# CONSERVATION OF LINEAR MOMENTUM USING PHOTOGATES AND DIGITAL TIMER

## PURPOSE:

Assuming no external forces exist, the initial momentum of a system should equal the final momentum of a system. This laboratory will investigate the conservation of momentum when the initial momentum is zero and when it is greater than zero.

## EQUIPMENT

• 2 Dual Photogates
• 2 Digital Timers
• 2 Dynamics Carts (one plunger cart and one collision cart)
• various Masses
• Balance

## PROCEDURE I:

1. Set up one photogate at the total length of the cart track and one at the total length
2. Plug the phone cord from each photogate into slot A on separate digital timers. Set each timer as follows:
• Time (blue button on upper right) to read in milliseconds XXXX.
Mode (green button on left) to 00 "Stop on B". Both lights will be off.
Mode (white switches on left) to normal. Both switches will be down.
3. Place a flag on the top of the cart to use to block the photogate. Measure the width of the flag. This will be distance (d) to use in calculation of the velocity of the carts.
4. Measure the mass of each cart and add mass to make each cart equal in mass.
5. Push in the plunger on the plunger cart and place the collision cart and plunger cart as indicated below.
6. Ensure that the time has been reset to zero and release the plunger trigger.
7. Record time for each cart .
8. Reset the timer and repeat the steps 5-7 for a total of three times.
9. Complete the calculations required by the data table. Remember that the carts move in opposite directions. Be sure to define which is positive and which is negative.

## DATA:

 Trial 1 Trial 2 Trial 3 Cart 1 Cart 2 Cart 1 Cart 2 Cart 1 Cart 2 Mass(kg) Initial velocity(m/s) Initial momentum(kg m/s) Width of flag(m) Time(s) Calculated velocity(m/s) Final momentum(kg m/s) Impulse(Ns)

## QUESTION:

Calculate the total momentum of the SYSTEM before and after the collision. Explain your results.

## EXTENSIONS:

Repeat the experiment but add extra mass to one cart. For example, one cart may have a mass of 0.5 kg and the second cart may have a mass of 1 kg.

Repeat the experiment with just one cart colliding with a fixed object (the stop on the end of the track).  Calculate momentum of the cart before and after the collision.

## PROCEDURE II:

1. Set up one photogate at the total length of the cart track and one at the total length
2. Plug the phone cord from each photogate into slot A on separate digital timers. Set each timer as follows:
• Time (blue button on upper right) to read in milliseconds XXXX.
Mode (green button on left) to 00 Stop on B. Both lights will be off.
Turn Mode (white switches on left) to flag. First switch will be down and the second switch will be up.
3. Place a flag on the top of the cart to use to block the photogate. Measure the width of the flag. This will be distance (d) to use in calculation of the velocity of the carts.
4. Measure the mass of each cart and add mass to make each cart equal in mass.
5. Place the collision cart and plunger cart at opposite ends of the track.
6. Ensure that the time has been reset to zero and give each cart a gentle push to produce a head-on collision.
7. This step requires coordination and cooperation of the group. As soon as the time is read, push the reset button before the carts return through the gate. Record times for each cart .
8. Complete calculations required by the data table. Remember that the carts move in opposite directions. Be sure to define which is positive and which is negative.

## DATA:

 Trial 1 Trial 2 Cart 1 Cart 2 Cart 1 Cart 2 Mass(kg) Width of flag(m) Time 1(s) Initial Velocity(m/s) Initial Momentum(kg m/s) Time 2(s) Final Velocity(m/s) Final momentum(kg m/s) Impulse(Ns)

## QUESTION:

Calculate the total momentum of the SYSTEM before and after the collision. Explain your results.

## EXTENSION:

Repeat the experiment but add extra mass to one cart. For example, one cart may have a mass of 0.5 kg and the second cart may have a mass of 1 kg.

## TEACHER NOTES:

Procedure 1 is reproducible with less that 1% error.

Procedure 2 is more difficult to reproduce. A mechanical launcher would be preferable.

Note that for procedure 2 the mode setting on the digitial timer must be set to flag for the timer to record as the cart moves through the photogate twice.

Written by Janice Hudson, 1997