A. Initial Measurements
1. Measure the mass of each of the carts bare. Also measure the mass of the Force Sensor (without the cord on the scale) and the two black masses. The cart that will be closest to the Motion Sensor will have the flag in experiment 1 and the Force Probe attached in experiment 2, but they should have identical masses.
Place the angle indicator vertically in the slots of a cart and place the cart on the track. Level the track by means of the adjusting screw on one end of the track. The track may not be flat at all points. It may have a slight bow to it, so try to make it as level as possible.
2. Place the Motion sensor at the left end of the track. Be sure that the Motion Sensor is squarely on the track so that it makes a measurement of the carts and not the ceiling, the wall, or your body. Make sure that the yellow plug of the Motion Sensor is in digital Channel 1 and the black plug is in digital Channel 2.
a) Within DataStudio, drag and drop the Motion Sensor icon (click m in the Experimental Setup window) onto digital input 1.
b) Double click on the sensor. In the Measurement tab make sure that velocity and acceleration are the only data types selected. Then click the Motion Sensor tab and set the sampling rate at 20 Hz.
c) Click and drag the graph icon to the Motion Sensor icon. By default you will get a Velocity vs. Time Graph. In the Data window drag the Acceleration icon to the graph and drop onto the graph when you get a dotted rectangle around the entire graph. Click on the start button when you are ready to take data.
3. When you are convinced that the track is reasonably level, place a second cart at rest just beyond the first cart so that you can push the first cart start the experiment, get some good data for the velocity of the first cart before the collision, and also good data for the velocity of the two-cart system after the collision. This may take some practice
4. If linear momentum is conserved, then the following equation will be valid:
In this equation, m1 is the mass of the moving glider, m2 is the mass of the "target" cart, v1 is the velocity of the moving glider before the collision, and v2' is the velocity of the combined carts after the collision.
Run the experiment. If it does not turn out right the first time, click in each graph and then click the Data button and select No Data to clear out the graph to try again. When you are happy with the data you get from the experiment, Highlight the points on the graph corresponding to the points we are interested in (the points just before, during and just after the collision). Then use the expand graph button . From the Velocity vs. Time graph, we want the best estimate for the velocity just before the collision and just after the collision. Use the Smart Tool button, , to get these points on the graph. Once the Smart Tool is selected, drag the crosshairs to a data point and read off the velocity. You can use these velocities to check whether momentum was conserved in the collision. Record these velocities in your notebook and make sure to get a print out of this graph.
Next, we will focus on the Acceleration vs. Time graph. We want to integrate (compute the area under) the acceleration curve. We do so by clicking in the Acceleration graph and then clicking the Statistics button (the S) and selecting Area. This calculation will appear on the graph. Also make sure to get a print out of this graph.
5. How do you expect vafter to relate to vbefore?
6. Discuss momentum and energy conservation in the experiment.
7. Can you explain why the Velocity vs. Time graph looks like it does? If you had a plot of the second cart's Velocity vs. Time graph, what would it look like? Draw it on your print out.
8. How does the value of the area calculation relate to the velocity data?