces(in N). Identify in words which forces cause cw and ccw torques. (Is l ≠ 0 for the clampforce?)

5. Use the rotational form of Newton's First Law to find magnitudes of the torques (in N·m)and forces (in N) on your extended force diagram.

cw(–)

ccw(+)

Fpu

ll sc

ale

= ?

vertical rod

clamp

l

horizontal rod

F || contact = ?

horizontal rod (seen from above)


03.03.18

Activity Cycle 9.2.1: Newton's First Laws

Learning goals:• Apply Newton's First Law (translational and rotational forms) to determine magnitude and direction

of forces and torques acting on extended object of interest.

A. Applying Newton's First Law translationally and rotationally. Record your data in(1), and then work on (2)-(4) simultaneously on the board. You should have aseparate force diagram and a separate extended force diagram for the aluminumchannel.

1. Inspect the aluminum channel that is free torotate vertically. Use a spring scale to pullup on the hook nearest the support rodsuch that the aluminum channel ishorizontal and stationary. Record thespring scale force (in N), and measure alldistances you need to make. Do notmeasure the mass of the channel yet!

2. Make a force diagram of your experimentin (1). (Hint: there are three forces that acton the channel.) Properly label all theseforces as acting on a dot. You do not haveto find the magnitudes of all your forces yet.

3. Make an extended force diagram of your experimentin (1). Identify your pivot point, and show anyrelevant distances (in m) and forces. Set up thecalculations (cw/ccw?) for each torque. You do nothave to find the magnitudes of all your forces yet.(Note: the l for the ⊥ contact force of the support rodon the channel is not zero, yet that force (which pointsstraight down) exerts no torque—look at the close-upview of the support rod, and explain how is this so.)

4. Explicitly show how Newton's First Law (translational and rotational forms) allow you todetermine (a) the mass (in kg) of the aluminum channel; and (b) the magnitude of the ⊥contact force of the horizontal support rod on the aluminum channel.

B. Challenge question—applying Newton's First Law translationally and rotationally,individually and separately. Put (5) on the board.

5. In general, what would happen to the rod if only the translational form of Newton's FirstLaw were true? What would happen to the rod if only the rotational form of Newton'sFirst Law were true? What would happen if neither forms of Newton's Law were true?

support rod

CG

Al channel

scal

e

F

Al channel

support rod

⊥ contact of rod on channel

l


03.03.18

DLM 12 Exit handout

Announcements Quiz 8 will be given during lecture on Tuesday, November 12, andwill cover the material in Block 8. Bring a pen or pencil, calculator, andprepare to show your UC-Davis student ID card (or similar photo ID)upon entering, and/or during the quiz.

FNTs1. Circle all of the forces shown acting on a disk of radius r (shown at

right) which exert a non-zero torque about the pivot point PP. Crossout all forces which exert a zero torque about PP. (This is a top viewof the disk, as seen from above.)

2. An aluminum channel of length L is heldstationary at an angle with respect to thevertical, by means of rope attached at aperpendicular angle to its upper end. Thebottom end rests on the floor, and there isnothing holding there other than the || and ⊥contact forces exerted by the floor (i.e., thereis no supporting object there other than thesurface of the floor itself). Determine themagnitude (in N) of the rope tension force.

3. Read the Block 9 Glossary in the Physics 7BStudent Packet, Fall 2002, and familiarizeyourself with the following terms that will beintroduced and used extensively in DLM 13.

"moment of inertia"Newton's Second Law, rotationalparallel axis theoremrotation axis R.A.rotational inertia/mass Isymmetry axis

4. Bring your yellow pull scales to DLM 13!

F1

F2

F3

F5

F4

F6PP

33.6

9°

Frope tension = ?

Fgravity

8.00

0 N


03.03.18

33.6

9°

Frope tension = ?

Fgravity

8.00

0 N

Activity Cycle 9.2.2: Quant. applications of Newton's First Laws

Learning goals:• Apply Newton's First Law (translational and rotational forms) to determine magnitude and direction

of forces and torques acting on the extended object of interest.• Using trigonometry to compute non-perpendicular forces

A. Summarizing FNT results. Discuss (1) in your group, and then put your answer upon the board.

1. State in words two reasons how a non-zero force on an extended object would notproduce a torque.

B. Analyzing forces and torques using translational and rotational forms of Newton'sFirst Law. This is an open-ended activity in the sense that you are not given anexplicit procedure, but in the end your group should have (2)-(4) answered on yourboard.

2. From FNT 2, determine the magnitudes (in N) anddirections of the following forces:(a) The rope tension force holding the channel up.

(Also find the x and y components of this force.)(b) The friction force (|| contact) of the floor on the

channel.(c) The ⊥ contact force of the floor on the channel.

3. Show (either using tail-to-head vector addition orcomponent-by-component addition) thatNewton's First Law is satisfiedtranslationally.

4. Show (by adding up torques) that Newton'sFirst Law is satisfied rotationally.

X. Challenge questions. Discuss and then putthese up on the board.

5. It is probably easiest to answer (4) and 2(a)first, using the floor as the pivot pointfor the channel. Explain why placing apivot point at a certain point wouldprobably be a good shortcut to look forin general.

6. Suppose now that the rope holding the channel up points vertically upwards.Demonstrate using Newton's First Laws (no explicit calculations required) that there canbe no frictional contact force on the bottom end of the channel whatsoever. Would this bethe only way to pull up on the channel to hold it at a stationary diagonal angle, if it wereresting on frictionless ice?


03.03.18

Activity Cycle 9.3.1: Rotational form of Newton's Second Law

Learning goals:• Apply the rotational form of Newton's Second Law to determine magnitude and direction of forces

and torques acting on the extended object of interest.• Relations between both rotational and translational forms of Newton's Second Law.• Rotational mass ("moment of inertia") I.

A. Parallels between different forms of Newton's Second Law. Discuss (1), and then putyour group's answer up on the board.

1. Write out in words, and then in brief equation form the translational and rotational formsof Newton's Second Law. Identify which variables/concepts correspond to othervariables/concepts in either form of Newton's Second Law.

B. Applying Newton's Second Law to understand "rotational mass" of extended objects.Record your observations in (2), and then work on (3)-(4) on the board.

