24 Apr, 2017: Collisions in two dimensions

Lab 15: Collisions in Two dimensions
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date of lab performed: 24-Apr-2017

Purpose of the lab: The purpose of the lab is to observe two different collisions (one with two marbles and one with a metal ball and marble) and determine if momentum and energy is conserved


Theory: The idea behind is lab is to see if the conservation of momentum and conservation of energy can be verified from the two different collisions. Conservation of momentum is defined as "m1v1o* + m2v2o = m1v1f* + m2v2f" (* o stands for initial and f stands for final). The conservation of energy is defined as "1/2 m1 vo^2 + 1/2 m2 v0^2 = 1/2 m1 vf^2 + 1/2 m2 vf^2".  To verify conservation of energy and conservation of momentum, we measured the masses of the marble and metal ball and the initial velocity of the balls before and after they collide.

Summary of the apparatus:

We used this apparatus to do the collisions between two marbles and between marble and metal ball. We first measured and recorded the mass of the marbles and metal ball. We put the slo-mo camera on top in order to record the change in position of the balls as they collide. After recording both collisions, we put the videos in logger pro to plot the change in positions of the balls. We put the points on a position (y-axis) vs time (x-axis) graph

position vs time for collision between one metal ball and one marble

Position vs time for collision between two marbles

We found the initial velocity of the balls by taking the slope of the lines of the balls in the y - direction before the collision began. The way we determined when the collision began is when the x and y position lines of the second ball goes from a straight horizontal line to a sloped line. We took the final velocities of the balls by taking the slopes of the x and y position lines after the collision.

 Measured data

Calculated results

position vs time Graphs shown above

Verified if conservation of energy applied to the same ball collision in the x -direction

Verified if conservation of momentum applied  to both collisions in x and y directions

Explanation of Graphs

The reason why we made a position vs time graphs for both collisions was because we were able to find the velocities of the ball by taking the slope of the position lines. We were able to find initial and final velocities in x and y directions (method mentioned above) using this method. 

Conclusion

 

Although conservation of momentum applied for the x-direction and y-direction of the same ball collision as well as the x-direction of the different ball collision, momentum was not conserved for the different ball collision in the y-direction. This error may have occurred because the plots may have not been plotted correctly, which may lead to different values for velocities. Since the surface the collisions took place was not frictionless, the balls may have lost velocity as it travelled on the surface, which lowered the value of velocity and affected our calculations for both momentum and kinetic energy of the balls. The surface may have not been as leveled as we thought, so the velocities we have recorded may not have been the true velocities of the balls. 

Although the conservation of energy was verified for the same ball collisions in the x and y directions  as well as the different ball collisions in the x-direction, energy for the different ball collisions in the y-direction was not conserved. Again, this error may have occurred because of friction, uneven surface, or error in plotting points.