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P H Y S I C S U N I O N M A T H E M A T I C S

Physics IIWork & Energy

Supported by the National Science Foundation (DRL-0733140) and Science Demo, Ltd.

Student Edition

PUM Physics IIWork & Energy

Adapted from:

A. Van Heuvelen and E. Etkina, Active Learning Guide, Addison Wesley, San Francisco, 2006. Used with permission.

This material is based upon work supported by the National Science Foundation under Grant DRL-0733140. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

Table of Contents

2 PUM | Work & Energy | Lesson 3: Reasoning with Energy Bar Charts Adapted from A. Van Heuvelen and E. Etkina, Active Learning Guide, Addison Wesley, San Francisco, 2006© Copyright 2009, Rutgers, The State University of New Jersey.

LESSON 1: HOW DO WE EVER GET ANYTHING DONE AROUND HERE?................4

LESSON 2: HOW AM I SUPPOSED TO KEEP TRACK OF IT?................................11

LESSON 3: REASONING WITH ENERGY BAR CHARTS........................................16

LESSON 4: SUCH GREAT HEIGHTS............................................................................26

LESSON 5: GALILEO’S PENDULUM............................................................................32

LESSON 6: HOW TO CALCULATE KINETIC ENERGY...........................................34

LESSON 7: THE ENERGY IN A SLINGSHOT AND OTHER PRACTICAL THINGS................................................................................................................................36

LESSON 8: SPRING INTO ACTION...............................................................................40

LESSON 9: CALCULATING THE INTERNAL ENERGY CHANGE........................43

LESSON 10: POWER UP...................................................................................................47

LESSON 11: PRACTICE & REVIEW.............................................................................50

LESSON 12: WHEN WORK IS NOT EASY...................................................................57

LESSON 13: OH BABY, DON’T LET ME GO...............................................................61

SUMMARY: DEFINITIONS AND PRINCIPLES..........................................................63

LESSON 14: SIMPLE MACHINES I...............................................................................65

LESSON 15: SIMPLE MACHINES: APPLICATIONS.................................................69

Lesson 16: Simple Machines II.............................................................................................72

PUM | Work & Energy | Lesson 3: Reasoning with Energy Bar ChartsAdapted from A. Van Heuvelen and E. Etkina, Active Learning Guide, Addison Wesley, San Francisco, 2006

© Copyright 2009, Rutgers, The State University of New Jersey.

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Lesson 1: How Do We Ever Get Anything Done Around Here?

1.1 Observe and find a pattern

In these three experiments, we will study the ability for a group of objects to smash a piece of chalk.

a) Consider a 1-kg block with a flat bottom and a string attached to the top, the Earth, and a piece of chalk. You pull up on the string so that the 1-kg block slowly rises 0.5 m above the piece of chalk. After this lifting process, you release the block. It falls and breaks the chalk.

b) Consider a 1-kg dynamics cart that can roll on a low-friction horizontal dynamics track and a piece of chalk that is taped to the fixed, vertical end of the track. You push the cart so that it rolls faster and faster toward the chalk at the end of the dynamics track and the cart breaks the chalk when it hits it.

c) Now consider a slingshot that holds a piece of chalk. You slowly pull back on the sling. When you release the sling, the chalk shoots out at a high speed and hits the wall, causing the chalk to break.

Complete this table.Experiment a) b) c)Draw an arrow indicating the direction of the force you exerted on each of the system objects that you studied ( ).

Draw an arrow indicating the displacement of the system object while you were exerting the force ( ).


Push wall wall

wallwall

Pull

1 kgLift

chalk

1 kg

d) Look for a pattern of what was done to the objects that we studied to give them the chalk-smashing potential. Then, devise a new physical quantity to describe this pattern.


Now, suppose that a friend decides to save the chalk in the first two experiments by exerting, with her hands, an opposing force on the block or on the cart after they are released. In each case, she pushes on the moving object opposite to the direction of its velocity. Below, give the direction of the force your friend exerts on the moving object relative to its displacement as she stops it, thus causing the system to lose its potential to break the chalk.

a) After lifting the block, you release the block and it starts falling. Your friend then starts pushing upward on the falling block, slowing it down, and the block does not break the chalk.

b) You push the cart so that it rolls faster and faster. You then stop pushing. Just before the cart reaches the chalk, your friend pushes it in a direction opposite to its direction of motion. This causes the cart to slow down and stop so that it does not break the chalk.

Complete this table. Experiment a) b)Draw an arrow indicating the direction of the force your friend exerted on the system object that you studied ( ).

Draw an arrow indicating the displacement of the system object while your friend was exerting the



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force ( ).

c) How could you modify the definition of the quantity you devised in the previous activity to account for the system’s loss of the chalk-breaking potential due to your friend’s intervention?


Consider the Earth and a 1-kg block.

a) You hold a string tied to a block so that it stays about 1 cm above a table. A piece of chalk is placed on the table under the block. If you release the block and it falls on the chalk, the chalk will not break (it’s too close to the chalk).

Next you slowly walk about 2 m beside the table, continually keeping the block 1 cm above the surface. After walking the 2 m, the block hangs over a second, identical piece of chalk. Draw the force exerted by the string on the block and the displacement of the block as you walked the 2 m.

b) Discuss whether the vertical force the string exerted on the block while moving it horizontally above the tabletop caused the Earth and block to have a better chance of breaking the second piece of chalk than the first piece.

c) Revise the quantity you devised in the last two activities to account for this result. Your revision will involve the angle between the external force exerted on the system and the system object’s displacement. We call this quantity work.

1.4 Observe and find a pattern (if you know trigonometry)

a) Consider a 1-kg dynamics cart being pulled at angle θ that can roll on a low-friction horizontal dynamics track and a piece of chalk that is taped to the fixed, vertical end of the track. You pull the cart so that it rolls faster and faster toward the chalk at the end of the dynamics track and breaks the chalk when it hits it. Draw the force exerted by you on the cart and the displacement of the cart while you were pulling it.

b) Discuss whether the angled force exerted on the cart while moving it horizontally gave it a better chance of breaking the piece of chalk than the force exerted in activity 1.1 part (b).


You are holding the string

Motion

θ θ

c) What trigonometric function would help you determine the system’s increase in chalk-smashing ability? Is this consistent with the increase, decrease, and no change in chalk-smashing potential for activities 1.1-1.3?

d) Revise the quantity you devised in the last three activities to account for this result. Your revision will involve the angle between the external force exerted on the system and the system object’s displacement. We call this quantity work.

Students familiar with trig, proceed to page 8; those who are not, continue here.

1.5 Practice

Jeff did 573 J of work on a sled. He pulled the sled for a distance of 30 m. What is the average force that he exerted on the system?



7

Work

xΔ

System

A woman pulls a box upwards.Since the force exerted by the woman on the box is in the same direction as the displacement,

System

System

A woman carries a box while walking at a constant pace. Since the force exerted by the woman on the box is perpendicular to the displacement,

A woman catches a ball thrown at her.Since the force exerted by the woman on the ball is in the opposite direction as the displacement,

1.6 Practice

Steve slowly lifts a 20 kg barbell 1 meter vertically. How much work does he do on the barbell?

1.7 Practice

Jessica, at a constant slow speed, moved a 1 kg book from a 2 m high shelf to the floor. How much work did she do on the book?

1.8 Practice

If Natasha slows a moving grocery cart by pulling on it exerting a force of 23 N over 2.3 m, what will be the work she does on it?

Homework

1.9 Relate

Describe a situation when you have done:

a) +1 J of work on a system.

b) -1 J of work on a system.

c) 0 J of work on a system.

1.10 Regular problem

While working out, a man lifts a 10-kg object a vertical distance of 0.80 m. He then carries it for 10 m where he sets it down a vertical distance of 0.80 m. How much work does he do on the object when he picks the object up, when he carries it, and when he sets it back down? What is the total work that he does on it?

1.11 Observe and explain

In another situation, you stretch a block-spring system and then release the block. The block slides toward the wall and smashes a piece of chalk. Label whether the ability of the block-spring-wall system to crush the chalk increases, decreases, or remains the same between each step.


v

Is this process consistent with the pattern we observed today between the net force exerted on an object and the displacement of the object?

Work-Trigonometry Section: In this section, students will use trigonometry to express work done for a more general range of situations.

Did You Know?

Work W: Work is a physical quantity that is equal to the product of the magnitude of the average force FEx on O that an external environmental object exerts on a system object, the magnitude of the system object’s displacement d, and the cosine of the angle between FEx on O and d.

W = (FEx on O cos ) d

1.12 Regular Problem

Suzanne is pulling a sled up a hill that makes a 24 angle with the horizontal. She keeps the rope parallel to the hill and exerts a 150-N force on it. How much work will she do if she pulls the sled 150 m?



9

Magnitude of force—always positive

Magnitude of displacement—always positive

Angle between and

System

Work

W = Fp on s cos() d

1.13 Regular ProblemA 4 kg grocery cart rolls down a 3 m long incline with an angle of 10°. How much work does the Earth do on the cart?

1.14 Regular Problem Juan pushes a box at an angle to the horizontal, doing 250 J of work over a distance of 10 m. If the force exerted is 30 N, what is the angle between the force exerted by Juan on the box and the horizontal?

1.15 Regular ProblemTo clean the floor, David exerts a 40 N force on a broom handle to push it 2 m. If the broom handle makes a 40° angle with the floor, what is the work done by David on the broom? If the broom handle were angled at 65° would David do more or less work?


Lesson 2: How am I Supposed to Keep Track of It?

2.1 Describe

You do work on a system to change its potential to do something (for example, to smash chalk or to make the touching surfaces of two objects in a system warm). In lesson 1, the work done on the system by the external force caused different types of changes in the system. Below, we describe each type of change in the system as a result of the work done on it. Devise a name for each type of change.

a) The external force caused the block to move higher above the Earth’s surface.

b) The external force caused the cart to move faster and faster.

c) The external force caused the slingshot to stretch.

d) The external force caused the surfaces of the touching objects to warm

Did You Know?