2. Consider [A] a ring, and construct[B] a mass on a string, both ofapproximately the same mass, andthe same radius (if you can't get themasses exactly the same, let's justsay they're the same mass). Hangboth objects at an angle of θ = 30°,and then let them go. State in wordswhich object has "more change inrotational motion per time" (i.e., agreater rotational acceleration α), andhow you know this from yourobservations.

3. Make an extended force diagram for both objects (ring and pendulum). Identify pivotpoints, and show any relevant distances (in terms of variables, not numbers) and forces(in terms of variables, not numbers). Which extended object [A]-[B] has more torqueexerted on it (assuming they have the same mass)?

4. Use the rotational form of Newton's Second Law and your results from (2)-(3) todetermine which extended object [A]-[B] has more "rotational mass" (i.e., moment ofinertia I).

X. Challenge question. Discuss and then put this up on the board.

5. Was it critical in your experiment in (2) that the pendulum and hoop had the exact samemass to compare how quickly they would swing down to θ = 0°? Be sure to carefullyjustify your answer using extended force diagrams, Newton's Laws, and the properties oftorques.

Rθ

Rθ


03.03.18

Activity Cycle 9.4.1: Method of Oresme: rotational motionLearning goals:• Apply the method of Oresme describe the rotational motion of and quantify the torques acting upon

an extended object.• Apply the rotational form of Newton's Second Law to determine magnitude and direction of forces

and torques acting on the extended object of interest.

A. Setting up the method of Oresme—drawing extended force diagrams to determinerotational accelerations. Record your observations, then put your results for (1)-(2)on the board.

1. Inspect your experiment setup where a stringis attached to a spool located below a cradlesupporting either a heavy solid disk, or a heavyring. (The string may be tangledup—completely unwind the spool, pull thetangle out, and then carefully wind the stringaround the spool.) Draw an extended forcediagram for this system, as seen from above,for a constant amount of rope tension forcepulling on the string as it unwinds from thespool.

2. Make whatever measurements you need (witha meter stick, and the large triple beambalance) in order to calculate the rotationalacceleration α of your disk or ring (you canneglect everything else), when you pull on thestring with a constant ___ N force, startingwith everything being stationary att = 0 seconds.

B. Applying the method of Oresme for rotational motion. Discuss (3)-(4), and then putyour group's answers up on the board.

3. Draw a rotational velocity ω(t) graph for your system, from t = 0 seconds to t = ___ s,when the spool runs out of string. Calculate the final rotational velocity (in rad/s) of yoursystem.

4. Use the ω(t) graph in (3) to calculate the change in angular position ∆θ (in radians) ofyour system for this process. How many total revolutions did your disk or ring goaround for your process? Verify your answer (in revolutions) experimentally.

X. Challenge question. Discuss and then put this up on the board.

5. Disk versus ring! If you decided to have a pulling contest with another table, using eithera disk or a ring of the same mass and radius, explain which item you would choose andwhy.

heavy ring (or disk)

massless cradle

pull scale

massless spool


03.03.18

DLM 13 Exit handout


FNT ("For Next Time")(Not a quiz question, but for the first activity 9.4.2 in DLM 14)X. An aluminum channel from DL, of length L and mass M, is held horizontally by your finger.

Consider what happens at the instant in time just after your finger is removed.

channel swings downwards as soon as finger is moved

out of the way

pivot point

Al channelCG

(a) Determine the rotational acceleration rα (in terms of the quantities L, M, and g) of the

channel, at the instant in time just after your finger is removed.(b) Determine the magnitude (in terms of the quantities L, M, and g) of the downwards

translational acceleration of the rightmost tip of the channel, at the instant in time justafter your finger is removed.

(c) Determine the magnitude (in terms of the quantities L, M, and g) of the downwardstranslational acceleration of the CG of the channel, at the instant in time just after yourfinger is removed.

DLM 14 is a problem-solving session that will consolidate the material covered in Block 9. Thefollowing six problems represent actual or sample quiz questions given in previous quarters.

(Block 9 assignment, Winter 2001)1. A laser "reads" a CD starting from the innermost tracks (songs), then

moves outwards towards the edges. (Note CDs spin cw, so we'll takethat rotational direction to be positive for the purposes of this problem.)Be sure to carefully justify your answer using extended force diagrams,Newton's Laws, and the properties of torques. Credit is assigned forthe completeness and clarity of your discussion, not necessarily foryour numerical results.(a) If the laser needs to "see" the information on a track at a constant

tangential velocity of 1.2 m/s, explain whether a CD spins slower or faster as it playstracks in consecutive order.

(b) The innermost track has a radius of 46 mm, and the outermost track has a radius of117 mm. If a CD player takes 2.5 s to jump from the innermost track to the outermosttrack, what is the (constant) angular acceleration of the CD?

(c) How many revolutions has the CD made in this time?

CD

laser

r

v tangential


03.03.18

(Block 9 assignment, Winter 2001)2. Consider two cylinders of radius 20 cm and 50 cm which are

attached to each other and share a common axle. Initially thesecylinders are at rest. They have strings wrapped around them andforces acting downwards on these strings. The smaller cylinderhas a mass of 30 kg, the larger, 50 kg. The force F1 acting on thesmaller cylinder is 98 N, on the larger, F2 has a magnitude of49 N. Be sure to carefully justify your answer using extendedforce diagrams, Newton's Laws, and the properties of torques.Credit is assigned for the completeness and clarity of yourdiscussion, not necessarily for your numerical results.(a) What is the rotational acceleration (magnitude and direction (cw (–) or ccw (+) looking

from the left)) of this system?(b) Through what angle (in radians, cw/ccw) will the cylinders rotate in 3 s? How many

revolutions is this?

(Block 9 assignment, Winter 2001, and Quiz 9, Summer Session I, 2002)3. A 1.6 m tall, 45 kg student is at the lowest point of a push-up.

Be sure to carefully justify your answer using extended forcediagrams, Newton's Laws, and the properties of torques.Credit is assigned for the completeness and clarity of yourdiscussion, not necessarily for your numerical results.(a) Calculate the magnitudes of the ⊥ contact forces of the student's feet and hands on the

ground, if the center of gravity is 0.8 m from the feet. The distance between the student'shands and feet are 1.45 m when doing a push-up.

