Physics 120 Lab Manual - Orange Coast Collegeocconline.occ.cccd.edu/online/sdrum/P120-130 Lab...

P120 Lab Manual Revised 4/20/1

Physics 120 Lab Manual

Spring 2014 Drum

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Physics 120 Lab Manual

Contents Subject Page

Lab 1 Free-fall 3

Lab 2 Motion 5

Lab 3A Newton’s 2nd Law 6

Lab 3B Forces and Collisions 7

Lab 4 Cannonball Range 8

Lab 5 Energy Conservation 10

Lab 6 Conservation of Momentum 12

Lab 7 Force Vectors 14

Lab 8 Buoyancy 16

Lab 9 Absolute Zero 18

Lab 10 Specific Heat 20

Lab 11 Latent Heat 21

Lab 12 The Oscillator 22

Lab 13 The Pendulum 24

Lab 14 Speed of Sound 26

Lab 15 String Resonance 27

Lab 16 Statistics 28

Lab 17 Galileo and the Pendulum 32

App. 1 Lab report format 33

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Lab 1: Free-fall Name: _________________________

1. Theory

An object is in free-fall if the only force on it is gravity.

2. Free-fall data (Falling Ball)

2.1 Use the apparatus to find x as a function of t.

Table 2.1 x vs. t for a Falling Ball

x (cm) t1 (s) t2 (s) Avg. t t2

5

10

15

20

30

40

50

60

70

80

100

120

Graph x vs. t2 on the computer.

Make a fit line to the graph.

Check with your instructor before printing the graph.

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3. Analyzing the Data

3.1 For a free-falling ball write down the theoretical formula relating x to t2:

_______________________________________________________

3.2 From the computer graph, write the equation of the fit line to your data:

_______________________________________________________

3.3 Circle each quantity in the top equation and draw a line to the corresponding quantity in the bottom equation.

From this, write down your experimental value for the acceleration:

a = ________ m/s2 g = ________ m/s2

3.4 How do you know from looking at the graph that the ball is in free-fall?

Draw below what the graph would look like if there was a lot of air resistance.

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Lab 2: Motion Graphs Name: _________________________

1. Matching a Position Graph

1.1 Open the file:

C:\Program Files\DataStudio\Library\Physics\P01 Position and Time.

1.2 Your instructor will tell you how to set up the program and will check to make sure the device is working properly.

1.3 Try to move so as to match the graph shown. Do this ONLY ONCE without practicing. Print out the result. Let everyone in the group do this. Each person’s printout should have only his or her own attempt on it.

Check with your instructor before continuing.

1.4 Now look at the graph and determine where you didn’t match the graph. Circle each area where the graphs don’t match and label it. Explain exactly why your motion didn’t match for each region.


1.5 Do several tries and erase all but the best one. Print it out, then let someone else in the group try. Do this until everyone in the group has his or her best graph printed out.


2. Matching a Velocity Graph

2.1 Follow exactly the same procedure, but with file

C:\Program Files\DataStudio\Library\Physics\P02 Velocity and Time.

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Lab 3A: Newton’s 2nd Law Name: _________________________

1. Predicting acceleration

1.1 A cart on a frictionless track is attached to a weight. The cart’s mass is M and the weight’s mass is m.

Draw two free-body diagrams: one for the cart and one for the weight. Don’t include friction or air resistance.

Write FNET = ma for the cart in terms of M, m, g, and the tension T.

Write FNET = ma for the hanging weight in terms of M, m, g, and T.

Eliminate T and solve for a.

2. Measuring F and a

2.1 You instructor will explain how you will measure a.

For each of the weights in the table below, find your expected acceleration and then measure a.

Table 2.1 Acceleration for Different Weights

m (kg) aEXPECTED aMEASURED % Difference

.050

.100

.150

.200

% Diff=|aMEASURED−aEXPECTED

aEXPECTED|×100

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Lab 3B: Forces and Collisions Name: _________________________

1. Collisions

1.1 Cart A is initially going tothe right. It collides with cart B. Force sensors measure the force appliedto each cart during the collision.