These changes in ability are energies. Each type of energy has a formal name: internal energy, kinetic energy, gravitational potential energy, and elastic potential energy. All of these fall under a larger category called mechanical energy.

e) In parts (a) through (d), you came up with names for different types of energy. See if you can match your answers to the traditional terms in the help box above.

f) Describe the amount of energy of a system if someone does positive work on it? Negative work?

2.2 Design an Experiment

Use materials on your desk to show an experiment in which for each item below, describe one real-life situation that is consistent with the processes described below.

a) Positive work causes an increase in the gravitational potential energy of the system.

b) Positive work causes an increase in the kinetic energy of the system.

c) Positive work causes an increase in the elastic potential energy of the system.

d) Kinetic energy in the system is converted to gravitational potential energy.

e) Kinetic energy in the system is converted to elastic potential energy.

f) Gravitational potential energy in the system is converted to internal energy.



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g) Gravitational potential energy in the system is converted to elastic potential energy.

2.3 Reason

Examine the picture to the right. One of your classmate says, “When the car gets to the edge it will have ‘the ability to fall’ or ‘falling ability.’”

a) If the Earth weren’t there, would the car still have “ability to fall?” Explain.

b) Should we include or exclude the Earth with the car when we analyze this problem?

Did You Know?

We have been examining a series of systems and analyzing the changes that occur to them. A system is an object or group of objects that we are interested in analyzing. REMEMBER! When we determine the objects in our system, we might need to include objects that aren’t in direct contact, like the Earth.

c) Create a story for what happened to the cart.

d) Decide what to include in your system. How did you decide?

e) Consider the situation. Is there a way this could be the final state of a process? Could it be the initial state of a process? Explain.

2.4 Explain

Why do we include the Earth in the system in some problems?

2.5 Observe and Describe

A system consists of a crate and a rough horizontal surface on which it sits (see the illustration below). The rough surface is made of a special material that changes color when it changes temperature.

a) On the picture to the right, identify objects in the system. Explain why you made this decision

You do positive work on the system by pulling the crate for about 10 m at a constant velocity. You observe the colors of the surface change indicating that the temperature increased.

b) Draw a force diagram that explain why the crate is moving at constant velocity


c) Describe how the system (crate and surface) is different after you do the work than before the crate started moving.

d) If the ground/surface were not there, would the crate have “warming potential?” Should we include or exclude the ground as part of our system?

e) Revisit your choice of a system. Do you want to make any changes? Write down your system below.

2.6 Observe and Explain

a) Complete the table below.

Describe the system.

Identify the objects that are

part of the system.

Identify the initial and final state.

Hector lifts a new television off the ground and places it on the TV stand.

TelevisionEarth

Jeff starts at the top of a hill and slides down on his snow sled. At the bottom of the hill, Jeff is moving really fast.

1 kg blockA spring

Earth

b) Eugenia slowly lifts a 5 kg box by exerting a constant force. She moves the box from the ground up onto the table, which is 1 m high.

1. Draw a force diagram for the box while she is lifting it.

2. What is the force Eugenia exerts on the box?

3. Calculate the work Eugenia has to do in order to lift the box onto the table.

4. Suppose Eugenia exerted a larger force on the box; what would she have to do to get the box to stop when it got to the table?

c) Mary rides in an elevator from the 1st floor to the 3rd floor. Answer the following questions.

1. Sketch the initial and final states, and then identify the system.

2. Make a reasonable approximation for Mary’s mass and the distance between the floors in the building.



13

3. Using the approximations, write an integer statement for the work the elevator does to lift Mary to the 3rd floor. Determine the work.

4. How much work would the elevator have to do if Mary’s twin sister joined her?

5. How much work would the elevator have to do if Mary decided to go to the 4th floor instead? (Determine the work both with and without her sister.)

d) Mary needs to ride the elevator back down to the first floor.

1. Sketch the initial and final states, and then identify the system.

2. Write an integer statement for the work the elevator does to move Mary from the 3rd floor down to the first floor. Use your approximations from the previous problem.

3. What if Mary were at the 4th floor instead? Write an integer statement for the work the elevator does to move Mary from the 4td floor down to the first floor.

4. What if Mary’s twin sister joined her, how much work would the elevator have to do to move them both from the 3rd floor to the first floor? Be sure to write an integer statement.

Homework

2.7 Observe and Reason

Lift a box from the floor to a tabletop very, very slowly at a constant velocity. Assume that during this process you do a total of 125 J of work. (There are no changes in kinetic energy or internal energy of the system.)

a) Identify the objects included in your system. What is not in your system?

b) Draw a picture of the initial and final states

c) Complete the table below.

Portion of the Process Work that has been done so far

Gravitational Potential Energy of the Box-Earth system

Before you start, the box is on the floor. 0 J

You have lifted the box ¼ of the way.

You have lifted the box ½ of the way.

You have lifted the box ¾ of the way.


You have lifted the box all the way to the table. 125 J

2.8 Reason

Describe a real-life situation in which an external force does the following and state explicitly whether the system’s energy increases or decreases:

a) Positive work on a system;

b) Positive work on a system but with a value that is less than in part (a);

c) Negative work on a system;

d) Zero work on the system even though an object in the system moves.



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Lesson 3: Reasoning with Energy Bar Charts

3.1 Represent and Reason

a) How can we use charts to represent data?

b) Create a chart that shows that you have $60 in your bank account, no money in you pocket, and $20 on a gift card.

c) Imagine that you withdraw $20 from your bank account and put it in your pocket. Create a new chart that represents your new situation.

d) If we place the two charts side-by-side, how does it express a process? Explain.

Need Some Help?

We can use a bar chart to represent transformations of a quantity during some process. We do this by placing the before bar chart next to the after bar chart.

We can also abbreviate the column headings in order to make this easier to read. We just have to make sure to include a key so that we know how to reading the chart. See below.

P represents the amount of money in your pocket CATM represents the amount of money in your ATM card CGIFT represents the amount of money on a rechargeable Best Buy gift card. Earn/Spend represents the amount of money that you gain or lose through

transaction with other people

e) What do you notice about the money before and after this process?

Did You Know?The total amount of money you have remains the same before and after, unless you earn some or spend some -- right? If the total amount of money you have does not change, we say it is constant. If it changes in a predictable way due to the expenses, we say that it is conserved, as it does not appear from nowhere and disappear to nowhere.


3.2 Represent

Situation Before and After Bar Chart Representation

a) You have $15 in your pocket, $60 in your ATM account, and a gift card with $20 on it. You withdraw $20 cash from the ATM.

Represent this transaction on the bar chart. Did you earn or spend any money?

Represent this transaction with a mathematical statement

b) Next, you buy a snow shovel for $10 cash at Jones Hardware.



c) After returning from the hardware store, you spend three hours shoveling snow for an old lady who gives you $20 cash.





17


d) When you are finished shoveling, you spend $20 cash to put gas in your car so you can drive to the Best Buy.



e) At Best Buy, you purchase a "Cher's Greatest Hits" DVD Box Set for $40. You empty out your gift card and use your ATM card to pay for the rest.



f) What happens next? Continue the story and make a graph to match.

g) Does this graph show something that could happen? If not, explain why not. If so, describe a situation it could match.



h) Draw the missing bar.

Write a mathematical statement to match the chart.

Describe a story that could match.

i) Make a chart to match this mathematical statement:

$20 + $0 + $0 + $40 = $20 + $40 + $0

Describe a story that could match.

j) For each problem, relate your money at the beginning to the money at the end with an equation.

k) Draw a comparison between money transfers and energy transfer. What similarities do you see?

l) What property of wealth is illustrated in this activity?

m) What other physical quantities (besides energy) exhibit this property? What quantities do not?


While working on the following problem, Alan decided that he could represent work-energy processes with a bar chart similar to the ones we used for money.

Problem: Jessica stands in an elevator on the first floor. The elevator doors close and the elevator delivers Jessica to the fourth floor. Identify all the changes that occur.

a) Identify the system of interest

b) Draw pictures of the initial and final states. (Make sure to include a description.)

c) Review the problem and create your own work-energy bar chart.



19

Need Some Help?

Work-energy bar charts provide a concrete way to represent work-energy processes. In a work-energy bar chart, a bar represents each type of energy initially in the system, as well as the final energies of the system. If external objects do work on the system (positive or negative), then there is a bar to represent work.

We don’t know the exact amount of energy or work usually but we can still make estimates based on the situation. The column for the work bar is shaded to indicate that it is not a type of energy but is instead a process involving an interaction between a system object and an object outside the system.


a) Kristen and her friend Peter go to the park to ride on the swings. Complete the tables below to describe all the energy transformations. Be sure to identify the system in each step.

Initial State Final State Construct the Work-Energy Bar ChartPeter has no velocity and is at the highest point of his swing.

Peter is at the bottom of his swing and is going really fast.

System: Equation:


Across the top of the chart, you see several symbols for different energies…

K – Kinetic energyUg – Gravitational potential energy Us – Elastic or spring potential energyW – Work∆Uint – Change in internal energy

(Difference between final and initial)

The i and the f represent initial and final states

Initial State Final State Construct the Work-Energy Bar ChartPeter is at the bottom of the swing moving really fast.

Peter gets to the top of his swing and slows down.

System: Equation:

Peter has no velocity and is at the highest point of his swing.

Peter is at the bottom of his swing and is going really fast backwards.

System: Equation:

Peter has come to a stop at the top of the swing’s motion and begins to swing forward.

After a few swings Peter eventually comes to a stop at the center of the swing.

System: Equation:

b) Describe how the system’s energy has changed in each step Peter swung back-and-forth.

c) How has the total energy of the system changed?