(b) Women and men of the same height and mass have different locations for their respectivecenter of mass, due to the different distribution of mass on their bodies. Generallywomen have a center of mass located closer to their feet than do men. Explain whichgender would have an easier time performing a single push-up, all else being equal otherthan the relative location of their centers of mass.

(Quiz 9, Winter 2001)4. Suppose you are interested in locating

the center of mass of a patient (of non-uniform density) of height H = 1.4 m.This person lies down horizontally, asstill as possible, on a uniform densityplank of 37.5 kg, which is supported ateither end by two weight scales asshown at right. The scale readings (inN) for this person (with the plank) areF1 = 534.345 N and F2 = 421.155 N.( gEarth = 9.8N/kg.) Be sure to carefullyjustify your answer using extended force diagrams, Newton's Laws, and the properties oftorques. Credit is assigned for the completeness and clarity of your discussion, notnecessarily for your numerical results.

1.45 m

0.8 m

center of mass

F1

F2

H

L?

scale 1 scale 2

F1 F2


03.03.18

(a) What is the mass (in kg) of this patient?(b) Where is the location L (in m) of this patient's center of mass, as measured from this

patient's feet?

(Quiz 9, Spring 2002)5. A diving board of length 12.0 m and mass

20.0 kg has two supports, one at one end of theboard and the other two-thirds of the way alongthe length of the board. Be sure carefullyjustify your answer using extended forcediagrams, properties of torques, and Newton'sLaws. Credit is assigned for the completenessand clarity of your discussion, not necessarilyfor your numerical answer.(a) How far away from the pivot point can an

80.0 kg person stand such that there is no force exerted by the left support on the divingboard (Fleft support = 0)? (gEarth = 9.8N/kg, and use the support closest to the person asyour pivot point .)

(b) Now suppose that the left end of the diving board were barely held down onto the leftsupport by a bolt, such that the person were able to stand on the very right edge of thediving board. Would the force of the right support up on the diving board be more than,less than, or the same as in (a)?

(Quiz 9, Spring 2002)6. A trebuchet is a throwing device that consists

of a 150.0 kg wood beam that has a heavyballast at one end, and a 50.0 kg projectile tobe thrown atop the other end. A force of400.0 N is applied as shown, in order to keepthe wood beam stationary. (gEarth = 9.8N/kg.)(a) What is the mass (in kg) of the ballast, if

the beam is 4.0 m long, and each of thephysical quantities on the beam is evenlyspaced every 1.0 m?

(b) At the moment in time just after the force of 400 N is removed, what is the motion of thewood beam? (Circle one.)

(A) The beam will accelerate rotationally in the ccw direction.(B) The beam will remain stationary.(C) The beam will accelerate rotationally in the cw direction.

Be sure to carefully justify your answer using extended force diagrams, properties oftorques, and Newton's Laws (First and Second). Credit is assigned for the completenessand clarity of your discussion, not necessarily for your numerical answer and cw/ccwchoice.

CG

diving board

person

8.0 m

12.0 m

l

horizontal support

CG

wood beam

400.

0 N

ballast

projectile


03.03.18

Activity Cycle 9.4.2: "Falling faster than gravity"Learning goals:• Apply the translational and rotational forms of Newton's Second Law to determine magnitude and

direction of forces and torques acting on the extended object of interest.• Relations between both translation and rotational motion variables

A. Summarizing FNT results. Discuss this FNT and then put your group's answer up onthe board.

channel swings downwards as soon as finger is moved

out of the way

pivot point

Al channelCG

1. An aluminum channel from DL, of length L = ___ m and mass M = ___ kg, is heldhorizontally by your finger. Consider what happens at the instant in time just after yourfinger is removed.

(a) Determine the rotational acceleration rα (in rad/s2 ) of the channel, at the instant in

time just after your finger is removed.

(b) Determine the magnitude (in m/s2 ) of the downwards translational acceleration ofthe rightmost tip of the channel, at the instant in time just after your finger isremoved.

(c) Determine the magnitude (in m/s2 ) of the downwards translational acceleration ofthe CG of the channel, at the instant in time just after your finger is removed.

B. Confirming your predictions with an experiment. Record your data in (2), and thenwork on (3)-(4) on the board.

2. Place a penny (or other type of coin) at the rightmost tip of the channel, and anotherpenny at the CG of the channel. Carefully observe what happens to the pennies afteryour finger is removed, as seen from the top, and from the side.

3. Explain in words using your observations from (2) what happens to the ⊥ contact forceof the channel on each penny at the instant in time just after your finger is removed.

4. Now explain in words using your results from 1(a)-(b) what happens to the ⊥ contactforce of the channel on each penny at the instant in time just after your finger is removed.


03.03.18

Activity Cycle 9.4.3: Analysis of the rotational motion of objects

Learning goals:• Apply the method of Oresme describe the rotational motion of and quantify the torques acting upon

an extended object.• Apply the translational and rotational forms of Newton's Second Law to determine magnitude and

direction of forces and torques acting on the extended object of interest.










03.03.18

DLM 14 Exit handout


FNT ("For Next Time")(Physics 7A review material needed for a calculation in the next DL.)1. A 0.5 kg basketball is released from a height of 1.0 m above a floor, is allowed to fall, bounce

off of the floor, and then rises back up to a maximum height of 0.8 m above the floor.(a) Using energy conservation, determine the downwards velocity (in m/s) of the basketball

just before it hits the floor.(b) Using energy conservation, determine the upwards velocity (in m/s) of the basketball just

after it bounces back up from the floor.


impulse, translationalmomentum, translationalNewton's First Law,

impulse-momentum forms("total momentumconservation")

Newton's Second Law,impulse-momentum forms

Newton's Third Law,impulse-momentum forms

system of objectstotal momentum

(translational)


03.03.18

Activity Cycle 10.1.1:Impulse/momentum forms of Newton's LawsLearning goals:• Analyzing motion using the impulse/momentum forms of Newton's First and Second Laws.• Analyzing motion using an initial-final state approach.

A. Impulse/momentum forms of Newton's Laws. Discuss (1)-(2) in your small group,and then put them up on the board.

1. Write out in words (using the words "impulse" and "momentum"), and then in briefequation form (using variables) the impulse/momentum form of Newton's First Law.