Fill in the “Predicted” column with a >, =, or < symbol.

Table 1.1 Action and Reaction

Masses Bumper A goes B goes FA ? FB

Predicted

FA FB FA ? FB

Observed

mA = mB Spring right left

mA = mB Spring right stopped

mA = mB Spring rt. slow rt. fast

mA > mB Spring right left

mA > mB Spring right stopped

mA > mB Spring rt. slow rt. fast

mA = mB Clay right left

mA = mB Clay right stopped

mA = mB Magnet right left

mA = mB Magnet right stopped

1.2 Open the file: C:\Program Files\DataStudio\Library\Physics\P12Tug_of_war.

Find the maximum force on each cart during the collision. We will say the forces are equal if they differ by no more than 10%.

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Explain any differences between predictions and observations.

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Lab 4: Cannonball Range Name: _________________________

1. Theory

The range of a cannonball depends on the angle of launch.

2. Range vs. Angle

2.1 Take shots to cover the range of 10 to 75.

Table 3.1 Range vs. Angle

Angle () Range

(1 click)

Range

(2 clicks)

10

15

20

25

30

35

40

45

50

55

60

65

70

75

Graph your data on the computer. Put both sets of data on one graph.

Print the graph. By hand, draw a smooth line through your data points.

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2.2 Place a target at a distance you know you can hit.

Using your graph, predict the angle needed to hit this target.

Distance to target: ________ cm Predicted angle: ________

Now try to hit the target. How close were you? D: __________ cm

3. Accuracy

3.1 Set your angle to 45 and find the range for 24 shots (1 click). Measure the range as accurately as possible.

Table 3.1 Variation of Range

Find the average of all 24 shots. Average range: _________ cm

Cross off the lowest 4 ranges and the highest 4 ranges. Write down the lowest and highest ranges remaining.

Low: __________ cm High: __________ cm

Take half of the difference between the low and the high. This is the uncertainty in the range.

Express your range in “plus-or-minus” notation.

Range = __________ __________ cm

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Lab 5: Energy Name: _________________________

1. Definitions

The formulas for kinetic energy (KE) and potential energy (PE) are:

KE=(1/2)mv2 PE=mgy

1.1 Open DataStudio

1.2 Write a formula expressing PE in terms of m, g, and x:

2. Energy

2.1 On the left-hand graph below, draw a plot of what you expect a graph ofthe PE to look like as the cart goes up and down the track.

On the right-hand graph below, draw a plot of what you expect a graph ofthe KE to look like as the cart goes up and down the track.

Graph 2.1: PE and KE of a Coasting Cart

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2.2 Find : ________

Weigh your cart. m: ________ (kg)

2.3 Get a good run for position vs. time. Check with your instructor. Erase all but the best run.

2.4 Your instructor will show you how to use the calculator function.

To graph PE, click on the calculator icon and enter the formula for PE.

To graph KE, click on the calculator icon and enter the formula for KE.

To graph E, click on the calculator icon and enter the formula for E.

2.3 Draw graphs of PE and KE on graph 2.1 using solid lines. How are the two graphs different? Explain any differences in your lab report.

Print out your graphs of PE, KE, and total E.

3. Energy loss

3.1 Find the total energy for the beginning and end of the run.

EINITIAL _________ J EFINAL _________ J

What % of the original energy was lost? Where did it go?

% lost=EFINAL−E INITIAL

E INITIAL×100

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Lab 6: Conservation of Momentum Name: ____________________

1. Collisions

1.1 In this lab we will measure the momentum and kinetic energy of two colliding carts. The formulas you will need are:

p=mv KE=(1/2)mv2

We will find p and KE of both carts combined before the collision and after the collision, and then find the % lost:

% lost= Final−InitialInitial

×100%

Open the file:C:\Program Files\DataStudio\Library\Physics\P38Mod2.

