**LABORATORY IV**

**ENERGY CONSERVATION **

In this lab you will use *conservation of energy *to
analyze the motion resulting from interactions that are difficult
to analyze with force concepts. In one problem, you will use the
conservation of energy to determine the coefficient of kinetic
friction from measurements you can make with a meter stick. In
the remaining problems you will explore how much energy is
dissipated in different kinds of collisions.

In collisions, as with any interaction, the total energy is
conserved. However, not all of the initial energy of the system
ends up as energy of motion. Some energy is transferred to the
motion of the molecules in the system. Since this energy is not
observable in the macroscopic motion of the objects, we sometimes
say that the energy is "dissipated" in the collision --
for example in the bending of the fenders of two colliding cars. ** We
can express the energy efficiency of a collision as the ratio of
the final kinetic energy of the system to the initial kinetic
energy.** You will explore the energy efficiency of
collisions on an air track, to reduce the complication of the
friction interaction.

**OBJECTIVES:**

Successfully completing this laboratory should enable you to:

* Develop an understanding of how the concept of energy is used in describing the world.

* Understand the principles of conservation of energy as a means of describing the behavior of systems.

* Practice the application of the energy conservation principle to real systems.

*** **Gain experience in making and testing qualitative
predictions about physical systems.

**PREPARATION:**

Read Fishbane, Gasiorowicz, and Thornton; Chapter 5, section 2; Chapter 6, sections 1, 2 and 4; and Chapter 7, sections 1 through 4. You should also be able to:

* Analyze the motion of an object from spark tapes.

* Calculate the kinetic energy of a moving object.

* Calculate the work done on a system by an external force.

* Calculate the gravitational potential energy of an object with respect to the earth.

* Calculate the total energy of a system of objects.

**PROBLEM #1: KINETIC ENERGY AND WORK ON THE AIR TRACK**

You are working at a company that designs and manufactures
tennis rackets. You have been asked to devise a test to determine
the efficiency of some new tennis racket strings. You know that
when a tennis ball rebounds off the racket strings, some of the
initial energy of motion is "dissipated" in the
deformation of the ball and strings. *The efficiency of the
collision is the ratio of the final kinetic energy to the initial
kinetic energy of the system.*

Since you want the efficiency of the strings (not the ball), you decide to use the air track with a sample of the tennis string mounted on one end of the track. You will then let gliders bounce off the string. Of course, there is experimental uncertainty no matter how you make the measurement. So you decide to measure the energy efficiency two different ways to determine the extent to which you get consistent results. For the first test you will use a level air track, and for the second test you will incline the air track.

What is the efficiency of the new tennis racket strings? How much energy is dissipated in an impact?

**EQUIPMENT**

You will use the air track that you used in the first lab, but with a special bumper on the end of the air track that is supported by two legs. The bumper is a U-shaped bracket that has a piece of elastic (string) across its open end. The bumper is designed to easily fit into the end-stop of the air track.

A special adaptation to the glider allows separate spark records to be made of the motion before and after the glider hits the bumper.

**PREDICTIONS**

Predict (quantitatively) the energy efficiency of the bumper in terms of quantities you that can measure in the two test situations: (1) a level air track, and (2) an inclined air track.

**METHOD QUESTIONS**

The following procedures may help with the predictions and the analysis of your data:

**1**. Make a sketch of the glider on the ** level air
track** before and after the impact with the bumper. Label
the kinetic energy at both these points.

** **a. Write an expression for the efficiency of the
bumper in terms of the final and initial kinetic energy of the
glider.

** **b. Write an expression for the energy dissipated
during the impact with the bumper in terms of the kinetic energy
before the impact and the kinetic energy after the impact.

