Investigation: Conservation of Energy for a Bouncing Ball
John Boehringer, McKinney High School, 2005
Any first-year physics student can recite the Law of Conservation of Energy by wrote,
but how does it actually apply in real life? After all, we speak of “ideal” systems that
are closed so that no energy “escapes,” and we tend to ignore non-conservative
forces as they are often inconvenient to the demonstration of the principles we
discuss in class. Many first year students model energy conservation in a system of
a bouncing ball or some other falling body. However, in real life, physics is burdened
with having to deal with non-conservative forces like friction and somewhat less than
ideal elastic materials and thus fails at some level in our basic demonstrations.
Interestingly, many principles like the perfect transformation of gravitational potential
energy into kinetic energy for a falling body, were first envisioned to describe events
on the macro (or human) scale. While we, as students of physics, often take these
for granted as being approximations of real life due to the presence of various
frictions we have difficulty accounting for, many principles like nearly perfect elastic
collisions, actually exist, but on the quantum level. Ironically, most of these quantum
level systems were not discovered until the last century, while human scale
mechanics had been in full swing since the 1600’s. Indeed, in the year 1900, many
otherwise knowledgeable people thought that physics was essentially a dead
science, with little room for further discovery or investigation. Thanks to visionaries
like Albert Einstein and Niels Bohr and their successors such as Schroedinger and
Enrico Fermi, a new, quantum realm of existence was opened, and old principles, like
the conservation of energy and momentum took on new importance.
Problem
 What is the acceleration of a freely falling body?
 What quantity of energy is “lost” by a bouncing ball and where does it go?
Materials
Windows PC w/ Logger Pro Software
LabPro interface
Motion Detector
Large elastic ball (basketball or volleyball)
Procedure (Part I)
Using only the equipment available for this lab, devise a method to find the
acceleration due to gravity of a falling body.
Drawing Conclusions:
1) Describe your method and give the average of several results for your value of the
gravitational constant, g, below.
2) Is the total mechanical energy of the ball constant? Don’t just give the default
ideal physics-land answer. Look at your data. Is the total energy constant? If not,
name some places where the energy is going.
3) Are the relevant parts of the position-versus-time graphs a straight line? Why or
why not?
4) Are the relevant parts of the velocity-versus-time graphs a straight line? Why or
why not?
5) What is the value of the slope, dv/dt? You may give the average value for several
trials.
Procedure (Part II)
1) Again using only the motion detector, determine a procedure to analyze the
changes in energy for a bouncing ball. You may find it useful to have your computers
show both the graphs of displacement and velocity on the same scale.
2) Sketch your graphs accurately on the graph paper provided.
3) Using data from your experiment, create a data table below of relevant points
from your graph that you wish to use in your analysis. You may use data values from
either your graphs of displacement, velocity or both together.
Data:
4) Using your selected data, use either the tools in Logger Pro, Microsoft Excel or
your graphing calculator to determine a function that describes the loss in energy of
the ball with respect to each bounce. (You may also find the change in energy with
respect to time, but it is not necessary to do so in most cases).
Drawing Conclusions
1) Describe your theory of how to find the function to describe change in energy for
each bounce of the ball. Be sure to include any equations as you feel necessary.
2) What function did you come up with to describe this change?
3) What device did you use for your analysis (i.e., calculator, MS Excel, LoggerPro,
etc.)?
4) Describe how you input the data into the device above and what steps you took to
analyze it (e.g., your keystrokes on the calculator).
Assessing
1. How might you go about producing a potential energy function from your graphs
of displacement?
2. (AP only) What would the derivative of such a function represent?
3. What information would you us to produce a graph of the work done by gravity on
the bouncing ball? How?
4. What is the percent error on your value of g (found in part I) versus a theoretical
value of 9.81 m/s2. Show your calculations.
Extending
1. Does your function describing change in potential energy per bounce work
(approximately) for another ball of the same type (i.e., if you used a volleyball, do you
get the same data for another volleyball). What about a ball of a different type (e.g.,
a basketball)?
2. Name some factors that might change the elasticity of your ball, thus changing the
outcome of the energy per bounce function you obtained in part II.