Print the graph only from trial 1.

Magnetic bumpers: 1. Equal mass cars, one car at rest.2. Unequal mass cars, one car at rest.

Clay bumpers: 3. Equal mass cars, cars in motion towards each other.

“Explosion:” 4. Unequal mass cars.

Trial 1 m v p KE

InitialCart A

Cart B

FinalCart A

Cart B

Trial 1 p KE

Tot. Initial

Tot. Final

% Diff

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Trial 4 m v p KE

InitialCart A

Cart B

FinalCart A

Cart B

Trial 4 p KE

Tot. Initial

Tot. Final

% Diff

Trial 3 p KE

Tot. Initial

Tot. Final

% Diff

Trial 3 m v p KE

InitialCart A

Cart B

FinalCart A

Cart B

Trial 2 p KE

Tot. Initial

Tot. Final

% Diff

Trial 2 m v p KE

InitialCart A

Cart B

FinalCart A

Cart B

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Lab 7: Force Vectors Name: _________________________

1. Theory

For an object in equilibrium, FNET=0

2. Two forces

2.1 Put hangers on the table at 0 and 180. Put 100g on m1.

Find the range for m2 at equilibrium. mMIN = _____ g mMAX = _____ g

3. Three forces

3.1 Put hangers on the table with 100 g at 0 and 180 g at 140.

What mass and angle on the third hanger do you predict will create equilibrium? Draw a free-body diagram; show your work. Check your prediction with the instructor.

PREDICTED = _______ MEASURED = _______ % difference _______

mPREDICTED = _______ mMEASURED = _______ % difference _______

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4. Three forces

4.1 Put hangers on the table at 0 and 120. Put 100g on m1 and 150g on m2. Adjust the mass and angle of m3 until you get equilibrium.

m3 = _______ 3 = _______

What is the net force? Draw a free-body diagram and show all your work.

FNET = __________

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Lab 8: Buoyancy Name: _________________________

1. Theory

1.1 The theoretical buoyant force is given byFB=ρ gV

ρ = 1000 kg/m3 for water g = 9.8 m/s2

V is the volume of the object in m3

To measure the buoyant force, compare the weight of an object in and out of

the water: FB=W OUT−W IN

The volume for various shapes is

V ( sphere)=43πR3 V (cylinder )=πR2h V (block )=LWH

For this lab, use meters, kilograms, and newtons.

2. Predicting Buoyancy

2.1 For each object, measure the dimensions and calculate V and FB.

Table 2.1 Theoretical Buoyant Force

Object Dimensions (m) V (m3) FB (Theory) (N)

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3. Measuring Buoyancy

3.1 Calibrate your force sensor. Your instructor will explain this. Find the buoyant force of various objects. Compare to the predictions.

% Difference= Measured−TheoreticalTheoretical

×100%

Table 3.1 Measured Buoyant Force

Object WIN (N) WOUT (N) FB (Measured)

Table 3.2 Summary

Object FB (Theory) FB (Measured) % Diff

4. Capacity of a boat

4.1 Find the maximum buoyant force the water could exert on your “boat” (really it’s a tuna can). Show your work on a separate sheet.

Use this to predict the maximum load of your boat.

4.3 Load up your boat until it sinks. How much could it hold?

Predicted Capacity: __________ Measured Capacity: __________

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Lab 9: Absolute Zero Name: _________________________

1. Theory

The ideal gas law is PV=nRT , where T is measured from absolute zero.

2. Constant-volume thermometer

2.1 Draw a picture of the setup here.

2.2 Immerse the bulb in hot water and measure T and P.

Table 2.1 Pressure of air at different temperatures

T (C) Absolute P (cm Hg)

Graph your data. Draw a fit line and extend it back to P = 0.

At what T does P = 0? What is the significance of this?