2. Write out in words (using the words "impulse" and "momentum"), and then in briefequation form (using variables) the impulse/momentum form of Newton's Second Law.

B. Using the impulse/momentum forms of Newton's Laws in an initial-final approach.Record your data in (3), and then work on (4) on the board.

Consider two cases [I] and [II] of dropping a m = 0.5 kg basketball from a height of 1.0 mabove the floor.[I] A partially deflated basketball that splats on the floor (the splat itself takes 0.5 seconds to

take place, once it contacts the floor).[II] A fully inflated basketball that bounces back up to a height of 0.8 m from the floor. The

bounce itself takes 0.2 seconds to take place, while in contact with the floor.

We are going to analyze the splat/bounceprocesses, so initial state = instant intime just before splat/bounce begins;final state = instant in time just aftersplat/bounce ends.

3. Draw the and label the direction(up/down) and magnitude (in kg·m/s)of the pi and p f momentum vectorsof the basketball for the cases [I]-[II]. Determine the direction (up/down) and magnitude(in kg·m/s) of the ∆ →pi f vector of the basketball for cases [I]-[II].

4. Use the impulse/momentum form of Newton's Laws to determine the magnitude (in N) ofthe (average) net force (in N) on the basketball, and magnitude (in N) of the ⊥ contactforce of the floor on the basketball during the splat/bounce process. Draw two properlylabeled and scaled (magnitudes indicated in N, 1" ↔↔↔↔ 1 N) force diagram for thebasketball in either case [I]-[II], for the splat/bounce process.


initial state

final state

initial state

final state

bounce process [II]splat process [I]


03.03.18

Activity Cycle 10.1.1:Impulse/momentum forms of Newton's Laws (continued)

C. Analyzing and generalizing this initial-final of impulse/momentum approach. Workon (5)-(6) on the board.

Throughout this activity we have assumed that the netforce

F∑ on the basketball [II] during a bounce

process was constant. Realistically the net force onthe basketball versus time during the bounce is not astraight line, it should be "peaked" as shown at belowright.

5. Whether or not the net force

F∑ on thebasketball can be considered as constant ortime-varying during the bounce, why do theareas contained under each graph have to bethe same?

6. How would the maximum magnitude (in N) ofthe ⊥ contact force of the floor on thebasketball during the bounce process change ifthe more realistic time-varying

F∑ versus

time graph were used instead?

t

F∑

0

constant during bounce

t

F∑

0

time-varying during bounce

F ∑( )∆t∆p = area =

F ∑( )dt∫∆p = area =


03.03.18

Activity Cycle 10.2.1: Systems of objectsLearning goals:• Newton's Laws, in impulse-momentum form, applied to systems of objects.• Determining whether momentum of a system is conserved or not, by applying Newton's Laws in

impulse-momentum form to a system.

A. Kinetic energy conservation and impulse/momentum forms of Newton's Laws, appliedto systems. Your TA will assign to your group one of the three collisions[I]-[III] on the back of this worksheet. Discuss (1)-(2) below and then put yourgroup's answers upon the board.

1. Use the following generalized procedure to determine what happens in the final state ofyour collision:(a) Find the magnitude (in "massless" cm/s units) and direction (left/right) of the initial

momentum vectors of the two balls.(b) Find the magnitude (in "massless" cm/s units) and direction (left/right) of the initial

momentum vector of the system.(c) Find the magnitude (in "massless" cm/s units) and direction (left/right) of the final

momentum vector of the system, assuming that total momentum of the system isconserved.

(d) Find the magnitude (in "massless" cm/s units) and direction (left/right) of the finalmomentum vectors of the two balls.

(e) Find the magnitude (in cm/s) and direction (left/right) of the final velocity vector ofball B. (You may check your final velocity directions by actually colliding them.)

2. All these collisions just so happen to be elastic, that is, total kinetic energy of the system isconserved (this is not always the case, even for collisions involving frictionless surfaces).Verify that this is true for your assigned collision (to within round-off errors).

B. When is momentum conserved? Discuss (3)-(6) and then put your group's answers(with brief explanations) up on the board.

3. When Newton's First Law

Second Law

applies to an object, its momentum is conserved.

4. When Newton's First Law

Second Law

applies to a system of objects, their total momentum is

conserved.

5. In the collisions [I]-[III], Newton's First Law

Second Law

applied to ball A.

Explain why this is so, according to the given information!

6. In the collisions [I]-[III], Newton's First Law

Second Law

applied to the system of ball A and ball

B. Explain why this is so, according to the given information!(Why are you allowed to "cancel out" the two forces in a Third Law pair in this case?)


03.03.18

For your assigned collision (I)-(III), assume that there are no external impulses on these systems oftwo objects (i.e., no friction nor air resistance). Use total momentum conservation to determine allunknown initial and final momentum and velocity vectors for these collisions.

I. A billiard ball A slides along a frictionless surface and collides with a stationary billiard ball B.Determine the magnitude (in cm/s) of the final velocity vector of billiard ball A. These billiardballs have the same mass.

pAinitial pB

initial= ?

psysteminitial

vAinitial vB

initial= 0

pAfinal

= ? pBfinal

psystemfinal

vAfinal

= ? vBfinal

50 cm/s

= ?

= ? = ?

= ?

= 50 cm/s (direction?)

II. A golf ball A slides along a frictionless surface and collides with a stationary billiard ball B.Determine the magnitude (in cm/s) and direction (left or right?) of the final velocity vector ofgolf ball A. The golf ball has a mass that is 0.288× the mass of the billiard ball.

pAinitial pB

initial= ?

psysteminitial

vAinitial vB

initial= 0

pAfinal

= ? pBfinal

psystemfinal

vAfinal

= ? vBfinal

50 cm/s

= ?

= ? = ?

= ?

= 22.36 cm/s (direction?)

III. A billiard ball A slides along a frictionless surface and collides with a stationary golf ball B.Determine the magnitude (in cm/s) and direction (left or right?) of the final velocity vector ofbilliard ball A. The golf ball has a mass that is 0.288× the mass of the billiard ball.

pAinitial pB

initial= ?

psysteminitial

vAinitial v initial

= 0

pAfinal

= ? pBfinal

psystemfinal

vAfinal

= ? vBfinal

50 cm/s

= ?

