# BUNGEE CART (CBL)

## PURPOSE:

In this lab we will investigate the effects of different methods of stopping a moving cart. We will also do a mathematical analysis, looking at the impulse delivered to the object and the resulting change in its momentum.

## PROCEDURE:

1. Connect the CBL interface to the TI-82 using the Link Cable. Plug the Motion Sensor into the SONIC port on the CBL. Plug the Force Sensor into CH1, using the DIN-CBL adapter. Turn the CBL on, turn the TI-82 on.

2. Mount the Motion Sensor as far away as practical from the cart.

3. Connect one of the elastic cords (or rubber bands) between the cart and the end of the thread. The upper part of the thread should be vertical, pulling straight down on the Force Sensor, and the lower part should be parallel to the table.

4. Run the program BUNGEE. Follow the directions on the screen. Move the cart until it is near the pulley, taking care to keep the elastic and thread from knotting or jumping off the pulley. Push the cart towards the Motion Sensor when you hear it begin clicking.

5. Once the data is collected, a menu will appear. Either of two graphs can be drawn, Force vs Time or Velocity vs Time, or both. The program has been designed to "auto-scale", meaning the graph will expand so the data will fill the entire screen.

6. Examine each of the individual graphs. Can you determine where the cart reached the end of its free roll and began stretching the elastic cord? (Motion is negative going towards the sensor, while motion away from it is positive.) Can you see where the cord begins to stretch, exerting increased force on the Force Sensor? If this isn't clear, get help from the instructor.

7. The function "TRACE" is automatically chosen with each graph. On the Velocity vs Time graph, choose a place where the velocity is turning from negative to positive. Move the blinking cursor to that point and record the values T1 and V1. Move the cursor to a point near where the velocity has its maximum positive value, then record T2 and V2.

8. Return to the menu by pressing [ENTER] twice and select "Integrate". When asked, give the values for T1 and T2, which will be the limits for integration of the force graph. The numerical integral, the area under the graph from T1 to T2, is the impulse given by the elastic cord during that time interval.

9. Repeat the experiment with different elastic cords or combinations of elastic cords. Be aware of differences in duration of the impulse, size of the force, etc. Be prepared to discuss these differences and why they're different.

## DATA:

Mass of Cart: ___________________

 Trial T1sec V1m/s T2sec V2m/s Area (I) N s Dpkg m/s 1 2 3 4 5

## ANALYSIS:

1. Calculate the change in momentum for each run. Enter the results in the table.

2. Theory states that the change in momentum is equal to the net impulse. Does your data support this? What sources of error could account for any differences?

Click here to get the original MS Word document, bungee.doc. It is in Word 6.0 for Mac format.

Click here to get the UUEncoded CBL program, BUNGEE.UUE. It is for TI-82, and once it is decoded, it can be converted to the correct format for other calculators using the appropriate TI-Graph Link program.

Updated 5/16/98