Conservation of Energy II
Modified 8/14/03
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.

Part A - Review of Energy of a Cart on an Inclined Plane - With Low Friction

• 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. Make sure that your cart has no friction pad until Part B.
  • Don't let the cart get closer to the motion detector than 50 centimeters.

1. Get the file "ConservofEnergy.MBL" if you don't already have it from the previous class. 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.

2. 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".) Change the height-time graph to a potential energy-time graph. Change the position-time graph to a mechanical energy-time graph. Sketch these graphs on your activity sheet. Carefully note the points on your graphs where the push and catch of the cart occur.

3. Explain in one complete sentence what "conserved" means in relation to conservation of energy. Is energy conserved if the initial and final values of the energy are the same but the amount of energy at intermediate moments of time are different? Is the kinetic energy of the cart conserved? Is the gravitational potential energy of the cart conserved? Is the mechanical energy conserved? Why or Why not? Check your answer with your TA or Professor either now or before you leave class.

4. We will now consider some specific points on the graphs of the cart's PE, KE, and Mechanical Energy. Turn the analysis tool on by clicking on the 8th icon from the right (labeled x=?) in the toolbar. Pick 5 points of time after the push and before the catch of the cart as follows: 1 = just after the push, 2 = about half way up the track, 3 = at the highest point (velocity = 0 or max PE), 4 = about half way down the track, and 5 = just before the catch. Measure and record in a table (like the one shown below) the following values from the graphs: Time, PE, KE and Mechanical Energy. Record these values AS MEASURED from the graphs for each of the 5 times.

Time PE KE Mechanical Energy

5. How is mechanical energy related to PE and KE? Are your values in the table consistent with that?

6. Calculate the change in the PE and the change in KE between each time listed above. You will have exactly 4 intervals, one between each adjacent pair of steps in the previous table. Calculate the change in the mechanical energy in each interval. Do this in two ways: 1) by taking the difference in the values of mechanical energy recorded for those times in your table from step #4 and 2) Calculating Delta PE and Delta K from the values in the table above and then adding them together to get the change in mechanical energy. That is, make and fill in a table which looks like the one shown below. Recall that the change in a quantity in a time interval is defined to be the value at the end of the interval minus the value at the beginning of the interval. It could be positive, negative, or zero.

7. By how many Joules does the mechanical energy of the cart change over the entire time period you investigated? What percent of the initial mechanical energy does that represent? Why is it not zero?

Part B - Energy of a Cart on an Inclined Plane - With Significant Friction

• We will now consider a cart with a fraction pad on the bottom, so that now there is a significant amount of friction between the cart and the track. (Recall from a previous activity that it takes about 3 layers of felt.) The cart is given a quick push at the bottom of the track. It rolls up the ramp slowing down as it goes, reaches its highest point and then rolls back down the ramp speeding up on the way.

  8. Give the cart with friction pad a push and collect new data. Sketch the graphs on your paper. List at least 3 things that are different about these graphs as compared to those for the motion with very little friction. Show the regions of the graphs that correspond to the push and catch of the cart.

9. Make new tables like the ones you made in steps 4 and 6. In addition, use LoggerPro functions to find the distances at the first, third (highest or max PE) and last points in your table and record the values. To do that, click on the axis of the first plot and change it to distance, or just look in the data table.

10. By how many Joules does the mechanical energy of the cart (with friction pad) change from the first point to the third point? By how many Joules does the mechanical energy of the cart (with friction pad) change from the third point to the last point? By how many Joules does the mechanical energy of the cart change over the entire time period you investigated? What percent of the initial mechanical energy does that represent? Why is it a higher percentage than without the pad (easy question)?

11. Assume that the friction force on the cart going up the track is constant, and the friction force going back down the track is another constant. Calculate the friction force (magnitude) on the cart as it moves up the track from the first point in your chart to the third (highest) point. You will use the distance the cart moved and the mechanical energy lost. (See the lecture notes if you want a hint how to do this.) Calculate the friction force (magnitude) on the cart as it moves down the track from the third (highest) point to the fifth (last) point. Is the friction force greater on the way up or the way down, or about the same? Challenge Question (no credit): Can you explain why?