In this experiment, students use the GLX to determine the relationship gravitational potential energy GPE and kinetic energy KE of a bouncing ball. Further investigations can explore energy before and after a bounce.

• Xplorer GLX (PS-2002)
• Motion Sensor (PS-2103)
• Universal table clamp (ME-9376B)
• 2 Pulley mounting rods (SA-9242)
• Multi-clamp (SE-9442)
• Ball
• Meter stick

1. Arrange a Universal Table Clamp, two rods, a Multi-Clamp, and a Motion Sensor as in the picture at right. Make sure that the motion sensor is pointed down (the dial on the side should read 90).
2. Place the ball under the sensor, on the floor. Measure the distance from the top of the ball to the screen on the motion sensor. Enter the number here:

Top of ball to sensor distance= _______________ m

3. Measure the mass of the ball:

Mass of ball, m = ______________ kg

1. Turn on the GLX .
2. Press the Home Button.
3. Press to select the Sensors Icon.




4. Using the Arrow and Check Buttons, change the Sample Rate to "50" and set Velocity "Visible", as in the picture above.
5. Press the Home Button.
6. Press to select the Calculator Icon.
7. Press to select the Edit function. Press to turn off "Num Lock".




8. Enter the equations above. Note: To enter [Position (m)] and [Velocity (m/s)] press then select the appropriate measurement. To enter ^2, press and arrow to ^2 and press to select. Note: The ball had a mass of 2 kg and the motion sensor was 57 cm above the ball at rest on the floor in this example.
9. Press the Home Button.
10. Press to select




11. Press to select graphs options. Press the 6 button to select "Two Graphs".
12. Press then arrow keys until the top y-axis label is selected. Press to get options for y-axis. Select gpe for gravitational potential energy.
13. Press then arrow keys until the bottom y-axis label is selected. Press to get options for y-axis. Select ke for kinetic energy.

1. Hold the ball 20 cm from the motion sensor.
2. Press the Start button. Drop the ball immediately. Let it bounce a couple of times.
3. Press the Stop button.
4. To print the graphs, press the button and select "Print."

1. Press to select the Calculator Icon.
2. Add another quantity. Total Energy, totale = gpe + ke.
3. Display combinations of gpe, ke and totale to understand the energy within the different systems.
4. Use the smart tool (Press on the graph display) to read energy values before and after collisions with the floor.

1. Is energy conserved between interactions with the floor? Give data to support your finding.
   
   
   
   
2. Are the ball's collisions with the floor elastic or inelastic? Give data to support your finding.
   
   
   
   
3. Coefficient of restitution, C_R, is a term used to describe the interaction of a ball with a surface.

   
   

   For example, C_R approx. 0.6 for a basketball.
   Determine the C_R for your ball/floor situation.
   
   
   
   Determining an accurate velocities before and after the collisions with the floor can be difficult. Another formula for C_R is to use the height on rebound. For this to be valid, there can be very little effect due to air resistance. Then, the kinetic energy before impact is equal to the gravitational potential energy at the top of the flight. This leads to the following relationship between v and h.

   
   

   Using this result and substituting in the coefficient of restitution equation we arrive at the following expression:

   
   

   Is the height version of the coefficient of restitution value valid for this experiment? Determine C_R using the height and compare to the velocity derived value.
   
   
   Which approach seems more accurate? Explain your reasoning.