_________________________________________________________

_________________________________________________________

_________________________________________________________

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3. Constant-pressure thermometer

3.1 Find V for your gas at various T’s.

Table 3.1 Volume of air at different temperatures

T (C) h (cm) Total V (cm3)

Graph your data. Draw a fit line and extend it back to V = 0.

At what T does V = 0? What is the significance of this?

_________________________________________________________

_________________________________________________________

_________________________________________________________

4. Questions

4.1 Would V really be zero at absolute zero? Why or why not? How about P?

4.2 Of the two measurements of absolute zero, which do you trust the most?

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Lab 10: Specific Heat & Abs. Zero Name: _________________________

1. Theory

Heat energy (Q) is related to temperature by Q=mc ΔT The ideal gas law is PV=nRT , where T is measured from

absolute zero.

2. Specific Heat of a Metal

2.1 Weigh out a metal sample in a cup.

Add about 200 cc of hot water.

Find c for your metal.

Mass of sample cup: ______________

Mass of calorimeter: ______________

Mass of calorimeter cup: ______________

Room Temperature: ______________

Metal mMETAL mWATER TI,WATER TF,WATER

Summary

Metal c cBOOK % Diff

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Metal Amount

Aluminum 200 g

Copper 500 g

Iron 500 g

Lead 800 g


3. Constant-volume Thermometer

3.1 Graph P vs. T. Graph your data. Draw a fit line and extend it back to P = 0. At what T does P = 0? What is the significance of this?

Table 3.1 Pressure of air at different temperatures

T (C) P (kPa)

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Lab 11: Latent Heat Name: _________________________

1. Phase Change of Ice

1.1 Weigh out about 50 g of ice. Find L for ice.

L ________ cal/g LBOOK ________ cal/g % Diff ________

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Lab 12: The Oscillator Name __________________________

1. Theory

Hooke’s Law is an approximation for a spring: F=−kx

“k” is called the spring constant or stiffness.

The period (T) is the time for one complete oscillation.

2. Static Stretching and “k”

2.1 Measure the stretching “x” as a function of mass for your spring. Use two significant figures.

Table 2.1 Position vs. Weight

Mass (kg) Force (N) Position (m) x (m)

0 0 0

Graph the data. Put x on the x-axis and F on the y-axis.

Draw a fit line. Find the slope, the intercept, and k. Don’t forget units.

Slope: ________ Intercept: ________ kSTATIC: ________

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3. Spring oscillations and “k”

3.1 Find the period of oscillation for various amplitudes. Use m = 200 g.

Table 3.1 T vs. Amplitude

Amplitude (m)

Time for 10

oscillations

T (s) Amplitude (m)

Time for 10

oscillations

T (s)

.04 .16

.08 .20

.12 .24

How does T change as the amplitude changes?

3.2 Find kDYNAMIC=4 π 2M /T 2 where M = mWEIGHT + (1/3)mSPRING.

Compare kSTATIC to kDYNAMIC.

3.3 Measure T with M (not m) = 100 g and with M = 400 g. How do they compare?

T (100 g) ________ T (400 g) ________

3.4 Measure T with one spring and with two springs. How do they compare?

T (one spring) ________ T (two springs) ________

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Lab 13: The Pendulum Name __________________________

1. Static “stretching”

1.1 Hold the pendulum at various angles. Measure the amount of sideways force you need to hold the pendulum in place.

Table 1.1 Force vs. Position

Angle Force (N) Angle Force (N)

5 40

10 50

20 60

30 70

Graph the data. Put on the x-axis and F on the y-axis. Draw a fit line.

2. Pendulum oscillations

2.1 Measure the period for various displacements. Graph your data.

Galileo thought that T was constant for a pendulum. Was he right?

Table 2.1 Amplitude vs. Period

Angle 5 10 15 20 30 40 50 60

# of swings

Time (s)

T (s)

2.2 Measure T with different m’s: T (100 g) ________ T (200 g) ________

2.3 Measure T with different L’s: T (L) ________ T (¼ L) ________

3.2 How does the period of the pendulum change with the size of the swing, the mass on the string, and the length of the string?