21

d) If the rope from the swing is not in the system, how is accounted for in the bar charts?

Homework

3.5 Bar Chart Jeopardy In the table that follows, invent a process using words and a sketch (the system, its initial and final situations, and any work done on the system). Be sure both are consistent with the qualitative work-energy bar chart shown below.

Bar chart for a process. State what is in your system. Describe in words one possible consistent process.

Sketch the process just described.

Relate these quantities mathematically:

Bar chart for a process. State what is in your system. Describe in words one possible consistent process.

Sketch the process just described.

A car screeches to a halt, the tires of the car start smoking.

Relate these quantities mathematically:

3.6 Explain

Read through the following problem and then read Alan’s solution below. Use it and your response to activity 3.3 to answer the questions.

a) How does your answer compare with Alan’s?

b) Does Alan’s bar chart help him understand the problem? Explain your answer.


Ki + Ug,i + Us,i + W = Kf + Ug,f + Us,f +∆Uint

0

+

before after

-


0

+

before after

-

c) What do the lengths of the bars represent in Alan’s Work-Energy bar chart?

d) How do you think Alan decided to make the lengths of the bars in his bar chart? Explain.

Problem: Jessica stands in an elevator on the first floor. The elevator doors close and the elevator delivers Jessica to the fourth floor. Identify all the changes that occur.

Alan’s solution: The system includes Jessica, who might be moving so we may need to consider kinetic energy. The system also includes the Earth, so we will have to consider gravitational potential energy, too. But because Jessica’s initial and final velocity is zero, the kinetic energy does not change. I put the initial energies of the system on the left side of the bar chart and the final energies on the right side. However, I had no energy on the left but some on the right, which can’t be possible. Then I remembered the elevator that pulled Jessica up. The elevator is not in my system, so it must do positive work on Jessica. I put the work done in the column labeled W for work.

e) Use the rubric below to assess you work-energy bar chart. How did you do? Describe your difficulties.

Rubric to self-assess your work-energy bar charts

Absent An attemptNeeds some

improvementAcceptable

No work-energy bar chart is constructed.

Work-energy bar chart is constructed but is missing or contains extra energy bars; the initial and final states described do not match the initial and final states on the chart. The initial quantities plus the work do not equal the final quantities.

Work-energy bar chart lacks a key feature such as labels, the zero energy is not indicated, or quantities are not drawn to scale.

The chart is labeled clearly so that one can understand the initial and final states of the system. The relative lengths of the bars are correct. And the zero energy is indicated.

3.7 Reason

a) Look back at the bar charts from the previous activity. If the elevator only went ½ as high, which of the bars would change and by how much?



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SystemJessicaEarth

Initial StateJessica is not moving, standing in the elevator on the first floor.

Final StateJessica is not moving, standing in the elevator on the fourth floor.

b) How would the work-energy bar chart look if we chose a final state when Jessica was still moving?

c) How can we convert Alan’s bar charts into an integer statement?

d) Describe a situation with Jessica that could be represented by this energy bar chart.


Use a bar chart to represent transformations of a quantity. This time, the exercise concerns the food in your house, and we are going to make bar charts with estimated quantities instead of exact numbers. Fill in the bar charts provided. Write a mathematical equation represented in each chart that relates the quantities of food and shopping and discarding.

FP = food in your pantryFR = food in the refrigeratorFS = food on the stoveΔUate = food "U" ate


You have some food in your pantry and refrigerator already.

You go shopping and come home with bags of groceries.

You put some away in the pantry and some away in the refrigerator.

Represent this on the bar chart.


FP,i +FR,i + FS,i+ =FP,f +FR,f +FS,f +∆Uate

0

+

buy or discard

before after

-


The situation starts from where we left off in the previous question.

You take some ingredients from the pantry and some from the refrigerator and make a meal on the stove.


You eat half of the food you cooked and store the rest in the refrigerator.


The next day you come home with a takeout from White Castle. You eat the stack of White Castles and throw out your leftovers from the day before.


e) Why do we show ΔUate on the "after" side but not on the "before" side?



25


0

+

buy or discard

before after

-


0

+

buy or discard

before after

-


0

+

buy or discard

before after

-

Lesson 4: Such Great Heights


Imagine that a cart is rolling down an inclined plane. The initial state is when it is on top of the incline, the final state is when it is moving fast at the bottom.

Case A: Our system is the cart only therefore, it does not have any potential energy. There is also no initial kinetic energy. Earth pulls down on the cart; the surface exerts a force perpendicular to the direction of motion. Because the cart rolls, its kinetic energy increases. Earth does positive work and the surface of the plane does no work because the force is perpendicular to the direction of motion. Case B: The system is the cart and Earth together. It has initial gravitational potential energy. As the cart rolls down, some of this energy is transformed into kinetic energy. Earth does not do any work because it is internal to the system.

Draw a diagram for the situation and circle the system.

Complete the bar chart for this process and relate the quantities mathematically.

Case A

Case B:



before after

0

+

-


before after

0

+

-


Complete the table that follows. Consider a 20 N brick sitting on a table which is 1 m high.

Word description of a process.

Sketch the initial and final state. Circle the system.

Complete the work-energy bar chart for this process

(a) Hector lifts the brick 1 m up off of the surface of the table. He then moves the brick horizontally so it is held over a piece of chalk on the floor.

Write an equation relating these quantities:

(b) Eva lifts an identical brick 2 m from the floor to a spot right next to Hector’s brick. It is also hanging over a piece of chalk on the floor.

Write an equation relating these quantities:

c) When dropped, the bricks in parts (a) and (b) will both smash the chalk on the floor the same amount. You found different initial potential energies for each system, though. How can this be? Compare and contrast Hector’s situation with Eva’s situation to help you answer this.

The energy of each system measures its ability to smash a particular piece of chalk. For Hector’s final state, the 20 J of energy actually measures the system’s ability to smash a piece of chalk on the table. Since you have decided that when the block was on the table, the system begins with no energy, you must have been describing the ability to smash the chalk if it were on the table.



27

Ki + Ug,i + Usi + W = Kf + Ug,f + Us,f +∆Uint

before after

40 J

20 J

0

-20 J

-40 J


before after

40 J

20 J

d) Redraw your work-energy bar chart for Hector, but now describe the ability to smash chalk on the floor. Below, relate the quantities mathematically.

e) Redraw your energy-bar chart for Eva, but use it to represent the system’s ability to smash the chalk on the table. Is the final state identical to Hector’s final state in part (a)?Below, relate the quantities mathematically.

4.3 Reason

You smash open walnuts on a picnic table by lifting a block from the table to a height of 1 m above the walnuts and then dropping the block on the walnuts.

a) Draw a work-energy bar chart and a diagram for the initial and final states representing the block-Earth system’s ability to smash these walnuts as you lift the block.

Your friend is in a tree house that is 10 m above the picnic table. Your friend has walnuts for a snack in his tree house.

b) Draw a work-energy bar chart and a diagram for the initial and final states representing the block-Earth system’s ability to smash these walnuts in the tree house as you lift the block 1 m above the picnic table below.

c) In parts a) and b), you have a system with a negative gravitational potential energy. What does a negative value represent about the ability of the system to accomplish a task?

Need Some Help?When calculating the gravitational potential energy of a system, you must pick a reference level. When an object is at this reference level, the gravitational potential energy of the system is zero.



before after


before after

4.4 Derive the Relationship

To develop a mathematical expression for gravitational potential energy, we analyze the following situation. To build the foundation for a new skyscraper, a construction company needs to drive metal poles into granite stone. To hammer the poles into the ground, a crane lifts a massive block at a slow constant speed from a height yi above the pole to a height yf above the pole. The crane then drops the massive block onto the top of the pole, which is at height yf = 0.

Below is a picture of the initial and final states of the process. The system for analysis is the block and Earth.

a) Complete a work-energy bar chart for this process. Write a mathematical expression representing this process.

b) Write an expression for the work the cable does on the block during its displacement yf – yi. Substitute this into the expression in part a.

c) Draw a force diagram for the block during this process. Use it to find an expression for the force that the cable exerts on the block in terms of its mass and the gravitational constant g. Substitute this expression into the expression in part b.

d) Examine the expression that you derived in part c. Do you see that the work that the cable did on the block equals the change in a quantity: mgyf – mgyi? Discuss how this expression can be used to write an expression for the gravitational potential energy of the block-Earth system.

4.5 Test the Relation

You are the head engineer for the construction company discussed in the last problem. Before you build the machine to drive the poles into the ground, you need to test whether the ability of the block-Earth system to do something (to smash chalk or clay, to dent Styrofoam, to splash water, etc.) depends on the mass of the block and the initial height of the block above the target.

Describe two experiments that you can perform to test these relationships. Include a sketch. What does the relationship predict will happen? What are your assumptions?



29

- 0

- yi

- 0

- yf

4.6 Reason

Imagine that you could use one of two ramps to slowly move a cart to a position that is 2 m above the ground.

a) Using a work-energy bar chart; determine how much work you will have to do to move the cart up each ramp slowly.

b) Determine the value of the force that you will need to exert on the cart to slowly push it up each ramp.

Homework

4.7 Equation jeopardy

Write a problem that would require the mathematical equation below to solve it.

10 J = m*9.8 (N/kg) (15 m – 3 m)

4.8 Reason

When you crushed the chalk with a block, you released the 5 kg block from a height of 1 m above the chalk. What is the gravitational potential energy of the block-Earth system before you released it? What did you set as your reference level?

4.9 Reason

A skier slides down an icy hill. He has a mass of 70 kg and begins 50 m above the bottom of the hill. What is the skier’s kinetic energy at the bottom of the hill? What is his kinetic energy when he is ¾ of the way down the hill? What system did you choose for analysis?

4.10 Reason

Jeff and Jim are both demolition experts skilled in using a wrecking ball to destroy old buildings. The motion of the wrecking ball is shown below.