**2**. Make a sketch that has the glider on the ** inclined
air track** at its initial position (before you release the
glider) and just before the glider hits the bumper. Label the
kinetic energy at these two points, the distance the glider
traveled, the angle of incline, and the initial height of the
glider above the bumper.

a. Draw a force diagram of the glider as it moves down the track (ignore air friction). Which force component does positive work on the glider (i.e., causes a transfer of energy into the glider system)? Write an expression for the work done on the glider. How is the angle of incline related to the distance the glider traveled and the initial height of the glider above the bumper?

How does the kinetic energy of the glider just before impact compare with the work done on the glider?

b. Now make another sketch of the glider on the inclined track just after the collision with the bumper at its maximum rebound height. Label kinetic energy at these two points, the distance the glider traveled, the angle of incline, and the initial height of the glider above the bumper.

c. Draw a force diagram of the glider as it moves up the track (ignore air friction). Which force component does negative work on the glider (i.e., causes a transfer of energy out of the glider system)? Write an expression for the work done on the glider. How is the angle of incline related to the distance the glider traveled and the maximum height of the glider above the bumper?

How does the kinetic energy of the glider just before impact compare with the work done on the glider?

d. Write an expression for the efficiency of the bumper in terms of the work done on the glider before the impact and after the impact.

** **e. Write an expression for the energy dissipated
during the impact with the bumper in terms of the work done on
the glider before the impact and after the impact.

**EXPLORATION**

__Level Air Track:__ Review your exploration notes for the
air track in Problem #1, Laboratory I. Find a usable range of
initial velocities and spark timer settings.

DO NOT TOUCH ANYTHING METAL ON THE APPARATUS WHILE THE SPARK TIMER IS IN OPERATION! It operates at 10,000 volts and can give you a nasty shock.

__Inclined Air Track:__ ** **Review your exploration
notes for the air track in Problem #2, Laboratory I. Decide how
you are going to measure the *height *of the glider.

**MEASUREMENT**

__Level Air Track:__ Take the measurements necessary to
determine the kinetic energy before and after the impact with the
bumper. What is the most efficient way to measure the velocities
from your spark records?

__Inclined Air Track:__ ** **Take the measurements
necessary to determine the gravitational potential energy before
and after the impact with the bumper (when the kinetic energy is
zero).

**ANALYSIS**

Calculate the efficiency of the bumper for your two tests:

(1) the level air track, and (2) the inclined air track.

Calculate the energy dissipated in the rebound with the bumper for the two cases. In case (1), how much energy is dissipated in its collisions with the air as it moves along the track? Is this large enough so that you need to make a correction in case (2)?

**CONCLUSION**

What is the efficiency of the new tennis racket strings (i.e., elastic bumper string)? How much energy is dissipated in an impact? State your results in the most general terms supported by your analysis.

How did the efficiency compare for your two tests? What were the sources of your uncertainties in the two tests? Which test is the 'best' and why do you think so?

**PROBLEM #2: ENERGY AND COLLISIONS WHEN THE OBJECTS STICK
TOGETHER**

You have a summer job with the Minnesota Traffic Safety Board. You are helping to write a report about the damage done to vehicles in different kinds of traffic accidents. Your boss wants you to concentrate on the damage done when a moving vehicle hits a stationary vehicle and they stick together.

You know that in a traffic collision, as with any interaction, some of the initial energy of motion is transformed or "dissipated" in the deformation of the vehicles. It's obvious that the higher the initial energy of the moving vehicle, the more energy is dissipated, so more damage is done to both vehicles. Your boss believes that, given the same initial kinetic energy, the damage done to the vehicles will be the same when a car hits a stationary truck or the truck hits the stationary car, since the total mass is the same in both cases. He asks your opinion.

To resolve the issue, you decide to model the collision with gliders on an air track and measure the energy efficiency of the collision -- the ratio of the final kinetic energy of the system to the initial kinetic energy.

When a moving object collides with a stationary object and they stick together, how does the energy efficiency depend on the relative masses of the objects?

**EQUIPMENT**

You will use the same air tracks as in Laboratory I. Special "ballast" masses can be added in a symmetric fashion to change the mass of the gliders.

