Conservation of Energy II
Studio Physics I
Review of Energy of a Cart on an Inclined Plane (with very 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 end of the track should not hang off of the table.
A block of wood is placed under the end of the track at the very edge (right at the end).
The far end of the track is elevated about 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. Open the file “Conservation of Energy.MBL”. You can get the file under the “activities” icon on the web page. The file is at the bottom of the activities list. Remember that you can only transfer the .mbl files with Internet Explorer. They do not transfer with Netscape. 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.
3. 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 where on your graphs the push and catch (or other stop) of the cart occur.
4. 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? Why or Why not? Is the gravitational potential energy of the cart conserved? Why or Why not? Is the mechanical energy conserved? Why or Why not? Check your answer with your TA or Professor either now or before you leave class.
5. We will now consider some specific points on the graphs of the cart's Ug, KE, and Mechanical Energy. Turn the analysis tool on by clicking on the 8th icon from the right (labeled x=?) in the toolbar. Pick points of time after the push and before the catch (or other stop) of the cart. Measure and record neatly (as a table like the one shown below) the following values from the graphs: Time, Ug, KE and Mechanical Energy. Record these values AS MEASURED from the graphs of each for at least EIGHT times of your choice. By how many Joules does the mechanical energy of the cart change over the entire time period you investigated?
Time / Ug / KE / Mechanical Energy6. How is mechanical energy related to Ug and KE? Are your values in the data table above consistent with your definition?
7. Calculate the change in the Ug and the change in KE between each time measured above. Calculate the change in the mechanical energy between any pair of time measurements. 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 #5 and 2) Calculating Ug and 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 is defined to be the final value minus the initial value.
Between which two times / Ug / KE / Mechanical Energy (from table in step#5) / Mechanical Energy (Ug+KE)8. What is the average value of the change in mechanical energy? If you got a value of zero for the change in the mechanical energy does this mean that the value of the change in gravitational potential energy is zero too? If so, why? If not, what does a zero value for the change in mechanical energy indicate?
We will now consider a cart with a fraction pad on the bottom, so now there is a significant amount of friction between the cart and the track. 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.
9. Make prediction graphs for the cart's gravitational potential energy Ug, kinetic energy KE and mechanical energy as a function of time. In making these predictions, it might be helpful to think about how these graphs will be the same as and different from the graphs for the same motion without friction that we have be analyzing.
10. Place a felt strip on the bottom of the cart so that there is now a frictional force between the cart and track. Give the cart a push and collect new data. Compare the actual graphs shown to your predications and sketch the actual 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.
11. Consider some specific points on the graphs of the cart's Mechanical Energy. Turn the analysis tool on by clicking on the 8th icon from the right (labled x=?). Pick points of time after the push and before the catch (or other stop) of the cart. Measure and record neatly (as a table like the one shown below) the Mechanical Energy for at least EIGHT times of your choice. Calculate the change in mechanical energy between adjacent time periods. That is, make and fill in a table like the one shown below.
Time / Mechanical Energy / Mechanical Energy from previous timeXXXXXX
12. Does the change in the mechanical energy average out to about zero? If not, where did the missing energy go? How much energy is lost during this time interval?
13. For the motion you are analyzing, how far does the cart move during the time period you investigated? How much energy is lost during this motion? Based on these answers, what is the force of friction between the cart and the track?
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