When asked to draw work-energy bar charts for the motion of the wrecking ball, Jeff and Jim drew the bar charts below. a) When would Jeff’s be correct and when would Jim’s be correct? Be sure to state the initial and final states, what objects you are including in the system, and where you are defining the reference level for zero gravitational potential energy.


2 m

15 m3 m


0

+

before after

-

Jeff’s Jim’s


0

+

before after

-

b) How should Jim and Jeff label their work-energy bar charts to prevent any more confusion?

c) Shouldn’t they include the work due to the force that the rope exerts on the ball on both charts? Explain your answer with a force diagram.


Imagine that you throw a baseball out of your dorm room window 5 stories up to a friend standing outside on the ground level. Determine which of the following work-energy bar charts could represent this situation. Decide what is included in the system and state the reference level for the gravitational potential energy for each correct bar chart.



31


before after

0


before after

0


before after

0


before after

0

Lesson 5: Galileo’s Pendulum

5.1 Test a Hypothesis

Suppose that you have a pendulum (a bob hung from a string) and a horizontal rod in its path (the device is called Galileo’s pendulum). The pendulum is pulled to the side and released. When the string swings into its vertical orientation, it hits a horizontal rod, causing the pendulum to swing in an arc with a smaller radius (as pictured below).

The height of the horizontal rod can be adjusted.

Design and conduct an experiment that uses this pendulum to test whether energy is conserved in any system or constant in an isolated system.

a) State clearly the hypothesis that you will test in the experiment.b) Play with the pendulum and decide what features of its behavior can be explained

using the concept of energy.c) Think of an experiment that you can perform whose outcome you can predict using

the ideas of energy conservation and energy constancy. Draw a picture. Decide what quantities you will measure and what quantities you will calculate. Decide what objects are in your system and whether any external objects do work on it.

d) Make a prediction of the outcome of the experiment based on the idea being tested (the hypothesis). Make sure that you include the experimental uncertainties in your prediction.

e) What are the additional assumptions that you are making? Can you validate them? If these assumptions are not valid, how will they affect your result?

f) Perform the experiment as many times as you think is necessary, collect the data, and calculate the result. How close is it to your prediction?

g) What is your judgment about the hypothesis that you were testing?h) Use the rubrics below to improve your lab report.

5.2 Test a Relation

Using the available equipment, you will conduct an experiment to test the relation you developed for the gravitational potential energy of a system. To do this, you will use this relation to predict the positions that two plumb bobs must be moved to in the drop chute to give each Earth-bob system the same initial gravitational potential energy. Then, you will use the apparatus to measure whether or not the system has the same initial potential energy.

a) State clearly the relation that you will test in the experiment.b) For the two plumb bobs, determine the height of each in the Earth-bob system so that both systems have the same potential to smash the clay. Be certain to state the reference level that you are using.


Pendulum Bob

Pivot

Horizontal bar

c) Explain how you can use the apparatus to measure whether each system has the same initial gravitational potential energy. State your assumptions. d) Perform the experiment as many times as you think is necessary, collect the data, and calculate the result. How close is it to your prediction?e) Repeat the experiment one more time but use a different reference level. f) What is your judgment about the relation that you were testing?

Homework

Write a lab report for the first experiment you performed in class. Use the rubrics to guide your writing.

Hypothesis-prediction-testing rubric (used for testing experiments)Scientific Ability Missing An attempt Needs some

improvement Acceptable

Is able to distinguish between a hypothesis and a prediction.

No prediction is made. The experiment is not treated as a testing experiment.

A prediction is made, but it is identical to the hypothesis.

A prediction is made and is distinct from the hypothesis but does not describe the outcome of the designed experiment.

A prediction is made, is distinct from the hypothesis, and describes the outcome of the designed experiment.

Is able to make a reasonable prediction based on a hypothesis.

No attempt is made to make a prediction.

A prediction is made that is distinct from the hypothesis but is not based on it.

A prediction is made that follows from the hypothesis but does not have an if-and-then structure.

A prediction is made that is based on the hypothesis and has an if-and-then structure.

Is able to make a reasonable judgment about the hypothesis.

No judgment is made about the hypothesis.

A judgment is made but is not consistent with the outcome of the experiment.

A judgment is made and is consistent with the outcome of the experiment but assumptions are not taken into account.

A reasonable judgment is made and assumptions are taken into account.



33

Lesson 6: How to Calculate Kinetic Energy

6.1 Hypothesize (Derive a Mathematical Model)

In a car crash testing facility, engineers evaluate the reaction of a car to an impact on its front. To create such an impact, a rod pushes a 1000 kg block on wheels over a distance d. This causes the block to accelerate from an initial to a final velocity. To measure the smashing potential of this block, let’s determine the change in the block’s kinetic energy after the piston pushes it a distance d. The initial and final states of the process are pictured to the right.

a) Draw a force diagram for the block. Use it to find an expression for the force that the piston exerts on the block in terms of its mass m and acceleration a.

b) Use a kinematics equation to convert the acceleration a in the equation from part (a) into an expression involving the block’s initial and final speeds vi and vf. Substitute this into the expression for force from part (a).

c) Substitute the expression for force from part (b) into the expression for work when the force is parallel to the displacement, W = Fd, and then simplify.

d) Using a work-energy bar chart, develop a mathematical representation of this process in terms of work, initial kinetic energy, and final kinetic energy. Compare this expression to the one from part (c).

e) What characteristics of an object do you expect kinetic energy to depend on? Its mass? Velocity? Acceleration? Height?

f) By comparing your answers from parts (c) and (d), do you see a term that could represent kinetic energy and that depends on the characteristics that you think kinetic energy should depend on?

g) Show that the units of this quantity are equal to the units for energy, joules.

6.2 Practice

If you drop a 0.3 kg baseball from a window 20 m above the ground, how fast will the ball be moving the instant before it hits the ground? Use the mathematical and visual representations for energy in solving the problem. Disregard the force exerted by the air on the ball.


vi

vf

d

0

+

-


before the block is lifted

after the block is lifted

6.3 Practice

If a stretched slingshot has 100 J of potential energy, how fast will a 0.5 kg softball be moving right after the launcher fires it? Using energy representations, how high will the softball go?

Homework

6.4 Regular Problem

A crane lifts a 50-kg crate so that the crate’s speed increases from 0 m/s to 5.0 m/s over a vertical distance of 10.0 m. Draw a bar chart representing this process. What is the force that the crane exerts on the crate? Specify the system, its initial and final states, and any assumptions you made. Explain how these assumptions affect your answer.

6.5 Regular Problem

A man throws a 0.4-kg softball vertically into the air with an initial speed of 10 m/s. How fast will it be traveling when it passes 1/3 of its maximum elevation?

6.6 Reason

Two identical water balloon slingshots are stretched the same distance so that they both having the same potential energy. The mass of one water balloon is 2/3 of the mass of the other water balloon.

a) Which water balloon leaves the slingshot traveling at a faster speed?

b) How much faster is this water balloon traveling?

6.7 Equation Jeopardy

Write a problem and draw an energy bar chart that would require the mathematical equation below to solve it.



35

Lesson 7: The Energy in a Slingshot and Other Practical Things


Complete the table that follows for three different processes. The goal is to devise a graphical method to determine the work done by an external force on a system object. Note: P = person and O = object.

Word description of a process.

Draw FP on O –versus-Δy (for vertical motion) or

Δx (for horizontal motion) graphs.

Describe how to use the graph to find the

work done by the force.

If an object moves a distance Δy or Δx,

what is the expression for the work done on

the object by the force on the graph?

a) Rona lifts a backpack from the floor to the desk, exerting a constant upward force. The backpack and the Earth (not Rona) are the system.

b) Kruti catches a medicine ball in the gym. The ball and the Earth are the system (but not Kruti). Her hands move back toward her body while stopping the ball.

c) Carlos stretches a horizontal rubber cord (it behaves like a spring) with a spring constant k. The spring and the Earth are in the system but not Carlos.

d) Two men push a stalled car. For the first 50 m, they exert a force of 1000 N on the car. For the second 50 m, they exert a force of 500 N on the car.


FP on O

y

FP on O

Δy

y

FP on O

y

Δy

FP on O

y


Recall that the magnitude of the force exerted by an elastic spring on an object is F = kx where x is the distance that the spring has been stretched (or compressed) from its relaxed position.

a) Graph the force that must be exerted on an elastic spring by the object stretching the spring from its relaxed state to an extension xf. How does this force relate to the force that the spring exerts on the object?

b) Determine the work done by external forces exerted on the elastic spring to stretch it this distance.

c) Show that the units of this quantity are equal to the units of energy, joules.

d) Draw a work-energy bar chart for this process.

e) Write a mathematical expression for this process represented by the bar chart.

f) Use this mathematical expression in variable form (using k and x) to find an expression for elastic potential energy.


A spring with a spring constant k = 80 N/m is compressed 0.3 m. A 0.2 kg book is placed on top of the compressed spring.

a) Draw a picture of the process. What are the initial and final states of the process? What is the reference frame you are using?

b) What will happen when the spring is released?

c) Draw a picture of the process. What are the initial and final states of the process? What is the reference frame you are using?

d) Represent the process with an energy bar chart.

e) After the spring is released, how high will the book fly?

7.4 Equation Jeopardy

Create a problem where the following is the solution:

½ (50 kg) x (10 m/s)2 + m x (9.8N/m) x 20 m = ½ k * (1m)2

Draw a picture of the process. What are the initial and final states of the process? What is the reference frame you are using?



37

7.5 Regular Problem

How much work must be done on a spring with spring constant 100 N/m to change its stretch from 0.15 m to 0.25 m? Draw a picture of the process. What are the initial and final states of the process? What is the reference frame you are using? Include a work-energy bar chart.