For this problem, glider A is given an initial velocity towards a stationary glider B. A special accessory is available to get the gliders to stick together after the collision. A spark record can be made of the motion before and after the collision.

**PREDICTION**

Predict (quantitatively) the energy efficiency of the collision bumper in terms of quantities you that can measure.

Now consider the following three cases in which the total
mass of the gliders is the same (mA + mB = constant): (a) the
masses of the gliders are equal (mA = mB), (b) the moving glider
has a larger mass than the stationary glider (mA > mB); and
(c) the moving glider has a smaller mass than the stationary
glider

(mA < mB). Do you think the energy efficiency will be the same
or different for these three cases? If different, in which case
do you think the efficiency will be the largest? The smallest?
Make your best guess and explain your reasoning.

**METHOD QUESTIONS**

The following procedure and question may help with the prediction and analysis of your data.

**1.** Draw a sketch which shows the situation before the
collision and after the collision. Draw velocity vectors on your
sketch.

**2.** Write an expression for the efficiency of the
collision in terms of the final and initial kinetic energy of the
gliders.

**3.** Write down the total energy conservation equation
for this type of collision. Solve for the energy dissipation in
terms of the initial kinetic energy and the energy efficiency.

How does the energy dissipated in the collision depend on the energy efficiency? Does the energy dissipated increase or decrease as the energy efficiency increases?

**EXPLORATION**

Practice setting the glider into motion so that it does not wobble side to side on the track. Also, after the collision carefully observe the gliders to determine whether or not either glider wobbles significantly. Adjust your procedure to minimize wobbling.

Try giving the moving glider various initial velocities. Note qualitatively the outcomes. Keep in mind also that you want to choose an initial velocity that gives you a good spark record.

Try varying the masses of the gliders, keeping the total mass of the two gliders constant. Be sure to add the same amount of mass to each side of the glider. Also be sure the gliders still move freely over the track. What masses will you use in your final measurement?

DO NOT TOUCH ANYTHING METAL ON THE APPARATUS WHILE THE SPARK TIMER IS IN OPERATION! It operates at 10,000 volts and can give you a nasty shock.

You can also vary the spark timer rate in order to obtain more or fewer points per second. What spark rate gives you the best record? Make sure the spark timer cables are connected in such a way that you only get spark dots from the cart which is moving initially.

**MEASUREMENT**

Record the masses of the two gliders. Make a spark record of their collision. Examine your record and decide if you have enough positions to determine the velocities you need. Are there any peculiarities that you notice in the data that might suggest that the data is inappropriate?

Analyze your data as you go along (before making the next spark tape), so you can determine how many different spark tapes you need to make, and what the gliders' masses should be for each tape. Collect enough data to convince yourself and others of your conclusion about how the energy efficiency of this type of collision depends on the relative masses of the gliders.

**ANALYSIS**

Determine the velocity of the gliders before and after the collision from your spark records. Should you include all of the spark dots in your analysis? Why or why not?

For each spark record, calculate the kinetic energy of the gliders before and after the collision. Was a significant portion of it dissipated? Into what other forms of energy do you think the glider's initial kinetic energy is most likely to transform?

Calculate the energy efficiency of each collision. Given the
same initial energy, in which case (mA = mB, mA > mB, or

mA < mB) is the energy dissipation the largest? The smallest?
Explain your reasoning (see Method Question 3).

**CONCLUSION**

Was your boss right? Is the same amount of damage done to the vehicles when a car hits a stationary truck and they stick together as when the truck hits the stationary car (given the same initial energies)? If yes, state your results that support this conclusion. If no, describe how will you convince your boss.

**PROBLEM #3: ENERGY AND COLLISIONS WHEN THE OBJECTS BOUNCE
APART**

You still have your summer job with the Minnesota Traffic
Safety Board helping to write a report about the damage done to
vehicles in different kinds of traffic accidents. Your boss now
wants you to concentrate on the damage done *when a moving
vehicle hits a stationary vehicle and they bounce apart*.

