- To determine the relationship between the force acting on an object
and the change in momentum of the object.

- force probe
- motion detector
- pulley
- cart
- string
- mass set and holder
- CBL
- TI-83 or TI-82 graphing calculator
- link cable
- Program: BUNGEE.83P

- If a constant net force

where the product F Dt is called the impulse.

If the force varies with time, then Equation 1 can be rewritten in Calculus form as:

where the quantity **F dt** can be integrated to find the area under the graph which then equals the total change in momentum.

- Set up the equipment as shown in Figure 1. Be sure to adjust the string above the table to be horizontal.
- Select the program
**BUNGEE**on the graphing calculator. The program will monitor both the force being applied to the cart and the velocity of the cart. This will allow you to determine both sides of Equation 1. - Select
**INSTRUCTIONS**and read through them. - Select
**CALIBRATE**AND USE A 500-g mass to calibrate the force probe. - Select
**CHANGE TIME**to set the time to collect data to 3.0 seconds. - Select
**COLLECT DATA.**Attach a mass to the mass holder. - After data is collected, select
**FORCE-TIME**to see a graph of force versus time that already is in the**TRACE**mode. Wait until the labels are displayed and then use the left- and right-arrows to select the times you wish to use. Record these times. - Press
**ENTER**twice to return to the Menu. If the data collection time needs to be changed, or if you need to take a better data run, select**NEW DATA**. - Select
**INTEGRATE**and enter the two times that you have selected. Press**ENTER**to display the value for the area under the graph. Record the value for the area and press**ENTER**to return to the Menu. - Select
**VELOCITY-TIME**. The graph will be in the**TRACE**mode. Use the arrows to determine the velocities at the same times as used in step 7. Record these velocities. - Repeat for an additional accelerating mass.
- Determine the mass of the cart plus force sensor.

- Calculate the momentum at both of the selected times and then calculate the change in momentum, Dp.
- Compare the calculated change in momentum to the corresponding impulse.

I've included some data that I took using the new Vernier dual range force meter. It worked well on the 50 N range but not so well on the 5 N range. The Pasco probe worked very well.

A few tips:

- Start the timer a few seconds before releasing the cart. You should be able to see the difference between the static and dynamic force but I wasn't able to using the Vernier probe.
- View the velocity versus time graph to see when you are getting a fairly constant acceleration and then integrate the force over this time interval.
- When entering the times for integrating, it is not necessary to have the exact corresponding times. If you are within 0.2 sec of the exact time, that should work well.
- The lab can be extended to other forces such as attaching a rubber band to the cart and monitoring as the cart comes to rest and then speeds up again or pulling the
string by hand. To do this second one, it would be necessary to remove the pulley and attach a small tube through which the string could be pulled. The purpose of the tube is to keep the
string horizontal to the table.
- For the data shown, I calculate a change of momentum of 0.56 Ns and the impulse to be 0.63 Ns, a difference of about 11%.

Written by Larry Russel. If you have any comments, please e-mail me.