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Lab 14: Speed of Sound Name: _________________________

1. Resonances

1.1 Graph the resonance lengths as a function of n for two frequencies.

Table 2.1 Resonant Lengths

f (Hz) 1 2 3 4 5 6 7 8

1.2 Find and calculate v for all the groups in the table below.

Table 2.2 Speed of Sound

Group Number

f (Hz)

Nominal

f (Hz)

Actual

(m) v (m/s)

1 8002 9003 10004 11005 12006 14007 16001 18002 20003 22004 24005 27006 30007 3300

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Lab 15: String Resonance Name: _________________________

1. Theory

Everything has one or more natural frequencies of vibration and will resonate at these frequencies.

2. Resonances and nodes

2.1 Set L to 1 m. Put a mass of 200 g on your string. Find the first five resonant frequencies. For each resonance measure and calculate the wave speed. Make a graph with n on the x-axis and f on the y-axis. Print the graph.

n f (Hz) (m) v (m/s)

1

2

3

4

5

Table 2.1 Resonances

3. Resonance and length

3.1 Set m = 200 g. For lengths from 20 cm to 1 m, find the resonant frequency f. Make a graph with L on the x-axis and f on the y-axis. Print the graph.

L (cm) 20 40 60 80 100

f (Hz)

Table 3.1 Resonant Frequency vs. Length

4. Resonance and tension

4.1 Set L = 1 m. For masses below find the resonant frequency f.

m (g) 50 200 800

f (Hz)

Table 4.1 Resonant Frequency vs. Mass

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Lab 16: Statistics Name _________________________

1. Trials and Randomness

1.1 Put 8 pennies in a cup. Shake the cup, dump the pennies out, and count the number of heads. This is a “trial.”

Make a mark in the appropriate column on table 1. For example, if you get 5 heads, put an “X” in column labeled “5.”

Do 20 trials per person, making an “X” for each one. Every person should keep his or her own record.

After this, combine all the data from the entire group.This is called a histogram or a bar graph.

Column 0 1 2 3 4 5 6 7 8

# Heads 0 1 2 3 4 5 6 7 8

Table 1.1: Tossing 8 Pennies Per Trial

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2. Larger Numbers

2.1 Repeat exercise 1, but use 32 pennies for each toss instead of 8.

Column 0 1 2 3 4 5 6 7 8

#Heads 0-2 3-6 7-10 11-14 15-18 19-22 23-26 27-30 31-32

Table 2.1: Tossing 32 Pennies Per Trial

3. Averages

3.1 Your instructor will tell you how to find the various different kinds of averages.

“Heads” 8 pennies 32 Pennies

Expected

Mode

Mean

Median

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3.2 The mode is the column with the most X’s. There may be more than one.

3.3 The mean is the total number of heads for all trials ÷ by the number of trials.

8 Pennies 32 Pennies

Column # of X’s # of Heads Column # of X’s # of Heads

0 1

1 4.5

2 8.5

3 12.5

4 16.5

5 20.5

6 24.5

7 28.5

8 31.5

Total Total

3.4 Use the following worksheet to find the median:

Start by adding all the X’s in each column. 8 ¢ 32 ¢

(a) Which column did you get to without exceeding 30? ______ ______

(b) What was the total number of X’s up to this point? ______ ______

(c) How many more X’s would you need to equal 30? ______ ______

(d) How many X’s are in the next higher column? ______ ______

(e) Calculate the median: N [a+(c /d )+(1/2 )] ______ ______ (N = 1 or 4)

In what situations would the mode be the most useful average?

In what situations would the mean be the most useful average?

In what situations would the median be the most useful average?

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4. Comparing the Two Graphs.

4.1 Use Excel to graph your results for parts 1 and 2 on the same graph. Use a graph that connects the data points.

4.2 In what way are the two graphs different? The same?

4.3 Which experiment (8 pennies or 32) is more likely to give an “unusual” result?

4.4 In which case is an unusual result more significant, when the group being tested is large or small? (Hint: what do I mean by “significant”?)

