University of Virginia
Physics Department

## Energy of a Cart on a Ramp Version A

A Physical Science Activity

### Student Activity

Materials

• Texas Instruments calculator (TI-83 or 83 plus preferred, but TI-82 is okay)
• Texas Instruments CBL unit
• Vernier motion detector
• The PHYSICS suite of programs from Vernier
• Wooden board (about 2 m long and at least 20 cm wide)
• Books or something large to prop board on
• Cart (could be a toy truck or physics cart, anything that rolls with little friction).
• Large sponge or something soft to stop cart
• Mass scale (digital balance or triple beam balance)

Procedure
1. Measure the mass of the cart on the mass scale.
2. Connect the CBL unit to the TI Calculator with the unit-to-unit link cable using the I/O Ports located on the bottom edge of the units. Connect the motion detector to the CBL by the SONIC port on the side of the CBL.
3. Stack a few books (or something similar) beneath a wooden board, as shown in the setup diagram. Place the motion detector at the top of the ramp and position the dynamics cart at least 50 centimeters from the motion detector (you will receive spurious results if the motion detector is closer than 50 cm to the moving object). Place the sponge or something soft at the bottom of the ramp to catch the cart.

4. Measure the height of release of the cart (you can experiment with average value of height) and the height that the cart hits the sponge. It is important that you subtract the height of the cart at the end of the trip from the original height so that the change in height Dh is know to determine the potential energy.
5. Start the PHYSICS program on the TI calculator.
• In the Main Menu select 2. COLLECT DATA.
• In the Data Collection Menu select 2. TIME GRAPH.
• Enter in the following values: Enter Time Between Samples in Seconds: .05 Enter Number of Samples: 50 Then the calculator will determine how much time the experiment will take. With these values it will take .05 * 50 = 2.5 seconds. You may have to change these values for your particular set up.
• Then select 1. USE TIME SETUP. The device is now ready to collect data.
6. Hit the Enter button and release the cart. The motion detector will measure the position and velocity of the falling cart. Wait until the calculator is finished with its measurements.
7. In the Select Graph menu, choose 2.VELOCITY, and a graph similar to the one below will show up. It shows the instantaneous velocity in the y-axis for a given time in the x-axis.

8. The graph will have some spikes in the beginning which represent the time when the cart was let go. These can be ignored. The most important part of the graph is the peak that represents the final velocity right before the cart hits the sponge. The graph is already in the TRACE mode so by using the left and right arrows, place the cursor at the final peak velocity value and read off the y value at the bottom of the screen. The units are m/s. The x value represents the time in seconds.
9. Calculate kinetic energy ( ½ mv2) and potential energy loss {m*g*(h1-h2)} and compare results. Perform this calculation for varying heights of the ramp.

Data Sheet

 Trial #1 Potential Energy Calculation Measurement: Mass of the cart-M (kg) Measurement: Original height (m) Measurement: Final height (m) Calculation: Difference in height- h1-h2 (m) Calculation: Difference in potential energy U = M*g*(h1-h2) acceleration due to gravity, g = 9.8 m/s2 Kinetic Energy Calculation Calculator Measurement: Final velocity-v (m/s) Calculation: Final kinetic energy KE = (1/2)*M*v2

 Trial #2 Potential Energy Calculation Measurement: Mass of the cart-M (kg) Measurement: Original height (m) Measurement: Final height (m) Calculation: Difference in height- h1-h2 (m) Calculation: Difference in potential energy U = M*g*(h1-h2) acceleration due to gravity, g = 9.8 m/s2 Kinetic Energy Calculation Calculator Measurement: Final velocity-v (m/s) Calculation: Final kinetic energy KE = (1/2)*M*v2

 Trial #3 Potential Energy Calculation Measurement: Mass of the cart-M (kg) Measurement: Original height (m) Measurement: Final height (m) Calculation: Difference in height- h1-h2 (m) Calculation: Difference in potential energy U = M*g*(h1-h2) acceleration due to gravity, g = 9.8 m/s2 Kinetic Energy Calculation Calculator Measurement: Final velocity-v (m/s) Calculation: Final kinetic energy KE = (1/2)*M*v2

1. Why aren't the potential and kinetic energy readings that we compare exactly the same?

2. Pretend you were sliding down a snow hill on a sled with no friction, just like the cart in the experiment. During your descent of the hill describe how your gravitational potential energy, kinetic energy, and total energy change.

3. What would happen if we used a heavier cart in the experiment? Would it have gone faster or slower, or the same speed? Why?