= ? = ?

= ?

= 77.64 cm/s (direction?)


03.03.18

DLM 15 Exit handout


FNTs1. Three spherical asteroids are symmetrically placed about a fourth, in

outer space, far away from any other objects. Asteroids A, B, and C areidentical, while D is smaller in size and mass. These asteroids interactwith each other gravitationally, and they all start off at rest. For eachsystem defined below, indicate whether the total momentum of thatsystem is conserved or not conserved. Give reasons for each of yourconserved/not conserved choices.(a) System composed of A, B, C, and D.(b) System composed of A only.(c) System composed of A, B, and C only.(d) System composed of D only.(e) System composed of B and C only.

2. A system consists of two balls of different masses placed against (but are not attached to) acompressed spring. All objects are initially at rest on a frictionless table, and the effects of airresistance are negligible. The spring is released and the balls move away in opposite directions.If the system consists of the spring and the two masses, which of the following quantities (I)-(III) is conserved in the system?

I. The total energy (PE + KE) of the system.II. The kinetic energy of the system.III. The linear momentum of the system.

A B

C

D

x


03.03.18

3. Consider a ball A of mass mA = 40 g and initial velocity vAinitial = 50 cm/s (horizontally, to the

right) that collides into a stationary ball B (also of mass mB = 40 g), such that they sticktogether after their collision. Neglect friction and air resistance. (For the convenience of thisproblem, it is okay to consistently keep everything in "cgs" (centimeter-gram-second) units.)

vAinitial vB

initial= 0 vA+B

final= ?

50 cm/s

(a) Calculate the final velocity (magnitude and direction) of the stuck-together ball system interms of the above quantities, using momentum conservation only.

(b) Calculate the final velocity (magnitude and direction) of the stuck-together ball system interms of the above quantities, using energy conservation only.

(c) Can both conservation laws be satisfied in this collision? If not, which one conservationlaw must be obeyed, according to the given information?


impulse, rotationalmomentum, rotationaltotal momentum

(rotational)


03.03.18

Activity Cycle 10.2.2: Elastic/inelastic processesLearning goals:• Newton's Laws, in impulse-momentum form, applied to systems of objects.• Determining whether momentum of a system is conserved or not, by applying Newton's Laws in

impulse-momentum form.• Determining whether KE of a system is conserved or not, depending on the absence or presence of

other energy systems.

A. Summarizing FNT results; save board space for (4)-(6).

1. Put up your answers for FNT 1. For each system (a)-(e), put up "total momentumconserved/not conserved." Give a reason for each of your choices. In general, what mustyou "look for" in order to determine if a system's momentum is going to be conserved?

2. Put up your answers for FNT 2. For each of the different quantities (I)-(III), put up"conserved/not conserved." Give a reason for each of our choices.

3. Put up your work for FNT 3. (More discussion for this FNT follows below.)

C. When to apply the initial-final approach for momentum and/or for kinetic energyconservation? Work on (4)-(5) on the board.

4. Explain in words what conditions must be true for the total momentum of a system ofobjects to be conserved. Use "open/closed" and/or Newton's Laws terminology. Wastotal momentum conservation expected to be obeyed for this system, using only the giveninformation?

5. Explain in words what conditions must be true for the total kinetic energy of a system ofobjects to be conserved. Use "open/closed" and/or energy system terminology. Was KEconservation expected to be obeyed for this system, using only the given information?

6. How is KE conservation different than total energy conservation? Must both be true allthe time?


03.03.18

Activity Cycle 10.3.1: Rotational systems and momentumLearning goals:• Analyzing rotational motion in terms of the impulse/momentum forms of Newton's First and

Second Laws.• Analyzing rotational motion in terms of an initial-final state rotational energy approach.

A. Rotational impulse/momentum forms of Newton's Laws. Discuss (1), and then putyour group's answer up on the board.

1. Write out in words (using the words "rotational impulse" and "rotational momentum"),and then in brief equation form (using variables) the rotational impulse/momentum formof Newton's First Law, and for Newton's Second Law.

B. Using the initial-final state approach to rotational systems. Carry out yourexperiments in (2), and then work on (3)-(4) on the board.

2. Consider a rotational system that includes a person on a piano stool, and a bike wheel(each of which can rotate freely on its own). Perform these experiments, and observewhat happens to the person/stool in the final state in each case.

i f

bike wheel stationary; person/stool stationary

bike wheel moving after person makes it start to rotate ccw(what happens to person’s rotation?) i f

bike wheel spinning sideways; person/stool stationary

bike wheel moving after person holds it to rotate ccw(what happens to person’s rotation?)

(a) (b)

3. For each process shown below, indicate whether each of these terms increases, decreases,or remains the same. The total rotational momentum of this system is Ltotal =± ⋅ ± ⋅I Iperson stool person stool bike wheel bike wheel/ /ω ω (the ± signs depend on ccw/cw rotation, asseen from above); the change in total rotational momentum is given by Ltotal =± ⋅ ∆ ± ⋅ ∆I Iperson stool person stool bike wheel bike wheel/ /ω ω (here the ± signs depend on the final-minus-initial change in rotation, as seen from above).

∆ Ltotal

(+, –, or 0)∆ Lperson stool/

(+, –, or 0)∆ Lbike wheel

(+, –, or 0)

(a)(b)

4. Explain for (a)-(b) how you determined your answer for ∆ Ltotal .

5. Explain for (a)-(b) how you determined whether ∆ Lperson stool/ and/or ∆ Lbike wheel is ±, giventhe initial and final values of ω for each term. Be very careful about how ± signs workout differently in ω and ∆ω, this is a common source of problems in rotational momentumproblems!


03.03.18

DLM 16 Exit handoutAnnouncements Quiz 9 will be given during lecture on Tuesday, November 26, and will cover the material inBlock 9. Bring a pen or pencil, calculator, and prepare to show your UC-Davis student ID card (orsimilar photo ID) upon entering, and/or during the quiz. You must attend lecture on Tuesday,November 26, in order to take Quiz 9. As outlined in the Physics 7B Course Policy, there are to beno make-up quizzes.

FNTsDLs will be cancelled Tuesday, November 26, and Wednesday, November 27. DLM 17 is aproblem-solving session that will consolidate the material covered in Block 10, and will meet Tuesday,December 3, and Wednesday, December 4. The following six problems represent sample final examquestions given in previous quarters.

