LAB INSTRUCTIONS
Energy loss in an inelastic collision
General aim
The aim of this lab experience is to measure the energy loss in inelastic collisions that appear when a
ball bounces.
Instruction
The energy loss of different balls should be measured when they bounce off the floor. For this purpose
three different balls are available: a bouncing ball, a golf ball and a bandy ball
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Take one ball and lift it to a certain height.
Let the ball fall and determine the maximal height the ball can reach when it bounced off the
floor.
If possible note these heights also for the second and third bounce.
Do this experiment several times with every ball.
When you obtained these data, plot all the heights against the attempt you made. Do this for
each ball.
Determine an average maximum bouncing height for all number of bounces and for each ball.
Use these heights to determine the fraction of energy that the ball loses in the collisions.
Calculate the speed of the ball after the last bounce.
Are these fractions dependent on the collision energy or the kind of ball?
Tip: The potential energy of a ball when it starts falling is known, and can be converted into kinetic
energy before the collision.
STUDY OF THE BEHAVIOUR OF BOUNCING OBJECTS
Davide Ragazzon
Joachim Rausch
Example of a lab report for
MEKANIK HI
vår termin 2014
Uppsala University
Task
The purpose of this lab is to study the energy loss of an object in a collision with the floor. It will be
checked whether the energy loss is dependent of the kind of ball and/or on the collision energy. Finally
the speed of the object after the third bounce will be calculated.
Theory
Inelastic collisions
An elastic collision is a collision in which kinetic energy is only transferred from one collision partner
to another but not converted into other forms of energy like heat. In contrast to that an inelastic
collision is a collision where kinetic energy is converted into other forms.
In our case this means that the amount of kinetic energy of the ball before and after the collision with
the floor will change. The energy will be used to transform the ball or the floor and parts of this energy
will be converted into heat during this process.
The fraction of kinetic energy f that is lost in a collision is
where
the collision.
is the kinetic energy of the ball before and
the kinetic energy of the ball after
Potential and kinetic energy
To accelerate a ball to a certain energy we use the fact that a ball with a certain height has a certain
potential energy. The potential energy of an object is
where
is the gravitational acceleration on earth, m the mass of the object and h its height
with respect to the ground.
The kinetic energy is
where is the velocity of the object. Therefore, if the kinetic energy is known, the velocity can be
obtained as
√
When one lets a ball fall from a certain height, its initial potential energy
is completely
converted into kinetic energy just before hitting the ground, so in the last instant before the bounce the
kinetic energy of the object
can be expressed as:
An analogous formula can be used to obtain the kinetic energy
bouncing by measuring the maximal potential energy
ground.
of the object just after
the object reaches after it hits the
Using equations (5a) and (5b) as well as equation (2) into equation (1), we get
where
and
are the maximal heights of the ball before and after the bounce,
respectively.
This means that it is enough to measure
and
to calculate .
Finally, the velocity of the object after it bounced
can be obtained through the following relation,
obtained by combining equation (5b) and equation (2) with equation (4):
√
√
Method
During the lab experiment we let different object fall
from a height of 181 cm and bounce (two or three
times). We recorded the maximum heights the objects
had before and after every bounce. We estimate that the
precision we have when reading the height is about 5
cm, so we repeated the experiment until a significant
part of the data were less than 5 centimeters far from the
average.
This was done with a bouncy ball, a golf ball and a
bandy ball.
Figure 1.
Schematic description
of the experiment
√
Results
The data were analyzed using the same procedure for the three different objects, so in the following
we will present in detail the data analysis for the bouncy ball and then we will show the results
obtained by treating the data in a similar way for the golf ball and the bandy ball.
Finally, we compare the results obtained for the different objects.
Bouncy ball
Figure 2 shows the starting height of the bouncy ball and the maximal heights reached after bouncing.
These heights are plotted against the attempt number. The lines show the average values and were
obtained by drawing a horizontal line as close as possible to the experimental point.
Figure 2. Maximal heights reached by a bouncy ball after up to three bounces.
The fraction of energy lost in a bounce fbouncy can be calculated with equation (6). This is done as an
example for the first bounce:
The following table summarizes the results obtained for every bounce.
starting height
after one bounce
after two bounces
after three bounces
average fbouncy
average maximal
heights (cm)
181
132.5
92.6
62.5
average fraction of energy
lost in that bounce
0.268
0.301
0.325
0.298
The average velocity of the bouncy ball after the third bounce
can be calculated by using
equation (7) and the averaged maximal heights after the third bounce.
√
√
√
Golf ball
The data were treated in the same way as the ones of the bouncy ball. The measured heights are shown
in Figure 3, and the calculated values of fgolf are presented in the next table.
Figure 3. Maximal heights reached by a golf ball after up to three bounces.
starting height
after one bounce
after two bounces
after three bounces
average fgolf
average maximal
heights (cm)
181
141.7
100.6
75.1
average fraction of energy
lost in that bounce
0.217
0.290
0.253
0.253
The velocity of the golf ball after the third bounce
is:
√
Bandy ball
The data about the bandy ball were treated equivalently to the ones of the bouncy ball. It was not
possible to measure the third bounce because it happened fast after the second one. The data are
displayed in Figure 4 and the calculated values of fbandy are presented in the next table.
Figure 4. Maximal heights reached by a bandy ball after up to two bounces.
starting height
after one bounce
after two bounces
average fbandy
average maximal
heights (cm)
181
75.2
30.4
average fraction of energy
lost in that bounce
0.585
0.596
0.591
As discussed previously, it was not possible to measure the height reached after the third bounce, so
we calculate it using the fact that the maximum height is proportional to the energy, so the fraction of
energy lost is the same as the fraction of “heigh l ”. So the height after the third bounce h3rd can be
obtained from the one after the second bounce h2nd:
The average velocity of the bandy ball after the third bounce
is:
√
Discussion
A comparison of the measured values of f for the different objects is shown in Figure 5.
Figure 5. Average fraction of energy lost in every bounce plotted for different balls.
The first observation about this comparison is that the values of f for each ball are rather similar,
considering the experimental uncertainty. We can therefore confirm that f is rather independent from
the energy that the ball has when it hits the ground.
On the other hand, comparing the values of f for different balls, one can see that the golf ball actually
loses the least amount of energy, about 25%, followed by the bouncy ball with about 30%. The bandy
ball has a much higher energy loss per bounce of about 59%. These results show clearly that f depends
on the shape and on the material of the objects.
Finally, the speed after the third bounce was much lower for the bandy ball than for the other two,
since the bandy ball loses its energy much faster than the others: 1.56 m/s versus 3.50 m/s and 3.84
m/s respectively for the bouncy ball and the golf ball.
Conclusions
The energy loss of a ball bouncing of the floor was measured for three different balls. The measured
values presented significant differences, confirming that the energy lost when hitting the ground
depends on the shape and the material of the different objects.
A dependence on the impact energy could not be observed.
As one can see in Figure 2, 3 and 4 the kinetic energy of a ball after a collision with the floor can be
quite different although the kinetic energy of the ball before the collision was always the same. The
reason for this could be that we did only measure the height as an indicator of the kinetic energy of the
ball. This neglects that the ball could also start to move side wards or could start rotating when it
collides with the floor. The energy for these movements is not considered if only the height of the ball
is measured. This might decrease the precision of the results a little and a different experimental
design could improve the precision of our measurements. Anyway, the precision of our results is
probably sufficient for many applications, since the contribution of the effects measured above was
quite small.