14-Oct-2014: Collision in Two Dimensions

Purpose:
The purpose of this lab is for students to observe two-dimensional collision and determine if momentum and energy are conserved.
Apparatus:
The camera, attached to a pole, looks down at the glass board, and is able to view the entire board. By placing two balls on the board, the camera should be able to record the motion of both balls along a
xy-plane. The camera should be set up properly: shutter should be zero, reduce exposure, and increase gain so that camera can see the motion of both balls clearly. One ball should be set in place, while the other ball comes into contact with it at an angle, so that both balls should move at different angles.

Explanation:
With the apparatus all set up, we recorded to different trials: steel on steel and marble on steel. The first trial was steel on steel. One steel ball was set in place, and the second one was aimed to hit the stationary ball at an angle. With the camera recording, we rolled the ball out and both balls moved at different angles away from each other and at different speeds. We used the recording and traced the paths of both steel balls, and came up with position and velocity in x-direction and y-direction for both steel balls. We set the coordinates so that the origin is where the rolling ball first moved. The x-axis is aligned with the motion of the rolling ball so that the y-direction had no value until the balls collided.

By finding the slope of each line before the collision and after the collision, we are able to find the average velocity of each line. With the velocity, can find kinetic energy in the x and y-direction. The energies need to be consistent throughout the procedure of this lab. By plotting the energies on one graph we can see that the kinetic and potential energy has a slope closely to zero, which means that energy was not lost through the procedure.

Also, with the velocity, we were able to calculate the momentum of this trial. The initial momentum for both x and y-direction were both slightly larger than the final momentum, by a percent difference of 0.409%. During the collision, the rolling ball was spinning vertically, which is believed to have lost some energy in the spin.

The second trial was marble on steel, where the marble is the stationary ball, and the steel ball is the rolling ball. Since the steel ball is heavier than the marble ball, the motion of the marble after the collision will be more faster in general in comparison with the first trial. Knowing that the marble ball has a faster velocity, we can still assume that the energies are conserved in this procedure. We graphed the position of x and y-direction vs time, just like in trial 1, and found the velocity of each different motion.

 With the velocity, we can find the kinetic energy  for both balls. From the graph, we see that the energy has a slope of zero, which means that the energy was conserved.

After calculating the momentum, we can conclude that momentum was conserved with a percent difference of 13.8%, which is quite large since the value is higher than 10%. This is due to the difference in the mass, and the spin in the steel marble after the collision; the spinning was a cause of energy lost.

Conclusion:
In this lab, we discovered that energy and momentum was conserve by graphing kinetic energy and calculating the momentum of the initial velocity to the final velocity. There were lost in energy and momentum when the steel balls was spinning after the collision.