Of course, the higher the initial energy of the moving vehicle, the more energy is dissipated in the collision, so more damage is done to both vehicles. Your boss believes that, given the same initial energy, the damage to the vehicles in the collision when they bounce apart will be less than when they stick together for all three cases -- when the mass of the moving vehicle is the same as the mass of the stationary vehicle, when the moving vehicle has a larger mass than the stationary vehicle (e.g., a van hits a compact car), and when the moving vehicle has a smaller mass than the stationary vehicle (e.g., a compact car hits a van). Again, he asks your opinion.

To resolve the issue, you again model the collision with gliders on an air track and measure the energy efficiency of the collision -- the ratio of the final kinetic energy of the system to the initial kinetic energy.

How does the energy efficiency of collisions when the objects bounce apart compare with the energy efficiency when they stick together?

**EQUIPMENT**

You will use the same air tracks as in Problem #2, but in this problem glider A needs an elastic-string bumper.

As in Problem #2, additional "ballast" masses can be added to the gliders in a symmetric fashion in order to alter the mass of either glider. The gliders have a metal switch on top that can flip from one screw to another during a collision. This produces a vertical displacement in the spark record for the gliders, allowing you to distinguish "before collision" sparks from "after collision" sparks. Furthermore, the two gliders produce sparks at different heights on the spark paper.

**PREDICTION**

Predict (quantitatively) the energy efficiency of the collision bumper in terms of quantities you that can measure.

Examine the energy efficiencies you measured in Problem #2
for the following three cases in which the total mass of the
gliders is the same (mA + mB = constant): (a) the masses of the
gliders are equal (mA = mB), (b) the moving glider has a larger
mass than the stationary glider (mA > mB); and (c) the moving
glider has a smaller mass than the stationary glider (mA <
mB). Do you think the energy efficiencies will be the same or
different for these three cases *when the gliders bounce apart
instead of sticking together*? Make your best guess and
explain your reasoning.

**METHOD QUESTIONS**

The following procedure and question may help with the prediction and analysis of your data.

**1.** Draw a sketch which shows the situation before the
collision and after the collision. Draw velocity vectors on your
sketch.

**2.** Write an expression for the efficiency of the
collision in terms of the final and initial kinetic energy of the
gliders.

**3.** Write down the total energy conservation equation
for this type of collision. Solve for the energy dissipation in
terms of the initial kinetic energy and the energy efficiency.

How does the energy dissipated in the collision depend on the energy efficiency? Does the energy dissipated increase or decrease as the energy efficiency increases?

**EXPLORATION**

Your exploration for this problem will be similar to the one described for Problem #2: Energy and Collisions When the Objects Stick Together. Review your notes before you proceed.

Plan a procedure in which your spark record will provide
clear information on the motion of *both* gliders -- each
glider should leave spark dots on the paper, but at different
levels so you can tell them apart. Determine how to use the metal
switches mounted on the gliders to produce sparks at different
heights before and after the collisions. If you are having too
much trouble with this, consult with a group that has made a
successful spark record (or ask your lab instructor for help).
Your objective today is to study collisions, not switch and
glider design.

DO NOT TOUCH ANYTHING METAL ON THE APPARATUS WHILE THE SPARK TIMER IS IN OPERATION! It operates at 10,000 volts and can give you a nasty shock.

**MEASUREMENT**

Record the masses of the two gliders. Make a spark record of their collision. Examine your record and decide if you have enough positions to determine the velocities you need. Are there any peculiarities that you notice in the data that might suggest that the data are inappropriate?

Analyze your data as you go along (before making the next spark tape), so you can determine how many different spark tapes you need to make, and what the gliders' masses should be for each tape. Collect enough data to convince yourself and

others of your conclusion about how the energy efficiencies for collisions when the objects bounce apart compare to the efficiencies when the objects stick together.

