Introduction
The purpose of this experiment was to observe collisions between two carts, measure energy changes and classify the collisions. It was hypothesized the momentum would be conserved during the collisions.
- Consider a head on collision between two billiard balls. One is initially at rest and the other moves towards it. Sketch a position vs. time graph for each ball, starting with the time before the collision and ending a shot time afterward
Before collision, ball 2 moves with a constant velocity towards ball 1. Therefore, its position changes with time while the position of ball 1 does not change. After elastic collision, the two balls do not stick together, ball 2 stops and transfers its kinetic energy to ball 1. Consequently, ball 1 moves with the same speed ball 2 were moving at before collision. The positions of ball 1 change with time while the position of ball 2 remains constant (at rest) after collision. The assumption made is that the two balls have equal masses.
- Is momentum conserved in this collision? Is kinetic energy conserved?
Both momentum and kinetic energy is conserved in the collision. It is an elastic collision.
Materials
- Window PC running on Logger Pro
- Dynamics cart track
- Two low friction dynamic carts with magnetic and Velcro bumpers
- Two vernier motion detectors
- LabQuest 2 Interface
- Two DIG Cables & One MINI-USB cable
Procedure
- The masses of the carts was measured and recorded in data table
- The track was set until it was horizontal
- Cart 2 with magnetic bumper was placed in the middle of the track and cart 1also having a magnetic bumper was released. It was observed that cart 1 rolled towards cart 2.
- A motion detector was placed at each end of the track 0.5m away from the carts. The detectors were connected to DIG1 and DIG 2 of LabQuest 2 interface. Thereafter, Labquest2 interface was connected to the PC using Mini-USB cable
- The file named 18 Momentum Energy Coll.cmbl was opened.
- The Collect button was clicked. Procedure 3 was repeated and the resulting position time graphs were used to verify that the motion detectors tracked each cart properly throughout entire motion.
- Two carts were placed in the middle of the cart with Velcro bumpers facing each other and in contact. The Zero, button was clicked to zero the motion detectors.
Part 1: Magnetic bumpers
- The carts were repositioned such that the magnetic bumpers faced one another. The Collect button was clicked and procedure 3 was repeated.
- The average velocities for cart before and after collision were determined by clicking Statistics Button. The velocities were recorded.
- Procedure 9 was repeated as second run with magnetic bumpers and velocities recorded
Part II: Velcro Bumpers
- The carts were turned such that Velcro bumpers faced one another. New collisions were made starting with cart 2 at rest.
- The Collect button was clicked and the average velocities for the carts before and after collision were determined and reordered.
- Procedure 12 was repeated as second run with Velcro bumpers
Part III: Velcro to Magnetic Bumpers
- Velcro bumper on one cart was repositioned such that it faced magnetic bumper of the other cart. .
- The Collect button was clicked and the new collision was made. The velocities of the carts before and after collision were measured and recorded
- Procedure 15 was repeated as a second run to with Velcro to magnetic bumpers.
Results
Analysis
Momentum
Run 1
The momentum was calculated using the formula;
Mass X Velocity
mv
Momentum of cart 1 before collision
0.511 X 0.364 = 0.186 kg.m/s
Momentum of cart 2 before collision
0.510 X0 = 0 kg.m/s
Total momentum before collision
(0.186 + 0) = 0.186 kg.m/s
Momentum of cart 1 after collision
0.511 X 0.128 = 0.065 kg.m/s
Momentum of cart 2 after collision
0.510 X 0.316 = 0.161 kg.m/s
Total momentum after collision
(0.065 + 0.161) = 0.226 kg.m/s
Ratio of total momentum after and after collision 0.226/0.186 = 1.125
Kinetic Energy
The kinetic energy was calculated using the formula;
½ mv2
Run 1
Kinetic energy for cart 1 before collision
½ X 0.511X 0.3642
0.034 J
Kinetic energy for cart 2 before collision
½ X 0.510X 02
0 J
Total kinetic before collision
(0.034 + 0) = 0.034J
Kinetic energy for cart 1 after collision
½ X 0.511X 0.1282
0.004 J
Kinetic energy for cart 2 after collision
½ X 0.510X 0.3162
0.025 J
Total kinetic energy after collision
(0.004 + 0.025) = 0.029 J
Ratio of total kinetic after and before collision
0.034/0.029 = 1.360
If momentum is conserved, the ratio of the total momentum after collision to total momentum before collision would be equal to 1.
If kinetic energy is conserved, the ratio of the total kinetic energy after collision to total kinetic before collision would be equal to 1.
In all the collisions, magnetic bumpers, Velcro bumpers and Velcro to magnetic bumpers, the momentum was conserved because the ratio of the total momentum after collision to total momentum before collision was close to 1.
The kinetic energy was conserved in magnetic bumper collision because the ratio of the total kinetic energy after collision to total kinetic after collision was approximately equal to 1. The kinetic energy was not conserved for Velcro and Velcro to magnetic bumper collisions. The magnetic bumper collision was elastic because the total kinetic energy ratio was closer to 1. Velcro collision and Velcro to magnetic bumper collision were completely inelastic because the total kinetic energy ration was more than 1.5. This was an indication that the kinetic energy was gained during the collision.
Extensions
Momentum of cart 1 before collision
0.511 X 0.122 = 0.062 kg.m/s
Momentum of cart 2 before collision
0.510 X0 = 0 kg.m/s
Total momentum before collision
(0.062 + 0) = 0.062 kg.m/s
Momentum of cart 1 after collision
0.511 X 0.017 = 0.009 kg.m/s
Momentum of cart 2 after collision
0.510 X 0.132= 0.067 kg.m/s
Total momentum after collision
(0.009 + 0.067) = 0.067 kg.m/s
Ratio of total momentum after and after collision
0.076/0.062 = 1.226
The momentum is conserved because the ratio of total momentum after collision to the total momentum before collision is closer to 1
Conclusion
The experiment confirmed the hypothesis that the total momentum is conserved during collision. In all the collisions, the ratio of total momentum after collision to total momentum before collision was approximately equal to 1.