(Block 10 assignment, Winter 1996)1. A 0.25 kg ball rolls to the right at a constant horizontal speed of 2.0 m/s, and subsequently hits

and rolls back from a vertical wall. Neglect friction and air resistance.(a) What is the horizontal momentum of the ball before it strikes the wall?(b) If the ball bounces off the wall with a speed of 1.8 m/s in the opposite direction, what

horizontal impulse did the wall exert on the ball?(c) If the collision with the wall took place in a total time of 0.055 s, and the shape of the

force versus time curve is an isosceles triangle, what maximum horizontal ⊥ contact forcedid the wall exert on the ball?

(d) How much KE was lost in this process? Where did it go?

(Block 10 assignment, Winter 1996)2. A northbound 700 kg Volkswagen Bug moving at 30 mph collides head-on with a southbound

2,500 kg Buick Regal moving at 20 mph. They lock bumpers upon colliding.(a) Find the speed and direction of the conglomerate just after they collide.(b) Find the impulse exerted by the airbag and shoulder belt on the driver of each car. Take

the mass of each driver to be 50 kg.(c) If the collision lasts 0.025 s, what is the average horizontal net force that acts on each

driver during the collision?(d) Extend your results here to a Bug colliding with a 20,000 kg Unitrans bus. Discuss

qualitatively whether 50 kg passengers in the bus should bother wearing seatbelts, usingthe impulse-momentum forms of Newton's Laws.

(Block 10 "Lurching Earth" assignment, Spring 1998)3. Consider the process where basketball (m = 0.5 kg) falls 1.0 m towards the Earth

(M = 5 98 1024. × kg). Initial state = instant in time just after the basketball is released; finalstate = instant in time just before the basketball hits the ground. Neglect air resistance.(a) Explain whether total momentum is conserved (or not) for these (systems of) objects.

I. The basketball only.II. The Earth only.III. Both the basketball and the Earth, together in one system.

(b) For the systems (I)-(III) that do not conserve total momentum, calculate how muchimpulse (magnitude, in kg·m/s; and direction) goes in/out of that system.


03.03.18

(c) Determine the final velocity of the Earth. Use the method of Oresme to estimate thedistance that the Earth moves upwards during this process.

(Practice Quiz 10, Spring 2002)4. A 160 g billiard ball with an initial velocity of 10 cm/s

collides with a stationary 70 g golf ball. (Neglect airresistance and friction, which in this idealization means thatthese balls slide without rolling!) The final velocity of thebilliard ball is 3.913 cm/s in the same direction that it was initially moving.(a) With the only given information above and without doing any calculations, can you

conclusively say whether total momentum and/or total KE was conserved for the systemof the billiard ball and golf ball? Be sure to carefully justify your answer.

(b) If the collision contact between the two balls took place over a 0.02 second duration, whatis the magnitude (in N) and direction of the ⊥ contact force of the billiard ball on the golfball? You may assume that this magnitude was constant during the 0.02 second collision.Be sure to carefully justify your answer using Newton's Second and Third Laws.

(Block 10 assignment, Spring 2002)5. Two very small masses (m = 1.2 kg) rotates ccw (as

seen from above) at a rate of 0.5 revolutions/secondat a distance of r = 0.75 m from their rotation axis(for a person standing on a rotating platform, holdingbarbells at arm's length). This person then brings inthese masses to a new distance of r = 0.10 m, and aresult, the rotational velocity changes. Neglectfriction and air resistance.(a) Why might it be a reasonable assumption to neglect the rotational mass of the person,

compared to these barbells? (Make this assumption for the calculations below.)(b) With the only given information above and without doing any calculations, can you

conclusively say whether total rotational momentum and/or total rotational KE wasconserved for the system?

(c) Calculate the final rotational velocity ω (magnitude and direction) of this system.(d) How much energy (what form) was lost or gained by the person during this process?

(Block 10 assignment, Winter 1996)6. A Physics 7 student runs along a line tangent to the edge of a motionless merry-go-round and

jumps on at the very outside. The student's speed is 4.0 m/s right before jumping on. Thestudent's mass is 70 kg and the (light-weight) merry-go-round's mass is 30 kg. The merry-go-round has the shape of a uniform disk with a radius of the 3.0 m.(a) What is the rotational mass of the disk and person combined?(b) What is the final rotational speed of the merry-go-round with the person on it?(c) If it took 0.04 s for the person's feet to stop sliding on the merry-go-round, what was the

average torque applied to the merry-go-round in that time period?(d) What was the initial kinetic energy of the system of merry-go-round and student, just

before the student jumped on? What was the kinetic energy of the system just after thestudent jumped on? Based on your answers, would you say the collision of the personwith the merry-go-round is elastic or inelastic? Explain.

0.75 m

0.10 m

ω = 0.5 rev/sec ω = ? rev/sec

vgbinitial

= 0vbbinitial

= (+)10 cm/s


03.03.18

Activity Cycle 10.3.2: Initial/final state analysis of systems of objects

Learning goals:• Analyzing translational/rotational behavior of systems of objects in terms of the impulse/momentum

forms of Newton's First and Second Laws.• Analyzing translational/rotational behavior of systems of objects in terms of an initial-final state

rotational energy approach.










03.03.18

DLM 18 Exit handout (the last one!)

AnnouncementsNo more homework! But if you need something to do, why don'tyou download (http://physics7.ucdavis.edu) and get your Physics7B Certificate of Achievement signed? This is the last time thatDr. Len will ever be allowed to teach Physics 7B at UC-Davis, itwould sure look nifty on your refrigerator door, and you'll be theenvy of all your Physics 7A roommates. Regularly scheduled office hours will be canceled next week. Instead, review sessions will beheld in Walker Annex 114 as scheduled below. It is suggested that you come prepared to the reviewsessions to concentrate on this quarter's Quizzes, DL activities, and general questions that you mayhave, in order to make the best use of the instructor's time.