Homework

7.6 Jeopardy

Complete the table that follows and formulate a problem. Problem: Sketch with the reference frame:

Force-displacement Graph: Work-energy bar chart:

Mathematical Representation and Solution:Ig,i + W = Ug,f

W= Ug,f - Ug,i


I I

0m 10 m 20 m y

F

50 N –

25 N -


0

+

before after

-

7.7 Regular Problem

You are the coach of the two-man U.S. Olympic Bobsled Team. At the beginning of a race, one of the team members pushes the bobsled and its driver for 50 meters along the level track. For the first 20 meters, the athlete exerts a 400 N force in the horizontal direction on the sled and driver. For the next 20 meters, the member exerts a force of 350 N on the two. For the final 10 meters, he exerts a force of 300 N on the two. The total mass of the bobsled and driver is 330 kg. Let’s calculate the total work that the team member does on the bobsled.

a) Over the first 20 meters, how much work does the teammate do on the system?

b) Over the next 20 meters, how much work does the teammate do on the system?

c) Over the last 10 meters, how much work does the teammate do on the system?

d) What is the total amount of work that the teammate does on the system?

e) On the axes below, graph the force exerted on the system by the teammate versus the position of the system.

f) What property on the graph is equal to the work done by the teammate on the system?

7.8 Regular Problem

Kristen pushes her little sister on a sled on a packed icy surface. Her little sister and the sled have a combined mass of 20 kg. Ignore the frictional forces exerted on the sled.

a) Sketch a diagram of the situation and identify an initial and final state.

b) Represent the process with a work-energy bar chart

c) Determine the final velocity of Kristen’s sister.



39

x (m)

F (N)

Lesson 8: Spring into Action

8.1 Observe

You have a spring and a vertically mounted metal pole and other regular lab equipment. You can stretch the spring along the metal pole and release it to fire it upwards. Play with the spring and decide what features of its behavior can be explained using the concept of energy. What do you notice when you stretch the spring the same length each time?

Caution: Protect your eyes with goggles! Only stretch the spring when nobody is close to its pathway.

8.2 Hypothesize a Relation

Consider all of the activities that you have done so far. What is the relationship between the initial energy of the system, the external work done on the system, and the final energy of the system? Clearly state the hypothesis/relation that you will test in the experiment.

8.3 Test the Relation

a) Think of an experiment that you can perform whose outcome you can predict using the relation being tested. Draw a picture. Decide what quantities you will measure and what quantities you will calculate. Decide if you need to perform some additional experiments to determine the unknown quantities.

b) Use your relation to predict the outcome of the experiment. Make sure that you include the experimental uncertainties in your prediction.

c) What are the additional assumptions that you are making? Can you validate them? If these assumptions are not valid, how will they affect your results?

d) Perform the experiment as many times as necessary, collect the data, and calculate the results. How close is it to your prediction?

e) What is your judgment about the relation that you are testing?

f) Write a report about your experiment so that a person who did not see you perform the experiment can repeat it and can also understand your results and conclusions.

g) Use the rubrics below to improve your lab report.


Hypothesis-prediction-testing rubric (used for testing experiments)Scientific Ability Missing An attempt Needs some


Is able to distinguish between a hypothesis/relation and a prediction.


A prediction is made but it is identical to the hypothesis/relation.

A prediction is made and is distinct from the hypothesis/relation but does not describe the outcome of the designed experiment.

A prediction is made, is distinct from the hypothesis/relation, and describes the outcome of the designed experiment.

Is able to make a reasonable prediction based on a hypothesis/ relation.


A prediction is made that is distinct from the hypothesis/relation but is not based on it.

A prediction is made that follows from the hypothesis/relation but does not have an if-and-then structure.

A prediction is made that is based on the hypothesis/relation and has an if-and-then structure.

Is able to identify the assumptions made in making the prediction.

No attempt is made to identify any assumptions.

An attempt is made to identify assumptions but the assumptions are irrelevant or are confused with the hypothesis.

Relevant assumptions are identified but are not significant for making the prediction.

All relevant assumptions are identified and their effects on the accuracy of the prediction are correctly determined.

Is able to determine specifically the way in which assumptions might affect the prediction.

No attempt is made to determine the effects of the assumptions.

The effects of the assumptions are mentioned but are describe vaguely.

The effects of the assumptions are determined but no attempt is made to validate them.

The effects of the assumptions are determined and the assumptions are validated.

Is able to make a reasonable judgment about the hypothesis/ relation.

No judgment is made about the hypothesis/relation.




Is able to identify experimental uncertainty.

No attempt is made to identify experimental uncertainty.

An attempt is made to identify experimental uncertainty but most are missing, described vaguely, or incorrect.

Most uncertainties are correctly identified.

All experimental uncertainties are correctly identified.

Is able to evaluate specifically how experimental uncertainties will affect the data and calculations.

No attempt is made to evaluate experimental uncertainties.

An attempt is made to evaluate uncertainties, but most are missing, described vaguely, or incorrect.

The final result does take uncertainties into account but they are not correctly evaluated.

The experimental uncertainty of the final result is correctly evaluated.

Homework

Write up your lab using the rubric as a guide.



41

8.4 Regular Problem

Instead of traditional brakes, a spring is used to slow down a new type of roller coaster. The coaster has 5.0 x 105 J of kinetic energy before it compresses the spring and comes to a stop. The spring constant for the spring is 2.0 x 104 N/m. How far is the spring compressed? What are the system and the initial and final states that you chose for the situation? (When you are solving the problem, make sure that draw a picture of the process, identify the initial and final states of the process and specify the reference frame you are using.)

8.5 Regular Problem

A model airplane launcher uses an elastic cord to accelerate a small wood and paper airplane to flight speed. The 0.005-kg plane must be moving at 1 m/s to fly. If the elastic band has a spring constant of 120 N/m, how far should you stretch the elastic band so that the plane will accelerate to its flight speed? (When you are solving the problem, make sure that draw a picture of the process, identify the initial and final states of the process and specify the reference frame you are using.)


Lesson 9: Calculating the Internal Energy Change

9.1 Evaluate

Review the experiment report of your classmate using the rubric. Write a report describing your review without giving any scores. Think of the strong aspects of the report. Think of what could be improved. After you receive the review of your report written by your classmate, revise it based on the review and hand it in to your teacher.

Did You Know?

In the last four lessons, you have derived mathematical representations for gravitational potential energy, kinetic energy, elastic potential energy and a change in internal energy. These mechanical forms of energy can be summarized mathematically in the generalized Work-Energy Principle.

Generalized Work-Energy Principle:

The initial energy of the system Ui plus any work W done on the objects in the system by objects outside the system equals the final energy Uf of the system:

or

The energy can take many different forms: kinetic K, gravitational potential Ug, elastic potential Us, internal energy change ∆Uint, and others introduced in later chapters. The unit of energy is the joule (J), where 1 J = 1 N•m.


Determine an expression for the change in internal energy due to friction in a system that consists of a crate and a rough horizontal surface on which it slides. You, outside of the system, pull on a rope attached to the crate so that it moves slowly at constant velocity. At the end of the process, the bottom of the block and the surface on which it was moving have became warmer.

a) Write an expression for the work done on the system by the external force of the rope on the crate as the rope pulls the block a distance s across the surface.

b) Choose the crate alone as the system (a different system than in the sketch above). Draw a force diagram for the crate. Apply Newton’s Second Law for the horizontal x-axis. How are FR on C (rope on crate) and Fs on C (surface friction on crate) related?



43

System

c) Now, combine (a) and (b) to write an expression for the work done by the force exerted by the surface through friction on the crate. Is it positive or negative?

d) Represent the process with a bar chart. The system is the crate, the surface, and the Earth. The rope is outside. In the initial state, the crate is moving but the surfaces are cool; in the final state, the crate is still moving with the same velocity but the surfaces are warmer. Think of what force does work on the system and what happens to the internal energy of the system as a result of this process.

e) Examine the bar chart. Write an expression for the change in internal energy and decide whether it increases or decreases.

f) Show that the units of this quantity are equal to the units of energy, joules.

Did You Know?

It is important to understand that the bottom surface of the crate is hotter, as is the rough surface on which it moves. Also, there may be parts of the surface that are rubbed off - a form of chemical internal energy change (such as the skid marks caused by a car coming to an abrupt stop). The system’s internal energy increase due to friction is:

9.3 Regular Problem

After sledding down a hill Tanya is moving at 7.0 m/s. Tanya and her sled have a mass of 58kg. On a horizontal surface Tanya slides to rest after 5m.

a) Sketch the situation; identify the initial and final states of the process and specify the reference frame you are using.

b) Use a bar chart to represent the process.

c) Where does all the kinetic energy go? Explain.

d) Determine the coefficient of friction between the snow and the sled.

9.4 Regular Problem

When a regular car slows down, all of its kinetic energy is converted into internal energy through work done on the car by frictional forces. In a hybrid car, an electrical generator exerts a force on the spinning wheels to slow them down. If the wheels don’t slip on the road, the generator can transform 20% of the car’s initial kinetic energy into reusable electrical energy. Later on, the car’s electrical motor can use this electrical energy to spin the wheels of the car.



0

+

before after

-

a) If a hybrid car slows down from 18 m/s to 1/3 of its speed, what is the amount of kinetic energy that the electrical generator converts into electrical energy? The car has a mass of 1200 kg. Remember that in order to express the energy in J, all quantities should be in SI units.

b) Soon afterwards, the hybrid car is traveling at 15 m/s. Over what distance can the car maintain the speed? Notice that the force exerted on the car is not the force of the motor; it is the force exerted by the Earth’s surface. When the motor rotates the wheels, they push against the ground and the ground in turn pushes back on them, making the car go forward.

c) The total force exerted on the car at this speed is 350 N. What is the work done by the ground during a 1-hour trip? Why doesn’t the hybrid accelerate if the surface exerts a constant forward force on it all the time?

