# Physics Active Learning (PAL)

```Name:_________________________________ Lab Section: _________ Group Number: __________
Physics 201
Experiment #5
Dissipation of Energy
Introduction Energy is a very useful concept, and one of the main reasons that it is useful is that it is conserved.
Energy may be transformed from one form to another, but it is not created or destroyed.
Pre-lab Questions (turn in at start of lab)
In part I of this experiment, you will be allowing an object to go down inclined plane, measuring its height and
speed, and thus its potential and kinetic energies.
1) Do you expect mechanical energy (kinetic energy plus potential energy) to be conserved as an object moves down
an inclined plane? If not, why not?
2) If it is not conserved, does the energy just disappear? Does it become some other form or energy? What form?
3) You will be allowing a block to slide down an incline, first on a wooden edge, then on an edge covered with felt.
After that, you will roll an object on wheels down the incline. Compare these three (wooden surface, felt surface,
and wheels). Which do you think will lose the greatest amount of mechanical energy? Which do you think will be
closest to conserving mechanical energy? Explain your reasons.
In part II of this experiment, you will be dropping a ball and watching it bounce. If mechanical energy were
conserved during the bounce, the ball should bounce back to the height it was dropped from.
4) Do you expect mechanical energy (kinetic energy plus potential energy) to be conserved as the ball bounces off the
5) If it is not conserved, does the energy just disappear? Does it become some other form or energy? What form?
6) What properties of the ball do you think will affect how high it bounces? Suppose you could look at a ball and hold
it in your hand, but weren’t allowed to bounce it. Describe what properties you would look for, if you wanted a ball
that would bounce high when dropped.
A quantity called the coefficient of restitution is a common measure of the elasticity of a collision, ranging from a
value of zero for a totally inelastic collision to a value of 1 for a perfectly elastic collision. This coefficient is
CR = -(v1f - v2f)/(v1i - v2i)
In this experiment, the two objects colliding are a dropped ball and the Earth. The Earth does not change its motion
measurably upon collision, so we can take v2f = v2i =0. Therefore, in this experiment,
CR = -v1f/v1i
OR
CR = |v1f/v1i|
You will not be measuring the speeds directly, but rather measuring the height the ball is dropped from and the height it
bounces back up to.
7) How is the height the ball is dropped from related to v1i, the speed just before it hits the ground?
8) How is the height the ball bounces back to related to v1f, the speed just after it hits the ground?
9) Using your answers to the previous two questions, derive an expression for the coefficient of restitution in terms of
hdrop and hbounce instead of v1f and v1i. You might want to write this expression on the lab sheets you don’t turn in, so
you will have it to use during the experiment and analysis.
Name:_________________________________ Lab Section: _________ Group Number: __________
Physics 201
Experiment #5
Dissipation of Energy
Introduction Energy is a very useful concept, and one of the main reasons that it is useful is that it is conserved.
Energy may be transformed from one form to another, but it is not created or destroyed.
Mechanical energy is the total energy due to the position or motion of an object, and thus includes potential and
kinetic energy. Some physical processes come very close to conserving mechanical energy; in other processes a
considerable amount is lost. In all cases, the lost mechanical energy is said to be dissipated, and it is turned into
thermal energy (energy related to the temperature of an object).
In perfectly elastic collisions, mechanical energy is conserved. Real collisions are not generally perfectly elastic, but
vary according to how inelastic they are. Besides collisions, kinetic friction can also dissipate energy – in this case,
the amount of energy dissipated depends on the coefficient of kinetic friction.
Procedure
When an object moves down a slope, it loses potential energy. If there were no dissipation, all the lost potential
energy would become kinetic energy, and the object’s speed would reflect that. There will be some dissipation due
to kinetic frictional losses. The wheel is specifically designed to minimize dissipation, because the frictional force
on a wheel is almost entirely static friction.
Prop up one end of the track to form a sloped surface.
Start up ScienceWorkshop and set it up to record both the position and velocity from the SmartPulley. The position
of the object will determine its potential energy, U, while its velocity will determine its kinetic energy, K. This
allows us to determine the total mechanical energy, Emech = K + U.
A string attached to the object and hanging over the SmartPulley allows the computer interface to detect the object’s
motion. Make a few dry runs to be sure you see how everything works - letting the block slide down the slope on
one of its narrow sides. Adjust the angle of the slope, if necessary to be sure the block accelerates down the slope.
1) Measure the height of the track at two different points, and from this information, determine the angle the slope
makes with horizontal
Start with the block near the top of the slope, and use ScienceWorkshop to record position and velocity data as it
slides down the slope. Try to record only while the object is freely moving, not while you are holding it or stopping
it. Look at the velocity graph and notice that the cart’s speed is indeed increasing as potential energy is converted to
kinetic energy.
Select two times, one near the beginning of the slide and one near the end. Record both the position and velocity at
these times (2 times, 2 positions, 2 velocities).
2) Taking the height of the cart at the later point to be zero, find the height of the cart at the earlier time, using the
difference in position along the incline (from the ScienceWorkshop data) and what you know about the angle of
the slope.
3) Calculate the initial and final potential energies, using U=mgh.
4) Calculate the initial and final kinetic energies from the recorded velocities, using K= &frac12;mv2.
5) Calculate the initial and final mechanical energies.
6) Is mechanical energy conserved to within the uncertainty of your experimental errors? If not, what percent of
the initial mechanical energy is dissipated?
Now repeat the previous procedure with the block turned upside-down (on the other narrow side). Note that the
surface is different and has different frictional properties.
Record your data in the data spreadsheet. Record here the calculated mechanical energies, the dissipated energy,
and the percent of energy dissipated.
7) Is there more or less energy dissipated in this case? Was your prediction in the pre-lab correct? If not, explain
why.
Now repeat the previous procedure with a rolling or wheeled object. Record your data in the data spreadsheet.
Record here the calculated mechanical energies, the dissipated energy, and the percent of energy dissipated.
8) Is there more or less energy dissipated in this case? Was your prediction in the pre-lab correct? If not, explain
why.
Energy is not only dissipated by friction, but can also be dissipated in a collision. A quantity called the coefficient
of restitution is a common measure of the elasticity of a collision, ranging from a value of zero for a totally inelastic
collision to a value of 1 for a perfectly elastic collision. This coefficient is given by
CR = -(v1f - v2f)/(v1i - v2i)
In this experiment, the two objects colliding are a dropped ball and the Earth. The Earth does not change its motion
measurably upon collision, so we can take v2f = v2i =0. Therefore, in this experiment,
CR = -v1f/v1i
CR = |v1f/v1i|
Write here the expression for CR in terms of hdrop and hbounce from your pre-lab.
Drop one of the balls five times, recording the height it was dropped from, and the height it bounces back up to.
Drop the ball from high enough that it will bounce back substantially, but not so high that you have trouble with it
not dropping straight down.
9) Compute the coefficient of restitution for this collision and record it here. Does this indicate a fairly elastic
collision? Explain.
10) What percent of the initial mechanical energy is dissipated in the collision?
Select another ball. Drop this ball five times, recording the dropped height and the bounce height each time.
11) Record its calculated coefficient of restitution here. Compare the coefficient of restitution in this case to that of
the previous case. Does this comparison indicate that this case more or less elastic than the previous case?
12) Compare the percent of energy dissipated in this case to that of the previous case. Does this comparison
indicate that this case more or less elastic than the previous case?