Walker Annex 114 Review Sessions:Wednesday, December 112:00-3:00 Dr. Patrick M. Len3:00-4:00 Brooke Haag4:00-5:00 Tracey Johnson

Thursday, December 1210:00-11:00 Dr. Patrick M. Len (note different time)3:00-4:00 Brooke Haag4:00-5:00 James Dann

Friday, December 132:00-3:00 Dr. Patrick M. Len3:00-4:00 Randy Nelson4:00-5:00 Randy Nelson

The Final Exam will be held on Saturday, December 14 at 1:30 PM-3:30 PM, and will becomprehensive with an equal emphasis on Blocks 6-9, with slightly more emphasis on Block 10.Bring a pen or pencil, calculator, and come early to show your UC-Davis student ID card (or similarphoto ID) before entering your Final Exam room. Room assignments for the Final Exam are asfollows:

Last 4 ID digits Room assignment0000-8285 2205 Haring8296-9999 55 Roessler (not 66 Roessler!)

Important note—if you have made extensive corrections and/or annotations to the Physics 7BStudent Packet (i.e., the Core Concepts and Glossaries), Dr. Len would be interested if you would bewilling to donate your Student Packet, along with any of your notes (or allow xeroxes to be made) inorder to improve physics instruction, in the event that he would be allowed to teach a similar coursesuch as this at another school, and in order to tailor the Physics 7C Student Packet to best meetstudent needs and concerns in Winter quarter, 2003.


03.03.18

Physics 7B Quiz ArchivesDisclaimer

Please carefully read the following information regarding these archivedPhysics 7B quizzes:

• These quizzes are presented "as is, where is" in as close to their originalform as possible, as it was presented to students in Physics 7B lecturesections taught by Dr. Patrick M. Len at the University of California atDavis in Fall quarter, 2002.

• The intent of presenting these quizzes is to provide to all students (and notjust those who are somehow able to procure class materials from formerPhysics 7C students) an additional resource in studying questions that havehistorically appeared on typical Physics 7B quizzes.

Be aware that these archived Physics 7B quizzes are not to be construedin any way, shape, or form as an indicator of the content, difficulty, or lengthof future Physics 7B quizzes.

• No effort has been or will be made to present worked-out solutions to thesearchived Physics 7B quizzes. This has been left to you as a unique andunprecedented opportunity to gauge your understanding relative to paststudents who have taken Physics 7B in previous quarters.

Be aware that your performance on these archived Physics 7B quizzes isnot to be construed in any way, shape, or form as an indicator of your actualperformance on future Physics 7B quizzes relative to current students.

By reading the following Physics 7B Quiz Archives, you acknowledge andaccept the above conditions and terms regarding the usage of these archivedPhysics 7B quizzes. If you neither understand nor accept the aboveconditions and terms, you are to tear out and discard these Physics 7B QuizArchives pages.


03.03.18

Quiz 61. [40%] An artery that

transports blood from[1] to [2] with anegligible amount offriction is shown atright. Note that thisartery does not have aconstant cross-sectional area.

Attached to the artery is a bypass, which has a significant amount of friction, due to its constant(but narrow) cross-sectional area. As shown above, there is no appreciable change in verticalheight for either the artery or the bypass between points [1] and [2].

Decide which one of the following mutually exclusive statements below must be true. Credit isassigned for the completeness and clarity of your justification using fluid conservation laws,and not necessarily for finding the correct choice below.

Choose and defend one statement only.(A) Blood will flow through the bypass in the same direction ([1]→[2]) as through the artery.(B) Blood will flow through the bypass in the opposite direction ([1]←[2]) as through the

artery.(C) No blood will flow through the bypass at all.(D) Not enough information is given to determine the direction of blood flow (if any) through

the bypass.

2. [60%] Consider two real batteries, each with the same emf E = +1.5 Volts, and the sameinternal resistance r. These real batteries are connected (with ideal, perfectly conducting wires)to a single light bulb of resistance R as shown in either circuit (A) or circuit (B). The resistanceof the light bulb is the same value as the internal resistance of a battery (R = r). Determinewhich circuit has the brighter light bulb, and explain why. Credit is assigned for thecompleteness and clarity of your justifications using fluid conservation laws, and notnecessarily for choosing the correct circuit below.

1 2

artery flow

bypass

(significant friction)

(negligible friction)


03.03.18

–– +

r

"real" battery

E

+

rE

"real" battery

R

light bulb

– +

r

"real" battery

E

– +

rE

"real" battery

R

light bulb

Circuit (A) Circuit (B)

Useful equations and constants:

∆( ) ∆ ∆ + ∆( )total head P g y v = +ρ ρ12

2 ; ∆( )total head or ∆ ±V E= – IR; I Iin out= ; I A v= ⋅ ;

P V= ⋅ ∆I ; ρair ≈ 1.0 kgm3 ; ρwater = 1,000

kgm3 ; g = 9.8

Nkg

; 1 Atm ≈ 101,000 Pa.

Quiz 71. Consider the following two examples from Schrödinger's Cat, John Gribbin (page 8, Bantam

Books, 1984, ISBN 0-553-34103-0):

"...Newton's Third Law tells us something about how the object reacts to being pushedaround: for every action [force] there is an equal and opposite reaction [force]. [a] If I hit atennis ball with my racket, the force with which the racket pushes on the tennis ball is exactlymatched by an equal force pushing back on the racket; [b] the pen on my desk top, pulleddown by gravity, is pushed against with an exactly equal reaction by the desk top itself..."

Separately determine whether Newton's Third Law(s) is relevantly discussed for the forcesexplicitly mentioned in each of these two examples. Credit is assigned for the completenessand clarity of your justification using force diagrams and Newton's Laws.

(a) [20%] "If I hit a tennis ball..."(b) [20%] "...the pen on my desktop..."


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2. [60%] Two solid boxes are positioned asshown, as seen from the side. Box 1 weighs5.0 N (i.e., Fgravity of Earth on box 1 = 5.0 N); while box2 weights 2.0 N (i.e., Fgravity of Earth on box 2 = 2.0 N).Box 1 rests on a completely frictionless floor.The interface between box 1 and box 2 iscompletely frictionless. The interface betweenbox 2 and the wall does have a significantamount of friction. A force Fapplied = 16.0 N isapplied to box 1, as shown.

Decide which one of the following mutually exclusive statements below must be true. Credit isassigned for the completeness and clarity of your justification using force diagrams, vectoraddition, and Newton's Laws, and not necessarily for finding the correct choice below.