Homework

9.5 Reason

A hockey puck slides across an ice rink at a speed of 2 m/s. The frictional force exerted by the ice on the hockey puck is 0.6 N. The puck has a mass of 0.4 kg.

Describe the motion of the object in words and sketch the situation. Specify the reference frame.

Find the distance the puck will travel using Newton’s laws and kinematics.

Find the distance that the puck will travel using your knowledge of energy. Include the surface of the ice in your system.

Use the energy approach again, but this time, do not include the surface of the ice in your system.

Discuss whether the distance traveled by the puck is the same for all three methods. Explain.



45

9.6 Regular Problem

A sled slides down a frictionless hill that is 17.6 m high. At the bottom of the hill, the sled hits a long patch of rough snow that slows down the sled by exerting an average force of 190 N on the sled. The mass of the sled and riders is 86 kg.

a) Draw a picture of the process, identify the initial and final states of the process and specify the reference frame you are using.

b) How fast is the sled traveling after sliding for 10 m on the rough snow?

c) How far must the sled travel on the rough snow before it is traveling at ½ of its maximum speed?

d) How far will the sled slide on the rough snow until it comes to rest?


Lesson 10: Power Up

10.1 Reason

Hans, a weightlifter, can bench press 100 kg (220 lbs). Hans can lift the 100 kg, from a height of 0.8 m above the ground to a height of 1.3 m in 0.2 seconds. Hans wants to determine the rate at which work is done on the barbell and weights. What would you tell Hans to do, to determine the rate at which he does work on the barbell and weights?

10.2 Represent and reason

a) A skier with a mass of 70 kg is pulled up a slope by a motor driven cable. Assume the ski slope is frictionless. What is the smallest work required to pull him to the top of the hill, 60 m high?

b) How much power does the motor need to pull the skier to the top of the hill in 30 seconds?

c) How fast does the skier move up the hill? What assumption did you make about the skier’s motion?

d) Read the definition for power. How did your definition compare? Correct your answer and decide if you need to revisit the questions above now that you have this information.

Did You Know?

The physical quantity of Power (P) describes how much work is done on a system per time interval or the energy is transferred into or out of a system each time interval.

Power has units of joules per second (J/s). Joules per second are often called watts (W), named after the 18th century Scottish engineer James Watt.


Determine how much power you exert while lifting:

a) a 10-kg object 1.0 m in 1.0 s

b) a 10-kg object 1.0 m in 0.5 s

c) a 10-kg object 2.0 m in 1.0 s

d) a 20-kg object 1.0 m in 1.0 s



47

10.4 Regular Problem A crane lifts an I-beam up the side of a building. The crane’s power output is 1750W for 20 seconds. After 20 seconds the I-beam was moving at 2 m/s and the mass has 200 kg. Use the work-energy process to determine the change in height of the I-beam.

10.5 Explain

The luminosity of the Sun is the amount of power the Sun emits in the form of electromagnetic radiation. The Sun’s luminosity is 3.8 x 1026 (W). If you were able to collect all of the Sun’s energy, estimate how long you have to collect it in order to light all of the Earth’s light bulbs. Explain how you came to this conclusion.

Homework

10.6 Reason

There are two types of light bulbs, incandescent and CFLs. Incandescent light bulbs are commonly rated at 60 Watts. CFL bulbs are rated at 14 Watts.

a) In one minute how many Joules of energy would be converted for each bulb? In one hour?

b) If you are charged $0.11 per Kilowatt●Hr estimate how much money you could save per year using a CFL compared to an incandescent light bulb. What assumptions did you make in your calculations?

Did You Know?

The physical quantity of Kilowatt●Hour (kWh ) describes the Power multiplied by time. If you examine the units, we can find out that how much energy is transferred.

10.7 Real World Applications

Power plants supply electrical potential energy to be used in our households. Consider the different types of power plants, describe various the energies a power plant uses that are converted into electrical potential energies. Do some research and find out how these energies are converted to electrical potential energy.



An 82 kg hiker climbs to the summit of Mount Mitchell in western North Carolina. During one 2.0 hr period, the climber's vertical elevation increases 540 m.

a) Draw a picture of the process, identify the initial and final states of the process and specify the reference frame you are using.

b) Determine the change in gravitational potential energy of the system climber-Earth

c) Determine the power generated to increase the gravitational potential energy of the system.


Determine how much power you exert while lifting:

a) a 3-kg object 1.2 m in 1.0 s

b) a 6-kg object 10.0 m in 6.0 s

c) a 10.4-kg object 2.6 m in 2.3 s

d) a 200-kg object 0.2 m in 10.0 s



49

Lesson 11: Practice & Review

Problem-Solving Strategy: Work-Energy Problems

Sketch and Translate: Sketch the physical process described in the problem. For work-energy processes,

the sketch should include an initial state and a final state and a reference frame. Decide on your system. Objects such as the Earth, springs, and surfaces of

interacting objects are usually included in the system. Objects that belong to the system do no work on each other but do possess different types of energy. External objects can do work on the system objects, thus causing the system’s energy to change.

Simplify and represent using the work-energy bar chart: Decide what internal or external interactions you can ignore. Construct a work-energy bar chart. Use the bars to represent the initial energies in

the system, the work done on the system by any external objects, and the final energies in the system. Consider whether the following change:

A system object’s elevation above the Earth (gravitational potential energy); A system object’s speed (kinetic energy); An elastic system object (like a spring) stretches or compresses (elastic potential

energy); The surface temperature of system objects increase as they rub against each other

while one moves relative to the other (internal thermal energy change); A system object(s)’s shape during a collision changes (internal potential energy).

Represent Mathematically: Apply the generalized work-energy principle; Convert the bars in the bar chart into a mathematical description of the process (one

term for each bar in the bar chart).

Solve and Evaluate: Use the mathematical description of the process to determine the unknown. Evaluate

the results (units, magnitude, and limiting cases) to make sure they make intuitive sense.


Set 1: Internal Energy


As a traffic cop investigating a car accident, you want to determine how fast a car was moving before its driver began to brake. While braking, the car left skid marks that are 70 m long. According to your reference book, the mass of the car is 1600 kg and the coefficient of kinetic friction between the tires and road is 0.2. Was the car traveling faster than the 40 mph speed limit? Fill in the table below to determine the car’s initial speed.

Sketch and translate

Represent using a work-energy bar chart

Represent mathematically

Solve and evaluate

Homework


As part of your new job as a car safety engineer, you have been asked to predict the average force exerted on a crash test dummy during a simulated car crash. The car accelerates to a speed of 20 m/s and then collides with a piston that stops the car. The crash test dummy moves a total of 1.7 m as the car comes to a stop. The dummy has a mass of 70 kg. Determine the average force that the seat belt exerts on the dummy. What assumptions did you make? Is the force exerted by the seat belt on the dummy a safe amount?



51

Set 2: Elastic Potential Energy


A popular new spring hockey game that Jay got for his birthday uses springs to move a 0.0030-kg puck. It works like a regular table hockey game but instead of hitting the puck, the players use small springs. Each spring has a 120-N/m spring constant and can be compressed up to 0.020 m. How fast does the puck move when it departs a spring that was initially compressed this distance? Fill in the table below.

Sketch and translate

Represent using a work-energy bar chart

Represent mathematically

Solve and evaluate

Homework


You are designing a new Bungee-jumping system for beginners. An 80-kg cart (including its passenger) is to start at rest near the top of a 30 incline. The uphill side of the cart is attached to a spring. The other end of the spring is attached securely to a post farther up the hill. The spring is initially relaxed. After you are secure in the cart, it is released and you coast 40 m down the hill before coming to a stop. For every 1 m that you coast down the hill, the height of the cart above the ground decreases by 0.5 m. What is the spring constant of the spring that you should buy for this invention? Follow the problem-solving strategy.


Set 3: A Trigonometric Expression of Work


A man exerts a force of 50 N on a wagon at an angle 35o above the direction of motion. He exerts this force over a distance of 15 m. What is the change in energy of the wagon-Earth system?


A 10 kg cart is traveling at 4 m/s. Aneta exerts a force of 10 N on the cart at an angle of 145 below its direction of motion. Over what distance must Aneta exert this force before the cart comes to rest?


A skier starting from rest slides down a slope that is 55 m long. The slope makes an angle of 32o with the horizontal.

a) Consider only the skier to be in the system. What is the total energy of the system when the skier reaches the bottom of the hill?

b) Now, consider the skier and the Earth to be in the system. What is the total energy of the system when the skier reaches the bottom of the hill?

11.8 Evaluate the Solution

Problem: You are traveling in your 2000-kg Chevy at 20 m/s up a hill with a 6.0o incline when you see a goose crossing the road 24 m in front of you. You know from previous experience that when you hit the brakes, a 16,000-N friction force opposes your motion. Will you hit the goose?

Solution: (1/2)(2000 kg)(20 m/s)2 = (16,000 N)x or x = 25 m. Oops!

a) Identify any errors in the solution.

b) Provide a corrected solution if you find any errors.

11.9 Evaluate the Solution

Problem: A 40.000-N/m spring initially compressed 0.50 m is released and launches you and your cart (100 kg total) up a 30o incline. What distance along the incline do you travel before coming to a stop?

Solution: (1/2)(40,000 N/m)(0.50 m) = (100 kg)(9.8 m/s2)y or y = 10.2 m.

a) Identify any errors in the solution.

b) Provide a corrected solution if you find any errors.



53

Set 4: Bar Charts


Fill in the table that follows.Experiment: Describe the

system and process.Draw a sketch showing

the initial and final states. Circle the object(s) in the

system.

Construct a quantitative work-energy bar chart and mathematically relate the quantities

to each other.

A motor pulls a roller coaster up the first hill of the track via a chain.

Initial state: The roller coaster is at rest at the bottom of the hill.

Final state: The roller coaster is moving at a moderate speed at the top of the hill.