**ANALYSIS**

Determine the velocity of the gliders before and after the collision from your spark records. Should you include all of the spark dots in your analysis? Why or why not?

For each collision you observed and recorded, calculate the total kinetic energy before and after the collision. Was a significant portion of it dissipated? Into what other forms of energy do you think the glider's initial kinetic energy is most likely to transform?

Calculate the energy efficiency of each collision. Given the
same initial energy, in which case (mA = mB, mA > mB, or

mA < mB) is the energy dissipation the largest? The smallest?
Explain your reasoning (see Method Question 3).

**CONCLUSION**

Was your boss right? Is the energy dissipated in the collision when the vehicles bounce apart less than when they stick together for all three cases -- when the mass of the moving vehicle is the same as the mass of the stationary vehicle, when the moving vehicle has a larger mass than the stationary vehicle (e.g., a van hits a compact car), and when the moving vehicle has a smaller mass than the stationary vehicle (i.e., a compact car hits a van)? If yes, state your results that support this conclusion. If no, describe how you will convince your boss.

**PROBLEM #4: ENERGY AND FRICTION**

You have been hired as an assistant to the stunt coordinator on a new action movie about an earthquake hitting San Francisco. In one scene a bus is knocked over on its side on a street going down a steep hill. It stays at rest for just enough time for the passengers to escape. Then a small tremor starts the bus sliding down the hill. At the bottom of the hill the street becomes level. On the level part of the street is another bus which has also been knocked on its side and is still full of people. The exciting script calls for the first bus to slide down the hill and hit the second bus. For the stunt the movie company will install special bumpers on the buses so that the buses bounce apart after the collsision.

To position the cameras correctly, the stunt coordinator asks you to calculate the final positions of the two buses from the known masses of the buses, the distance the first bus slides down the hill, the distance the first bus slides along the level road before it hits the second bus, and the coefficient of kinetic friction between a sliding bus and the road.

Before you decide to risk a million dollar stunt on your calculation, you decide to build a laboratory model to check your calculation (see Problem #3, Laboratory V). Your first task, however, is to determine the coefficient of kinetic friction for your model, which is shown below. But you only have a meter stick on the movie set!

How can you determine the coefficient of kinetic friction (uk) using only a meter stick?

**EQUIPMENT**

In this problem you will use the apparatus pictured below.

It is a brass track with two sections, an inclined section and a level section. A brass or aluminum cylinder can slide from rest

down the incline and across the level portion of the track until it stops. The angle of the incline can be adjusted.

**PREDICTIONS**

Determine an expression for the coefficient of kinetic friction between the cylinder and the track that depends only on quantities you can measure with a meter stick.

Examine the Table of Coefficients of Friction on page 18 of Laboratory III. Make your best guess of the values of the coefficient of friction for brass on brass and aluminum on brass.

**METHOD QUESTIONS**

It is useful to have an organized problem-solving strategy such as on page 35 in your text:

**1**. Make a sketch of the problem situation similar to
the one in the equipment section.

**2.** Write down the energy conservation equation for
this situation (see top of page 211 of your text). What is the
initial energy of the system (cylinder and earth)? What is the
final energy of the system?

**3.** Draw a force diagram for the cylinder as it slides
down the incline. Draw another force diagram for the cylinder as
it slides across the level track. Identify the forces that do
work on the cylinder (i.e., result in the transfer of energy out
of the system).

You should now be able to solve for the coefficient of kinetic friction as a function of distances that you can measure with a meter stick.

**EXPLORATION**

Practice sliding the cylinder down the inclined portion of the track to find out what initial heights result in a smooth transition over the bend in the track. If the cylinder "bounces" during this transition, an unknown amount of energy is dissipated.

**MEASUREMENT**

Make the measurements that you need to answer the major prediction for the brass cylinder. You will need to repeat this measurement several times to see if it is reproducible.

Repeat the measurements for the aluminum cylinder.

