2015-April-22 Lab 15: Collisions in Two Dimensions

PURPOSE:  To determine whether energy and momentum are conserved in a two-dimensional elastic collision.

Set up with a camera above the table to record an aerial view of the collision of balls.

The three balls we used:
in first experiment: 2 steel balls (same masses)
in second experiment: 1 steel ball and 1 aluminum ball

Using a video camera, we recorded from aerial view the position of a steel ball rolling and hitting another steel ball at rest, which then caused the steel ball at rest to move.  The video recorded x-direction and y-direction of the ball as separate lines.  We used Logger Pro to trace the path of the first ball in each direction, and took the slope of the position before and after the collision, which gave us velocity in the x and y directions.  We did the same for the second ball, starting from the collision, to find its velocities.

With this information we were able to use the equation for conservation of momentum in the x-direction and then in the y direction to see if momentum before the collision was equal to momentum after the collision.

The results for momentum in the y direction look like the would be within 50% error, but if you take it in relation to the total magnitude, we can see that momentum is relatively conserved.

We then used the equation for conservation of energy to see if kinetic energy was conserved during the collision.  However, our value for kinetic energy before and after the collision were not equal, proving that kinetic energy was not conserved.  We can assume that some was lost to heat during the collision.

We then did the same for a collision with a steel ball and aluminum ball, to see if momentum and energy were also conserved in a collision with two different masses.

Again, we used the conservation of momentum to find momentum before the collision and after the collision, in both the x and y directions.

In relation to the magnitude of momentum, both momentum in the x and y direction were conserved.

Then we used conservation of energy to see if kinetic energy was conserved during the collision.  Our results showed that kinetic energy was not conserved, and we can assume it could be lost to heat during the collision.

CONCLUSION:

Based on our experiment, we can conclude that momentum is conserved in an elastic collision, but kinetic energy is not.  Total energy is conserved, but some of the kinetic energy is converted to heat during the collision.  For both kinetic energy equations, kinetic energy was greater before the collision than after the collision.  We showed that momentum was conserved by breaking up velocities of the balls in both the x and y directions and multiplying by the masses of the respective balls.