System: Includes the roller coaster, chain, and Earth but excludes the motor that pulls the chain up the hill.


Repeat the previous activity with a different system.Experiment: Describe the

system and process.Draw a sketch showing

the initial and final states. Circle the object(s) in the

system.

Construct a quantitative work-energy bar chart and mathematically relate the quantities

to each other.

System: Includes the roller coaster and the chain but excludes the Earth and the motor that pulls the chain up the hill.


11.13 Equation Jeopardy The first column in the table that follows applies the generalized work-energy equation to two different processes (in fact, there are many possible

processes described by each equation). For each mathematical description, construct a sketch, a word description, and a bar chart that is consistent

with the equation.

Generalized work-energy equation applied to a process.

Sketch a process that might be

described by the equation.

Describe the process in words.

Construct a bar chart.

a)

b)

Set 5: Experimental Design



55

Ki Ugi Usi W Kf Ugf Usf∆Uint

0

Ki Ugi Usi W Kf Ugf Usf∆Uint

0


You have a Hot Wheels car, a Hot Wheels track, a loop-the-loop piece for the track, a Hot Wheels car launcher, a surface that can be inclined at different angles, masking tape, and a meter stick. Use any or all of this equipment to design an experiment to test whether the total energy of a Hot Wheels-Earth system is constant if there are no external forces exerted on it by other objects.

Describe the experiment in words.

Sketch the apparatus. List quantities that you will

measure.

Use the generalized work-energy principle and other principles (if

needed) to make a prediction.

List assumptions

that you made.

11.15 Design an experiment

You have a flexible track that can be tilted at different angles with the horizontal and a small metal ball. Use them to test the following idea: “The kinetic energy of the ball is directly proportional to the distance it travels along a tilted track.”


Go outside and find skid marks on the pavement. Using the skid marks estimate the initial speed of the car and the amount of its kinetic energy that went into the internal energy of the car-pavement system. Clearly state all assumptions you made in your estimation.


Lesson 12: When Work is not Easy

12.1 Derive a Relation

To launch satellites into space quickly and inexpensively, NASA wants to design an “elevator” spacecraft to slowly pull new satellites from the ground into space along a special tether. The new satellite will move at a constant velocity upwards along the tether. As a scientist working for NASA, you need to determine the amount of work the elevator spacecraft must exert on the new satellite to move it into space.

Below are sketches of the initial and final states of this process.

a) As the new satellite moves higher, the spacecraft will be able to exert a smaller force on it to keep it moving at a slow, constant speed. This graph shows the force exerted by the spacecraft on the satellite-Earth system as the satellite is pulled into space.



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EarthEarth

Elevator spacecraft

New satellitev

Elevator spacecraft

New satellite

v

Ri Rf

Rs

Fcraft on sat

| |

Ri Rf

Separation between Earth and satellite

b) Which of the following graphs could represent the gravitational potential energy of the Earth-satellite system as a function of the separation between the two?

If a graph cannot represent Ug, explain why not.


Ug

| |

Ri Rf


| |

Ri Rf


Ug


Ri Rf

| |

Ug

c) Which of these mathematical expressions could represent universal gravitational potential energy? If one cannot, explain why not.

Ug =−GMems

r+C Ug =

€

−Gms

rUg =

€

GME msr

12.2 Reason

The two expressions for gravitational potential energy look very different. The first one (Ug = mgy) was developed for processes with elevation changes on or near the Earth’s surface. Does the new expression produce a similar result for such a change? Suppose you lift a pile driver of, mass m from, position y, to a higher position y + ∆y, where ∆y is a relatively small elevation change:

a) Use the first expression for gravitational potential energy to write an expression for the gravitational potential energy change.

b) Now, does the new expression for gravitational potential energy produce the same result? The pile driver starts at distance r from the Earth’s center and ends at distance r + ∆y from the center. You will have expressions for the initial and the final energies. Find a common denominator and combine the two expressions. Note that g = GM/r2. Can you get this expression to be the same as the expression in part (a)?



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Homework

12.3 Reason

Instead of moving the satellite into space using the space elevator, NASA could also fire it from a cannon on the ground. To move the satellite from the surface of the Earth (6.3*106

m

from the center of the earth) to an altitude of 3.58*107 m from the center of the Earth, how fast would the cannon have to fire the new satellite? At its final height, the satellite should not be moving relative to the earth.

a) Sketch the initial and final states of the system.

b) Represent this process using a work-energy bar chart.

c) Represent this process mathematically.

d) Determine the initial velocity of the satellite. (G = 6.67*10-11 Nm2/kg2, ME = 5.97*1024 kg)

e) Should NASA move the new satellite into space using the elevator method from activity 11.1 or the cannon method from this problem? Why?


EarthEarth

New satellitev

New satellite

Ri

Rf

v = 0


0

+

before after

-

(Neglect the interaction with the Moon.)

Mass of the Sun = 2.0 x 1030 kgMass of the Earth = 5.96 x 1024 kgRadius of the Earth = 6.37 x 106 m

Lesson 13: Oh Baby, Don’t Let Me Go

13.1 Reason

a) Imagine a brick in a very deep well. At the top of the well, the gravitational potential energy of the system brick-Earth is equal to zero. Above the well, you have positive energy; below the well, there is negative energy. We are going to draw an analogy to a person with credit card debt. A person in debt must earn money to pay back the credit collectors, similar to the brick-earth system, which needs a certain amount of money in order to escape debt.

1. List a number of ways, in terms of work and energy, that the brick can obtain the amount of energy needed to escape the well.

2. Using one of the examples in part (a), draw an energy bar chart such that the final position the object has enough energy to escape the energy debt of the well.

3. As the brick goes up the well, which energies increase and which decrease?

b) Now imagine that a satellite sits on the Earth waiting to get into space. Think about the interaction between the Earth and the satellite. Where is it the greatest? Where is it non-existent? Now imagine at the bottom of well is the Earth (and the well has disappeared) and the satellite is waiting on the Earth to get into space. Similar to the person in debt, the satellite is in “energy debt” to the Earth.

1. Consider the place where there is no interaction between the Earth and the satellite. Where is the value for zero gravitational potential energy?

2. List a number of ways, in terms of work and energy, that the satellite can obtain the amount of energy needed to escape the clutches of the Earth.

3. Using one of the examples in part (b), draw an energy bar chart such that the final position the satellite has enough energy to escape the energy debt it has on Earth’s surface.

4. As the satellite goes up the well, which energies increase and which decrease?

13.2 Reason

In the movie Armageddon, a motley crew of hard-nosed oil drillers rendezvous with a menacing meteoroid just as it passes the orbit of the moon. Imagine that an asteroid fell in from the Oort Cloud, a region of space in the depth of our Solar System which is very far away. What is the speed of the meteoroid as it passes the orbit of the Moon? The Moon orbits at a distance of approximately 60 Earth radii from the center of the Earth.



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a) Use multiple representations to show the meteoroid’s journey from the Oort Cloud to the Earth.

b) Determine the speed at which it passes the Moon’s orbit.

c) Let us say that Armageddon did arrive in that movie. With what speed would the meteoroid have collided into the Earth?

d) Are there any other real-life scenarios where people may consider the idea of a negative potential energy?

13.3 Reason

In 1865, Jules Verne wrote a novel where he imagined a space rocket fired to the Moon from Earth by using a cannon. If Verne wanted to fire the rocket into the depths of space, with what speed must the rocket have in order to escape Earth’s gravitational pull? Why is using a cannon impractical for space exploration? How do space explorations get around this problem today?

13.4 Reason

If we assume that no object can move faster than the speed of light in a vacuum, then what is the radius of an object of mass m, so that even light cannot escape? How big should the sun be to become a black hole? The speed of light is 3 x 108 m/s.


Summary: Definitions and Principles

Work W: Work is the product of the magnitude of the average force FEx on O that an external environmental object exerts on a system object, the magnitude of the system object’s displacement d, and the cosine of the angle between FEx on O and d.

The system gains energy if the work done on it is positive and loses energy if the work is negative.

Kinetic energy K of a system object is one-half times the product of its mass m and the square of its speed v:

Gravitational potential energy Ug of the system object-Earth depends on the relative separation of an object of mass m and the Earth. When the object is near the Earth’s surface, we calculate the Earth-object’s gravitational potential energy using

where y is the object’s elevation relative to a chosen zero reference level. When far from the Earth, we use the expression

where r is the object’s distance from the center of the Earth.

Elastic potential energy Us is the energy stored in a stretched or compressed object and depends on the force constant k (stiffness) of the elastic object and the distance x that the elastic object is displaced from its equilibrium position:



63

Ki Ugi Usi W Kf Ugf Usf ∆Uint

0

Increase in internal energy due to friction ∆Uinternal: When an object moves across a surface with friction, the contacting surfaces warm slightly. If the surfaces are included in the system, the increase in the system energy due to this friction is the product of the magnitude of the average kinetic friction force Fk between the object and the surface and the distance d that the object moves relative to the surface:

If the surface is not in the system, then the work done by the external friction force is:

Generalized work-energy equation (energy conservation): The total energy of a system is the sum of all the energies. In the initial state Ui = Ki + Ugi + Usi and in the final state Uf = Kf + Ugf + Usf + ∆Uint. If work is done on the system object(s), then the energy can change. Expressed quantitatively as the generalized work-energy equation:

Constancy of energy principle: If, during a process, the net sum of the work done on the objects in a system is zero, then the total energy of the system is constant (the same at the beginning as at the end). However, the types of energy in the system can change.


Lesson 14: Simple Machines I

14.1 Observe and Represent

Design an experiment to determine the amount of work it takes to move the cart from the bottom to the top of the incline. You have the following materials: two inclined planes that go to the same height but have different slopes, force probe or spring scale, a cart, meter sticks, and a scale. The goal of this experiment is to find patterns relating work and energy.

a) Determine what the system of interest is and the initial and final states. b) Decide what quantities you will have to measure to find the work it takes to move

the cart up the incline.c) Perform the experiment and record your data.d) Decide if you can make any assumptions that will help to simplify the problem.