**ANALYSIS**

Calculate the coefficient of kinetic friction for each cylinder on the brass track. What is the accuracy and precision for each result?

**CONCLUSION**

How can you determine the coefficient of kinetic friction (uk) using only a meter stick? Are your results reproducible? What are the limitations on the accuracy of your measurements and analysis?

Are your values of the coefficient of friction for brass on brass and aluminum on brass close to your predicted values? If not, why not?

1. A 1-kg ball dropped from a height of 2 meters rebounds only 1.5 meters after hitting the floor. The amount of energy dissipated during the collision with the floor is

(a) 5 joules.

(b) 10 joules.

(c) 15 joules.

(d) 20 joules.

(e) More than 20 joules.

2. Two boxes start from rest and slide down a frictionless ramp that makes an angle of 30o to the horizontal. Block A starts at height h; while Block B starts at a height of 2h.

a. Suppose the two boxes have the same mass. At the bottom of the ramp,

(a) Box A is moving twice as fast as box B.

(b) Box B is moving twice as fast as box A.

(c) Box A is moving faster than box B, but not twice as fast.

(d) Box B is moving faster than box A, but not twice as fast.

(e) Box A has the same speed as box B.

b. Suppose box B has a larger mass than box A. At the bottom of the ramp,

(a) Box A is moving twice as fast as box B.

(b) Box B is moving twice as fast as box A.

(c) Box A is moving faster than box B, but not twice as fast.

(d) Box B is moving faster than box A, but not twice as fast.

(e) Box A has the same speed as box B.

3. A hockey puck is moving at a constant velocity to the right, as shown in the diagram. Which of the following forces will do positive work on the puck (i.e., cause an input of energy)?

4. Five balls made of different substances are dropped from the same height onto a board. Four of the balls bounce up to the maximum height shown on the diagram below. Ball E sticks to the board.

a. For which ball was the most energy dissipated in the collision?

(a) Ball A

(b) Ball B

(c) Ball C

(d) Ball D

(e) Ball E

a. Which ball has the largest energy efficiency?

(a) Ball A

(b) Ball B

(c) Ball C

(d) Ball D

(e) Ball E

5. A skier is pulled a distance [[Delta]]x up a hill at a constant velocity by a tow rope. The coefficient of friction between the skies and the snow is uk.

a. Draw a force diagram of the skier. Which of the forces acting on the skier do positive work (i.e., cause an input of energy). Which of the forces do negative work (i.e., cause an output of energy)? Explain your reasoning.

b. Based on the definition of work, write an expression for the positive work done on the skier (i.e., the energy input). Write an expression for the negative work done on the skier (i.e., the energy output).

c. Which is larger, the positive work done on the skier or the negative work done on the skier? Or are they the same size? Explain your reasoning?

**PHYSICS 1251 LABORATORY REPORT**

**Laboratory IV**

Name and ID#: ______________________________________________________

Date performed: ________________ Day/Time section meets: ______________

Lab Partners' Names: ________________________________________________

__________________________________________________________________

__________________________________________________________________

Problem # and Title: _________________________________________________

Lab Instructor's Initials: ____________

Grading Checklist Points LABORATORY JOURNAL: PREDICTIONS

(individual predictions completed in journal before each lab session) LAB PROCEDURES

(measurement plan recorded, tables and graphs made as data is collected) PROBLEM REPORT:* ORGANIZATION

(clear and readable; section headings provided by you) DATA AND DATA TABLES

(clear and readable; units and assigned uncertainties clearly stated) RESULTS

(results clearly indicated; correct derivations with uncertainties indicated; scales, labels and uncertainties on graphs) CONCLUSIONS

(comparison to prediction & theory discussed; possible sources of uncertainties identified; attention called to experimental problems) TOTAL BONUS POINTS

(if all members of your group score 8 points or above)

* An "R" in the points column means to __rewrite
that section only__ and return it to your lab instructor within
two days of the return of the report to you -- no exceptions.