5. Proof

The 5-year survival rate for leukemia is about 50%, meaning about half of all people diagnosed with leukemia will be alive after five years.

Suppose you have an experimental drug which you give to a group of mice with leukemia. You start with eight mice and observe that, after the mouse equivalent of five years, 6 are still alive (that’s 75% of the mice).

What are the odds that this would happen by random chance? _______

What are the odds that the increased survival rate is from the drug? _______

If you work for the FDA (Food and Drug Administration), would you approve this drug for use in leukemia patients? Would you fund more experiments?

You decide to do a larger trial. You test 32 mice and find that 24 survive (again, this is 75% of the mice).

What are the odds that this would happen by random chance? _______

What are the odds that the increased survival rate is from the drug? _______

If you work for the FDA (Food and Drug Administration), would you approve this drug for use in leukemia patients? Would you fund more experiments?

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Lab 17: Galileo and the Pendulum Name: _________________________

1. Theory

According to Galileo, the period of a pendulum does not depend on the size of the swing.

The period is related to the length of the string: T=2π √d / g

2. Period and amplitude

1.1 Find the period of a pendulum for various amplitudes.

Table 2.1 Period vs. Amplitude

() # of Osc. Total t

trial 1

Total t

trial 2

T

2

4

6

8

10

15

20

30

40

50

60

1.2 Graph T() with the y-axis starting at 0.

Graph T() with the y-axis covering just the range of your data.

Each graph should have a linear fit line.

In your report, discuss the validity of Galileo’s hypothesis based on your evidence.

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2. Finding g with a pendulum

2.1 Re-write the equation T=2π √d / g to find g in terms of d and T.

2.2 Find d for your pendulum:

Length of string: ______ Dia. of ball: ______ d: ______

For an amplitude of 5, find T with a trial of 100 oscillations.

() N Total t T

5 100

Use this data and the formula to find your value for g. Compare this to the book value for g.

Experimental g: __________ Theoretical g: __________

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Appendix 1: Lab Protocol

At the beginning of each lab I will lay out cards with each student’s name and place the cards on the tables. You will have a different lab group each week.

It is very important to be on time. The doors will be locked at the beginning of each lab and roll taken. If you are late you must knock to get in and you will lose one point per minute you are late.

Lab reports are due the following week at the beginning of your lab session.

If you miss a lab call and see if you can attend another lab session. This will be done only if you have a good reason, such as a serious illness, for missing lab. If the lab cannot be made up an alternate assignment will be given. If you don’t have a good reason the lab will be scored as a zero.

The Lab Report

A report should have the following, all stapled together:

1. The original lab handout with my stamp on it.2. Any additional sheets on which you wrote down data.3. Any graphs you make in lab.4. A TYPED report.

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Grading

Each lab is graded from 0 to 100. Grading will be based on the following:

The lab is stamped. (100 points) You were ready for the lab and participated actively in the lab. (15 points) All the necessary data was taken. The data is clear and neat. (20 points) All data has units. (5 points) The number of digits is correct (not too many or too few). (5 points) Graphs: (10 points)

o The axes are labeled and units are shown.o The graph has a title at the top.o The data points are NOT connected.o A fit line is there if required.

All questions are answered in the report. (20 points) The report: (30 points)

o The report is not too short or too long (about one page is typical).o The phenomenon being studied is described and a theory is given.o The procedure is BRIEFLY described.o The theory is compared with the actual results. This will usually include a

BRIEF discussion of uncertainties.o A conclusion is drawn about theory. To what accuracy is it true? How

much confidence can you place in it based on your data? Is the theory true only within certain limits or under some circumstances?

Point values are given to show how many points might be deducted for incorrect procedure or missing items.

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Physics 120 Lab Manual - Orange Coast Collegeocconline.occ.cccd.edu/online/sdrum/P120-130 Lab...

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