Here’s an Idea!

You may notice that when the cart is pulled really fast up the incline, the force measured by the spring scale was hard to read. Try pulling the cart fast and then slow and steady. Which way makes it easier to take the force measurement? Why are the measurements different (Hint: Think of whether the cart is accelerating)?

e) Draw a work-energy bar chart that represents the process. Think of what is included in your system.

14.2 Observe and Represent

a) Repeat the same steps for a second set of trials; this time pull the carts straight up the side of the incline, starting from the ground and finishing at the top.

b) Look for patterns in the data you collected. c) How does the work-energy bar chart for each set of trials differ? How do the heights

of the bars compare between the diagrams?d) How does the amount of work it takes to move the cart to the top differ in each set

of trials (assume that the cart moves very slowly)?e) Was one method of getting the cart to the top “easier” than the other? Describe how.f) What was the gravitational potential energy of the system when the cart was at the

top of each of the inclines?



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Observational Experiment RubricAbility Absent An attempt Needs some

improvementAcceptable

Is able to decide what is to be measured and identify independent and dependent variables.

It is not clear what will be measured.

It is clear what will be measured but independent and dependent variables are not identified.

It is clear what will be measured and independent and dependent variables are identified but the choice is not explained.

It is clear what will be measured and independent and dependent variables are identified and the choice is explained.

Is able to use available equipment to make the measurements.

At least one of the chosen measurements cannot be made with the available equipment.

All chosen measurements can be made, but no details are given about how it is done.

All chosen measurements can be made, but the details of how it is done are vague or incomplete.

All chosen measurements can be made and all details of how it is done are clearly provided.

Is able to describe what is observed in words, pictures, and diagrams.

No description is mentioned.

A description is mentioned but it is incomplete. No picture is present.

A description exists, but it is mixed up with explanations or other elements of the experiment. A labeled picture is present.

It clearly describes what happens in the experiments both verbally and by means of a labeled picture.

Is able to construct a mathematical (if applicable) relationship that represents a trend in data.

No attempt is made to construct a relationship that represents a trend in the data.

An attempt is made, but the relationship does not represent the trend.

The relationship represents the trend but no analysis of how well it agrees with the data is included (if applicable), or some features of the relationship are missing.

The relationship represents the trend accurately and completely and an analysis of how well it agrees with the data is included (if applicable).

14.3 Hypothesize

a) In this experiment you determined the work needed to lift the cart straight up so it covers the distance x. Look back to your bar charts from the experiment. What type of energy increases as a result of doing work on the system?

b) Write an equation for the work-energy relationship in this problem.

c) How did we mathematically define work in the beginning of the unit? What is the force that is doing the work? What is the magnitude of the force that you need to exert on the cart to lift it up very slowly? To answer this question, draw a force diagram for the cart and decide which force on the diagram is doing the work.

d) How can we combine the two expressions above in terms of gravitational potential energy change?


e) How can we write the expression for the gravitational potential energy of the system that involves an object of mass m at the height x (displacement!) above the surface of the Earth?

14.4 Test Your Ideaa) Given the dimensions of another groups ramp, predict the amount of energy a cart

would have when at the top of the ramp. Perform the experiment and record your results. How did the outcome and your prediction compare?

b) Revise you hypothesis if necessary.

14.5 ReasonYou, Brianna, and Doug just finished bowling and are ready to put the bowling balls away. Doug uses a ramp to roll the ball to the top shelf while Brianna says it is easier to just lift the heavy ball straight up.

a) What are the pros and cons of both methods?b) If both bowling balls have the same mass, does Doug do less work than Brianna to

get the ball to the top shelf assuming that they both lift the balls very slowly. Why is this assumption important?

Did You Know?

Simple Machine: A simple machine is a device that only requires one force to do work on a system.

Mechanical Advantage: A simple machine or a compound machine (two or more simple machine combined to make one device) work in such a way to require a smaller force (usually over a greater distance) to perform the same amount of work.



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Homework


Integer statement Bar chart for a process Describe a Process

3+2=5

4−2=1+1

200+800=500+500

8.2+4.1=12.4


Lesson 15: Simple Machines: Applications

15.1 Represent and Explain

You are a member of a team hired by an architectural firm to design a wheelchair accessible entrance to a building. The Americans with Disabilities Act requires the steepness of wheelchair ramps to be less than a 1:12 ratio of vertical change to horizontal change.

a) Explain why the Americans with Disabilities Act is concerned with the steepness of accessibility ramps.

b) Draw three ramps that meet their requirement.

c) Decide which of the following ramps meet the recommendation. (Some are represented by a picture and some are represented by a ratio.)

(v) 1:10

(vi) 3:42

(vii) 2:28

d) Calculate the smallest amount of work that is required to push a 20 kg object up each of the ramps (i–iv). (lift the box)

Need some help?

Remember from our dynamics unit that we can draw force diagrams to solve this problem. Then we can begin to ask ourselves, “What objects are exerting a force on a box that you’re lifting? What is the magnitude of this force? How can we determine this?”



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(i)16m

2m

(ii)

46m

4m

(iii)

36m

3m

(iv)4m

0.5m

15.2 Reason

A notice came in the mail that revealed the staircase height, 2.5 meters. Now that we have this piece of information we can begin working on building the ramp. If the staircase is 2.5 meters high,

a) How long does a ramp need to be to fit the regulations?

b) The company controller argues that regardless of the length of the ramp, a person pushing the chair must do the same amount of work to get a wheelchair to the top. He suggests that we can save money by using less construction material by making the ramp as short and steep as possible. You need to make a ramp with a height of 1.5 m. What should the length of the ramp be to meet regulations?

c) The controller says that is too long. Give two reasons why it is important not to make the ramp any steeper.

15.3 Explain

One of your classmates is having trouble understanding the difference between the amount of effort it takes to lift or move something (the amount of force you exert on an object or system) and the amount of work required to lift or move something. He says, “If it is easier to do, it must be less work.”

a) Describe how you would help your classmate to understand this idea better.

b) Use examples like the ramps from the previous problem.

Homework

15.4 Regular Problems

a) A rollercoaster pulls the cart to the top of a hill by doing 150,000 J of work on the system. The internal energy of the system changes by 50,000 J. How much more kinetic energy does the system have when the cart makes it back to the bottom of the hill?

b) You do 50 joules of work to compress a system that includes an object on a spring. The spring launches a 30-g object straight up into the air. How high does the object go? What if the object were 30 kg; how high would it go?

c) A meteoroid, moving with high speed, enters the Earth’s atmosphere and falls toward the Earth. As it passes through the atmosphere, it warms due to friction with the air. When it hits the ground, it creates a giant crater. Explain the process using any or all of the ideas of work and energy changes (consider all possible types of energy change). Include a work-energy bar chart.


d) A skydiver who jumps out of an airplane at 3500 m above sea level accelerates towards the ground for about 15 seconds before the upward force exerted by the air on the skydiver is about equal to the downward force exerted by the Earth on the skydiver.

a. Draw a force diagram for the skydiver after she/he has been falling for about 15 seconds.

b. The skydiver’s speed remains constant at 55 m/s until he or she opens the parachute. Choose the skydiver, the Earth, and the air as the system. Draw a work-energy bar chart that describes the skydiver’s fall from when he or she leaves the plane until just before the parachute opens.



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Lesson 16: Simple Machines II

16.1 Test an Idea

In the previous lab, we found that using an inclined plane does not reduce the amount of work you have to do to lift an object. Your friend Cadence says, “I have a simple machine that allows me to lift an object by doing less work than if I lifted the same object without the machine.” She claims her machine reduces the amount of work that is needed to lift an object. Her simple machine is called a movable pulley. She draws a schematic of this machine for you.

a) Design an experiment to test her idea. You have the following equipment: Single moveable pulley, block, and spring scale

b) Describe your experiment; include all the details about what you will measure and how you will measure it; variables!.

c) Is it possible to reduce the amount of work needed to lift an object to a certain height? Explain.

Scientific Ability Absent An attempt Needs some


Is able to distinguish between a hypothesis and a prediction.


A prediction is made but it is identical to the hypothesis.

A prediction is made and is distinct from the hypothesis but does not describe the outcome of the designed experiment.

A prediction is made, is distinct from the hypothesis, and describes the outcome of the designed experiment.

Is able to make a reasonable prediction based on a hypothesis.


A prediction is made that is distinct from the hypothesis but is not based on it.

A prediction is made that follows from the hypothesis but does not incorporate assumptions.

A prediction is made that follows from the hypothesis and incorporates assumptions.

Is able to make a reasonable judgment about the hypothesis.

No judgment is made about the hypothesis.




a) Write an H-D Statement using your experiment and Cadences hypothesis Use the rubrics below to help you answer the questions in an informal lab report.

b) Perform the experiment and describe the outcome of the experiment

16.2 Evaluate


LiftPulley

Hanging object

a) Describe your data and highlight any important patterns you noticed.

b) What judgment can you make about Cadence’s hypothesis? Explain.

c) Write a revised hypothesis.

d) Does Cadence’s idea represent a mechanical advantage? Explain why it is easier to pull the block up using Cadence’s pulley.

e) Compare this device to the inclined plane. What is different and what is the same? Think about the purpose of both devices.

Homework

16.3 Evaluate

Using your textbook, the Internet, or encyclopedias, find more examples of simple machines. Compare them to the machines we worked with in class (movable pulley and the inclined plane).

Create one problem dealing with a simple machine and calculating work-energy.

Answer the problem with as many representations as you can.

Tomorrow in class you will exchange this with a classmate. You will answer your partner’s question and then discuss the answers.



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