Studio Physics I
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.
(If you are using a “Motion Sensor II” the cart can be as close as 15 cm.)
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.
After the push but before the catch, describe the direction of the net force acting on the cart (it is zero, up the incline, down the incline?) and magnitude of the net 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 11 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.
(If you are using a “Motion Sensor II” the cart can be as close as 15 cm.) 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 predictions or the data are wrong. 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
½ mv 2 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 KE zero? When during the motion is the KE a maximum? (Write your answers near your sketches of measured data.)
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.
Sketch a prediction graph of the potential energy (PE) of the cart (the energy due to raising the cart's mass in the gravitational field of the earth = mgh) as it goes up and back down the track. 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)
©1999-2001 Thornton, Sokoloff and Cummings; Rev. 2004 Bedrosian

7.
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.
8.
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) any change in the mechanical energy of the cart after the push and before the catch. Describe in words the changes of mechanical energy during the push and during the catch.
9.
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.
10.
State in complete sentences the differences in the graphs of the cart’s KE, PE, and mechanical energy.
11.
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 (at least approximately)? How do you know this?
12.
Where does the cart get its initial energy? Where does the energy go at the end of the motion?
13.
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"?
14.
Instead of giving the cart a push by hand, suppose we used its built-in spring to push against a fixed barrier at the bottom of the track. (This is a “thought experiment” – we will not actually do it.)
Assume the cart starts 1.00 m from the motion detector (along the track) and the motion detector is
5.0 cm above the level of the cart when the cart starts. Draw a sketch of the cart, track, and motion detector before the spring is released.
15.
Draw a sketch of the cart, track, and detector at the cart’s closest distance to the detector.
16.
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 along the track between itself and the cart. What is the mathematical relationship between the distance from the motion detector ( d ) and the cart’s height ( h ) above the level where it started? Draw a graph of h vs. d , from d = 0.00 m (touching the detector) to d = 1.00 m (the starting location). You should know h at the end points of the graph. Is the graph a straight line? Why or why not?
(Hint: Use facts from geometry and trigonometry to help answer this.)
17.
Calculate the closest distance of the cart to the motion detector after the spring is released. For the sake of the exercise, we assume that the spring is ideal with a spring constant of 2500 N/m. The spring is compressed 1.0 cm before it is released to push the cart up the track. Ignore friction and use m = 0.5 kg, g = 9.8 N/kg.
©1999-2001 Thornton, Sokoloff and Cummings; Rev. 2004 Bedrosian