Choose and defend one statement only.(A) Both box 1 and box 2 will remain completely stationary.(B) Box 1 will remain completely stationary, but box 2 will begin to move.(C) Both box 1 and box 2 will begin to move.


m

t

∆∆

∑r rv

F= ; "POFOSTITO"; F mggravity = ; F k stretchspring = ⋅ ( ) ; 0 ≤ F contact static| ,| ≤ µ F contact⊥ ;

F F|| contact, kinetic contact= µ ⊥ ; g = 9.8 Nkg

.

Quiz 81. [40%] Consider two balls, A and B, of unknown

mass, but of the same radius (and thus the samecross-sectional area).

Ball A is thrown straight upwards by a student. Afterleaving the student's hand, the velocity vector v1 of theball A at t = 0.1 seconds is shown at right, along withthe net force that acts on ball A at t = 0.1 seconds.

Ball B is thrown straight downwards by a student.After leaving the student's hand, the velocity vector v1

of the ball B at t = 0.1 seconds is shown at right, alongwith the net force that acts on ball B at t = 0.1 seconds.

After ball A and ball B are released, they experience the same (downwards) net force.

box 1 box 2Fapplied

µ = 0.0 µ = 0.2

6.0

m/s

v1

6.0

m/s

ball A after being released

v1

ball B after being released

Fon ball A

∑

Fon ball B

∑


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Use gEarth = 9.8 N/kg in all your calculations, and consider drag forces as significant for thisprocess.

Clearly circle and defend one choice only.

The mass of ball A (thrown upwards) is

greater than

the same as

lesser than

the mass of ball B (thrown downwards).

Wherever possible, explain your reasoning, and show your work. Credit is assigned for thecompleteness and clarity of your justification using the appropriate method(s), and notnecessarily for finding the correct choice above.

2. During the time interval of 0.0 < t < 1.0 seconds, an elevator ismoving upwards with a constant vertical speed of vy = +2.0 m/s.During the time interval of 1.0 < t < 5.0 seconds, the elevator (andeverything inside of it) accelerates (upwards) in the +y directionat a rate of ay = +0.7 m/s2. Inside this elevator, a passenger ofmass m passenger = 70 kg has a book of mass mbook = 5.0 kg atopher head. Use gEarth = 9.8 N/kg in all your calculations, andconsider any and all drag forces as insignificant for this process.

Wherever possible, explain your reasoning, and show your work. Credit is assigned for thecompleteness and clarity of your justification using the appropriate method(s), and notnecessarily for finding the correct numerical values and/or vector directions below.

(a) [30%] What is the direction (upwards or downwards) and magnitude (in N) of the⊥ contact force of the book on the passenger, during the time interval of 1.0 <t < 5.0 seconds (i.e., while the elevator is accelerating upwards)?

(b) [30%] Find the vertical distance (in m) that the elevator moves upwards from 1.0 < t < 5.0seconds (i.e., while the elevator is accelerating upwards).


m m

t

rr r

av

F= =∆∆

∑ ; "POFOSTITO"; F mggravity = ; F k stretchspring = ⋅ ( ) ;

0 ≤ F contact static| ,| ≤ µ F contact⊥ ; F F|| contact, kinetic contact= µ ⊥ ; F Avdrag ∝ 2 ; g = 9.8 Nkg

; r r rv v afinal initial t= + ∆ ;

a slopev

tx area v dt

= = ∆∆

∆ = = ⋅

∫.

book

passenger

aelevator

0.7

m/s

2


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Quiz 91. [30%] Consider a uniformly dense bar of mass

M1, attached to an ideal (massless andunstretchable) rope that suspends it from theceiling. Another mass M2 is attached withanother ideal rope to the end of the bar, as shownin the side view at right. M1 = 1.0 kg, andM2 = 0.8 kg. The bar makes an initial angle of30° with respect to the vertical. All distances (inmeters) are indicated.

Use gEarth = 9.8 N/kg in all your calculations, andconsider any and all frictional and drag forces asinsignificant.

Clearly circle and defend one choice only.

The rod will

begin to rotate counterclockwise.

remain completely stationary.

begin to rotate clockwise.

Wherever possible, explain your reasoning, andshow your work. Credit is assigned for thecompleteness and clarity of your justificationusing the appropriate method(s), and not necessarily for finding the correct choice above.

0.5

m

0.3

m

0.2

m

M 2M 1

30°


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2. Consider a uniformly dense bar of mass M1 andlength L = 1.5 m, attached to a frictionless pivot atone end. Another mass M2 is firmly glued to theend of the bar, as shown in the side view at right.Both M1 and M2 are 1.0 kg each. The rod (andattached mass M2) are initially held at an angle of30° with respect to the vertical, and then releasedto swing downwards at t = 0 seconds. Use gEarth

= 9.8 N/kg in all your calculations, and considerany and all frictional and drag forces asinsignificant.

Wherever possible, explain your reasoning, andshow your work. Credit is assigned for thecompleteness and clarity of your justificationusing the appropriate method(s), and notnecessarily for finding the correct answersbelow.

(a) [40%] Determine the rotational accelerationα of the rod/mass conglomerate (magnitude, in rad/s2; and ±ccw/cw direction) just at themoment it is released from rest.

(b) [30%] Clearly circle and defend one choice only. Which one of the four ω t( ) graphsshown below best describes the rotational motion of the rod/mass conglomerate, after it isreleased from rest at t = 0 seconds, until just as it swings through the 0° vertical line?

t [s]

ω [

rad/

s]

0

area = + π6

0

area

= +

π 6

0

area = + π6

0

area

= +

π 6


I I

t

rr

rα ω τ= =

∆∆

∑ ; r

lτ θ= ± F sin ; F mggravity = ; g = 9.8 Nkg

;

a r

v r

s r

tangential

tangential

==

∆ = ∆

αω

θ;

α ω

θ ω

= = ∆∆

∆ = = ⋅

∫slope

tarea dt

;

2π radians = 360° = 1 revolution; I MRpoint mass = 2; I MLrod pivot at end, = 13

2 .

M 1

30°

M 2

Physics 7B Discussion/Lab Manual - Waifer XPhysics 7B Discussion/Lab Manual "D" cell Multimeter used...

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