University of Virginia
Physics Department

## Energy of a Cart on a Ramp Version B

A Physical Science Activity

### Student Activity

Materials

• Texas Instruments CBR Ranger motion detector.
• TI graphing calculator
• Software program Ranger.83p
• 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 CBR 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. Turn on units.
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. Run the RANGER calculator program. Program the calculator to perform a velocity vs. time measurement and for the initiation of data recording by pressing the trigger button on the CBR. Start the velocity vs. time measurement by pressing the trigger button and release the cart, making sure not to give the cart any initial velocity when letting go. (Note: The RANGER program asks for a time period that the experiment will run and calculates the reading interval it needs to utilize all of its storage capacity for that given time. Hence if a longer time is used then the intervals of measurement are long, a short time gives smaller intervals. We found that a 5 s time interval works well.)
6. When the cart hits the stop, stop the calculator's measurements.
7. Read off the velocity at the point it hit the stop (where the arrow is pointing. The rapid oscillating values after this time are due to the bouncing back and fourth of the cart after it hit and should be ignored).

8. 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?