Ap Momentum Lab

Purpose: (tim)
The purpose of this lab is to investigate conservation of momentum and the transfer of momentum with objects of the same mass but with varying velocities in elastic collisions.

Equipment: (tim)
Air Track
Air Track cars (same mass)
Photo-gate timers
Laptop
Meter Stick

Procedure: (tim)
Set up the Air Track
Measure the mass and length of each Air Track car.
Set up the Photo-gate timers- each timer should be the same distance away from each end of the track.
Place one car in the middle of the track in between the two timers, and make sure it is at rest.Place the second car before the first photo-gate timer at the end of the track.
Using the photo-gate timers, push the second car, making sure you release the push before the photo-gate timer.
Measure the velocity of the first car before and after the collision, and measure the velocity of the second car after the collision using the photo-gate timers.
Repeat steps 4-6.
Now, place each car at the end of the track.
Have one person (this may take more than one try to get near accurate results) push each car, at the same time, with the same speed towards each other.
Using the Photo-gate timers, make sure the speeds of the cars are very similar after the push coming towards each other, and if they are, use the timers to measure the speeds of each car after the collision.
Repeat steps 8-10.
For the third scenario, the Photo-gate timers may need to be moved, one shifted so that both cars can fit before going through the timer, and the other moved more towards the opposite end of the track.
Now, place both cars at the end of the track with more space between the end of the track and the timer.
Have one person push the car in front, very slowly, so that its speed is recorded when it passes through the first photo-gate timer.
Then, have that person push the second car with a higher velocity, so that its speed is not only measured by the first photo-gate timer, but so the two cars collide between the two timers.
After the collision have one person at the opposite end of the track than where the cars were pushed, and immediately after the front car goes through the timer so that its velocity after the collision is measured, have the person pick up this car off the track.
Next, allow the second trailing car to go through the second timer and have its velocity be measured after the collision.
Repeat steps 12-17.

Data: (shelby)
Car 1/Car A:
Length: .198m
Weight: 300.9 g
Car 2/Car B:
Length: .189m
Weight: 300.0 g

Scenarios:
One car in motion collides with another car at rest
Trial One
Initial Velocity (m/s)
Car 1 : .1727
Car 2 : 0
Final Velocity (m/s)
Car 1 : 0
Car 2 : .1677
Trial Two
Initial Velocity (m/s)
Car 1: .2644
Car 2 : 0
Final Velocity (m/s)
Car 1: 0
Car2: .2351

Two cars in motion collide into each other with the same speed
Trial one:
Initial Velocity (m/s)
Car 1: .2946
Car 2: -.2916
Final Velocity (m/s)
Car 1: -.2075
Car 2: .2348
Trial two:
Initial Velocity (m/s)
Car 1: .2543
Car 2: -.2723
Final Velocity (m/s)
Car 1: -.2066
Car 2: .2179

Two cars collide traveling different speeds and in different directionsTrial one:
Initial Velocity (m/s)
Car 1: .2285
Car 2: -.0658
Final Velocity (m/s)
Car 1: -.0483
Car 2: .2203
Trial two:
Initial Velocity (m/s)
Car 1: .3554
Car 2: -.1179
Final Velocity (m/s)
Car 1: -.0791
Car 2: .3302

Two cars traveling in same direction, however car in back is faster so collides with the one in front.
Trial one:
Initial Velocity (m/s)
Car 1: .2498
Car 2: .0907
Final Velocity (m/s)
Car 1: .0963
Car 2: .2487
Trial two:
Initial Velocity (m/s)
Car 1: .1040
Car 2: .3184
Final Velocity (m/s)
Car 1: .3217
Car 2: .1071

Analysis(first three): (nate)
Is Momentum Conserved When…

One car in motion collides with another car at rest?
Yes, we found that momentum is conserved in this scenario.
Trial One
Initial Velocity (m/s)
Car 1 : .1727
Car 2 : 0
Final Velocity (m/s)
Car 1 : 0
Car 2 : .1677
Trial Two
Initial Velocity (m/s)
Car 1: .2644
Car 2 : 0
Final Velocity (m/s)
Car 1: 0
Car2: .2351

From the data in trial #1 and # 2 we see that the velocity of Car 1 is transferred to Car 2. Taking into account that the system is not frictionless these numbers confirm that momentum is conserved. Trial #1 is highly supportive while Trial #2 encounters more error due to frictional forces.

Two cars in motion collide into each other with the same speed?
Yes, we found that momentum is conserved in this scenario.

Trial One:
Initial Velocity (m/s)
Car 1: .2946
Car 2: -.2916
Final Velocity (m/s)
Car 1: -.2075
Car 2: .2348
Trial Two:
Initial Velocity (m/s)
Car 1: .2543
Car 2: -.2723
Final Velocity (m/s)
Car 1: -.2066
Car 2: .2179

From the data in trial #1 and # 2 we see that the velocities before and after the collisions support that momentum is conserved. The initial velocities of Car 1 and Car 2 begin at approx. the same velocity (accounting for human reflex/timing and frictional errors which are very slight in trial #1’s initial velocities) switch during the collision and exit the photo gates at approx. the same velocity, again accounting for frictional and human error. In the second trial we see the same pattern.

Two cars collide traveling different speeds and in different directions?

Yes, we found that momentum is conserved in this scenario.
Trial One:
Initial Velocity (m/s)
Car 1: .2285
Car 2: -.0658
Final Velocity (m/s)
Car 1: -.0483
Car 2: .2203
Trial Two:
Initial Velocity (m/s)
Car 1: .3554
Car 2: -.1179
Final Velocity (m/s)
Car 1: -.0791
Car 2: .3302

From the data in trial #1 and # 2 we see that the velocities before and after the collisions support that momentum is conserved. The initial velocities of Car 1 and Car 2 begin at different velocities, then switch during the collision and exit the photo gates at different velocities. In both trials we see the velocities switch during the collision, and the fast car becomes the slow car and the slow becomes fast, supporting that momentum is conserved. However, the data is slightly flawed due to frictional forces of the track.

Conclusion: (tim and shelby)
Overall, we found that momentum WAS conserved. In each scenario, disregarding friction and small human error, we found that the momentum we gave the car at the beginning of each scenario was conserved throughout the trial. Although the air track is not completely frictionless, it is good to test collisions over small distances. In each scenario, we tested the conservation of momentum equation. Since the masses of the cars were slightly different but taken to be the same, we realized the only variable was there velocities. Thus, theoretically the cars shouldswitch velocities after collidding.
Our data, despite being slightly skewed, due to friction and the small differences in mass and length in the cars, proves this theory. There were no surprising results because we thought the velocities would be slightly different, due to the small differences in mass and length the cars had, and also due to friction. Possible sources of error include friction (slowing down the velocities of the cars after the collisions), diffferences in mass and length of the cars (affecting the velocity changes), and human reaction time (pushing the cars at different speeds). If we could have a longer track with less friction, we would be able to measure these results more accurately because human reaction time would be virtually negligible. Overall this experiment proved our theory.