14- Oct.- 2014 2D Collision Lab

2-D Collision Lab

Objective: Show that momentum is conserved for a 2-D collision.

Set Up:

Figure 1. A screenshot of motion tracking
 one of our trials.

With a camera, smooth surface, and a camera set up above looking down (as seen in fig 1)we take 3 round balls 2 of which are made of steel and are similar masses while the third mass is made of aluminum with a smaller amount of mass than the steel balls but relatively the same size. We do two trials, one with two steel and another trial with one steel and the other aluminum.

Data Collection:
As we finished video recording the collisions, we tracked their path in each frame as it was graphed (as seen in Fig 2A. and 3A.) From there we created linear fits for each mass before and after collision to get an average velocity in both ends of the trial. We then made calculated columns for momentum of the system in the x and y axis at any given time and then another calculated column for kinetic energy (seen  in fig 2B, and 3B).:

1) We found that the momentum in the x and y directions:

before collision: (mass 1)*(V1 in x or y)+ (mass 2)*(V2)=
after collision:     (Vf in x or y)*(sum of both masses)

2) We also found momentum of the system to calculate average overall velocity for each mass for any given time during and after collision:

p^2 = px^2 + py^2
m*v^2 = m*vx^2 + m*vy^2

3) Then used the found velocity to find total Kinetic Energy at any given time:

KE= .5*mass 1*(v^2) + .5*mass 2*(V^2) = 5*mass 1*(vx^2 + vy^2) + .5*mass 2*(Vx^2 + Vy^2)

Our first trial with the two steel balls show that resulting velocities after collision are close to parallel since they are the same mass (seen in Fig 2A.). However, possibly due to spin on the ball, it does not seem to show much consistency or conservation in the Kinetic energy column. Nevertheless, it does show consistency in in each momentum column (as seen in Fig 2B.). In trial two since the aluminum ball was initially in motion in this collision, it makes little change to the velocity of the steel ball it collides with and does not seem to have a great change in velocity (seen in 3A.). Numerically, it seems to show much more conservation in kinetic energy compared to trial one while still maintaining consistency in momentum of the system (seen in Fig 3B.).

Figure 2A. Trial one positions before and after collision with linear fit graphs to
find each of the average velocities for calculating momentum in both x and y directions.

Figure 2A. Our numerical results for our first trial for momentum in both the x and y directions as well as our calculated kinetic energy at any given time.

Figure 3A. Trial two positions before and after collision with linear fit graphs to 
find each of the average velocities for calculating momentum in both x and y directions.

Figure 2B. Our numerical results for our second trial for momentum in both the x and y directions as well as our calculated kinetic energy at any given time

Conclusion:

This lab for the most part shows that in both systems there is a conservation in momentum, but conservation in kinetic energy is only found in trial two. Initially it was suspected it was due to misreadings of masses, but we remeasured our masses and found them to be the same once again. We believe that any source of uncertainty would be from spin of the ball, imperfections of the ball, imperfections of the surface and approximated motion tracking credited to human error.