Investigation: Conservation of Energy for a Bouncing Ball

John Boehringer, McKinneyHigh 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 SoftwareMotion Detector

LabPro interfaceLarge 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.