Introduction to Conservation of Energy
Modified 8/13/03
Copyright 1999-2001 Thornton, Sokoloff and Cummings; Rev. 2003 Bedrosian
With proper referencing, educators are welcome to use this for instructive purposes. Any other permission of publication (written or electronic) is denied without express prior consent from Dr. Philip Casabella.

• In this activity, we consider a cart given a quick push up an inclined track.
• Set up your equipment as follows:
  • The motion detector is at the very top of the track.
  • The lower end of the track should not hang off of the table, nor rest on anything other than the surface.
  • A block of wood is placed under the end of the track, right at the end.
  • The high end of the track (with the detector) is elevated about 5 cm (2 inches) by the block of wood
• The motion we will investigate is this:
  • The cart rolls up the ramp moving toward the motion detector, slowing down as it goes, reaches its highest point and then rolls back down the ramp speeding up on the way. The cart is then caught at the bottom of the track.
  • Don't let the cart get closer to the motion detector than 50 centimeters.

1. Sketch predictions of the velocity-time and position-time graphs for the cart (you can ignore friction). Show the push and the catch of the cart. Take the positive direction to be away from the detector (down the incline).

2. Describe the direction of the net force acting on the cart (it is zero, up the incline, down the incline?) and nature of the force acting on the cart (it is constant, increasing, decreasing?) as:
a) The cart moves up the inclined plane, slowing down as it goes.
b) At the cart's highest point,
c) As the cart moves back down the inclined plane, speeding up as it goes.

3. Get the file "ConservofEnergy.MBL". You can get this from the Studio Physics CD (Physics1 folder) or from our web site on the Activities page under Activity 12 as LoggerPro File A. Copy the file to your hard drive. Then double-click on it and you should launch LoggerPro with the file. Set up the equipment as discussed above and collect data for the motion described in the box at the top of the page. Don't let the cart get closer to the motion detector than 50 centimeters. Sketch the graphs of position vs time and velocity vs time on your activity sheet. Mark the turn around (or highest) point on both of your graphs. Compare this graph to the prediction that you made in Step 1. If the graphs are not VERY similar, either the prediction or the data is wrong. Determine which one it is. Collect better data if necessary.

4. Sketch a prediction graph of the kinetic energy (the energy due to motion) of the cart over time as it moves. Keep in mind that the kinetic energy (KE) is 1/2mv2 where m is the mass of the cart (in this case 0.5 kg) and v is the velocity. When during the motion is the kinetic energy zero (at the top?, bottom?…)? When during the motion is the KE a maximum? (Write your answers to these questions to the right of your sketch).

5. Change the velocity-time graph so that it displays the kinetic energy of the cart as a function of time. (This is done by placing the cursor tip over the word "velocity " on the y-axis of the velocity-time graph and clicking the left mouse button. Uncheck "velocity" and check "kinetic energy".) Compare the actual graph of the cart's kinetic energy to your prediction, and sketch the correct graph now. Mark on your sketch the regions associated with your push and catch of the cart.

6. The gravitational potential energy (PE) of the cart depends on the height of the cart above the table top (or other reference point). The motion detector measures the distance between the cart and the motion detector along the track. Is there a FIXED relationship between these two quantities (height and distance along the track) for YOUR set-up? If so, what is the relationship between the two? If not, why not?

7. Sketch a prediction graph of the potential energy of the cart (the energy due to raising the cart's mass in the gravitational field of the earth = mgh). Define the potential energy to be zero at the height at which the cart is first pushed. When is the potential energy zero again? When is it a maximum? (Write your answers to the right of the graph)

8. Change the height-time graph to display the PE of the cart as a function of time. (This is done by placing the cursor tip over the word "height" on the y-axis of the graph and clicking the left mouse button. Uncheck "height"-you may need to scroll down to find it- and check "Gravitational PE".) Compare the actual graph of the cart's gravitational potential energy to your prediction, and sketch the actual graph on your activity sheet.

9. Sketch your prediction of the total mechanical energy (the sum of the kinetic and potential energies) of the cart over time as it moves. Describe in words (using complete sentences) the nature of the mechanical energy of the cart after the push and before the catch ( is it increasing, decreasing….?). Describe in words the nature of the mechanical energy of the cart during the push. Describe in words the nature of the mechanical energy during the catch.

10. Change the distance-time graph to display the total mechanical energy of the cart as a function of time. (This is done by placing the cursor tip over the word "distance" on the y-axis of the graph and clicking the left mouse button. Uncheck "distance" and check "Mechanical Energy".) Compare the actual graph of the cart's mechanical energy to your prediction and sketch the correct graph now. Mark the push and catch on your sketch.

11. State in complete sentences the main differences in the graphs of the cart's KE, PE, and mechanical energy.

12. Explain what "conserved" means. Is the kinetic energy of the cart conserved? How do you know this? Is the gravitational potential energy of the cart conserved? How do you know this? Is the mechanical energy conserved? How do you know this?

13. Where does the cart get its initial energy? Where does the energy go at the end of the motion?

14. How would your graphs of PE, KE, and mechanical energy change (or not) if we chose a different point (one other than the cart's initial height) to call our "zero height"?