# Rotational Kinetic Energy of a Soup Can

When an object falls from rest, its potential energy is converted into kinetic energy. Initially, it contains only potential energy, PE. As it falls, this stored energy is converted into kinetic energy, KE. If there are no frictional forces acting on the object, the total energy (potential plus kinetic) will remain constant. In this experiment, we will see if this works for a falling soup can.

An interesting situation arises when an object unwinds down a string rather than simply falling. Not only is the object moving in a straight path toward the ground, but it is also rotating. Now the initial potential energy is converted into both translational and rotational kinetic energy. In this experiment, we will determine what fraction of the kinetic energy goes into rotating a soup can as it unwinds down a string.

### OBJECTIVES

• Measure the changes in potential and kinetic energy of a soup can as it falls and as it unwinds down a string.
• Observe how the total energy of the falling soup can changes.
• Determine the fraction of kinetic energy that goes into rotating the soup can as it unwinds down the string.

### MATERIALS

Computer running logger pro

Excel or Graphical Analysis

empty soup can

ULI interface

nylon cord or string

Vernier motion detector

ring stand

### PRELIMINARY QUESTIONS

• What kind of energy does the soup can before it is dropped?
• What kind of energy does the soup can have while it is falling?
• What kind of energy does the soup can have while it is rolling down the string?
• Which soup can will be moving faster, the one in free fall or the one rolling down the string?
• Do you think frictional forces will be significant for either the falling soup can or the unwinding one? Why or why not?

### PROCEDURE

1. Measure and record the mass of the soup can.
2. Hang the soup can from the ring stand using the nylon string. Make sure the can will be able to fall about 1.5 m before hitting the ground.
3. Using a small piece of string, tie the soup can in place at the top of the ring stand. This string will hold the can in place and can be cut when you are ready to record some data.
4. Set up the motion detector and position it on the floor directly beneath the soup can. Place a wire basket over the motion detector to protect it.
5. Set up Logger Pro for the motion detector.
6. Set up Logger Pro for data collection. Take data for about 10 seconds, sampling 50 points/second.
7. Set up four new data columns on Logger Pro: velocity, potential energy, kinetic energy, and total energy. You can do this by choosing DATA --> NEW --> COLUMN --> FORMULA and typing in an equation for each quantity.
8. Set up a graph of energy vs. time. Plot time on the x-axis. Plot PE, KE, and total energy on the y-axis.
9. When you are ready to take data, hit collect and wait for the motion detector to start. Without getting your hands in the way, quickly clip the supporting string on the can and let it fall.
10. When the motion detector has stopped running, zoom up on the portion of your graph that represents the time the can was falling. If this was a smooth run, save it. If not, repeat it until you have a smooth run.
11. Now roll the can up the string (like a yo-yo) and tie it in place. Repeat steps 9 and 10.

### ANALYSIS

1. Examine the graph for the free-falling soup can (Zoom in on the relevant section). What happens to the potential energy as the can is falling? What happens to the kinetic energy as the can is falling? What happens to the total energy as the can is falling?
2. Examine the graph for the rolling soup can (Zoom in on the relative section). What happens to the potential, kinetic, and total energy as the can is unwinding?
3. How can you explain the differences in total energy for the two soup cans?
4. To analyze the energy of the rotating soup can, you will need to look at the data taken while the can was falling.
• Look at the graph for the unwinding can. Highlight the section of the graph where the can is falling. Copy this data and paste it into a spread sheet such as Excel or Graphical Analysis.
• The graph for the unwinding soup can shows a loss of total energy. In a new column, calculate the amount of total energy that seems to have been "lost" at each time step. (This energy hasn't really been lost-it just went into rolling the can!) This "lost" energy is actually the rotational kinetic energy of the can.
• The total kinetic energy of the soup can is the sum of its translational and rotational kinetic energy. In a new column, calculate this total kinetic energy.
• In a new column, calculate the fraction of kinetic energy that is rotational energy. Take an average of all the values in this column.
5. What conclusions can you make about the energy of an object that rotates as it falls compared to an object that simply falls?

### EXTENSIONS

1. How does the rotational kinetic energy depend of the shape of the object? Try this experiment again with a solid cylinder, a solid sphere, or a hollow sphere.
2. Use a force meter to study the tension in the string of the unwinding soup can.

Check out some sample data!