22-Apr-2015: Collisions in two dimensions

Purpose: To look at two-dimensional collisions using a marble ball and steel balls in order to determine if momentum and energy are conserved.

Procedure: We have a flat square surface where we observe the elastic collisions between two steel balls and another elastic collision between a steel ball and a marble ball. A camera is attached to a horizontal rod and hangs over the square surface by a vertical rod.

Lab apparatus of collisions in two dimensions

camera for video capturing the collisions

To set up the camera, we open up logger pro and go to the video capture tab. We click "camera settings", then "adjustments", then "image". From here we set the shutter to zero ,reduce the exposer, and increase Gain so that we get a reasonable image from the camera onto the screen.






For the experiment, we start by setting the stationary ball around the middle of the leveled glass table. We wanted to aim the rolling ball so that it hits the side of the stationary ball, so that we create a two dimensional collision where the balls roll off at some decent angle from one another. The aim is record the position over time of the two balls in order to test whether or not momentum and energy were conserved in the two-dimensional collision. The equation for the conservation of momentum and conservation of energy are as follows, respectively.

M1*U1 + M2*U2 = M1*V1 + M2*V2

1/2*M1*U1^2 + 1/2*M2*U2^2 = 1/2*M1*V1^2 +1/2*M1*V2^2 

The first collision involved two steel balls of the same mass. We measured both masses to be equal at 66.6 g. We roll the ball into the side of the stationary ball and record so we can plot the position at each corresponding time on the video capture.

video capture of steel vs steel balls with point series

After recording the collision, we create an an axis so that it matches up with our collision and set the origin at the point of collision between the balls. Then we create a point series for both balls for the duration of the experiment. Using these points we can create a graph of the x and y positions over a substantial time period.

graph of x and y positions of both balls over time

We then collect the data for the initial velocity of the rolling steel ball and the final velocities of both balls after the collision in order to calculate whether momentum and energy were conserved or not.

Our calculations showed that momentum and energy were both in fact conserved.

For the second collision we wanted to see whether momentum and energy are conserved between two balls of different masses. We use the marble ball as the stationary ball and roll the steel ball into its side and capture the collision.

video capture of steel ball colliding with the marble ball

Using those points, we were able to plot the graph of the x and y positions over a substantial time period.

graph of x and y positions of both balls over time

Finding the initial velocity of the rolling ball and the final velocity of the two balls helped us to test whether momentum was conserved in this collision. Our results verified that momentum and energy were both conserved.

Conclusion/Uncertainty: Using video capture to record the position of the balls over time gave us the velocity of the balls before and after the collisions. The velocities of the balls before and after the collisions and the masses of the balls were inputed into the conservation of momentum and energy equations to see whether momentum and energy were conserved in these 2 dimensional elastic collisions. Our values came out very close, verifying that momentum and energy were in fact conserved.

Uncertainties in the lab came in tracking the balls using the video capture because sometimes it was hard to be accurate with the plotting of the points. Human error in measuring masses also skew the results slightly.