17-Oct-2016: Lab 15 Collision in two dimensions

1. Title: Lab 15 Collision in two dimensions
    Name: Qiwen Ye (Sherry)
    Lab Partners: Jae Yoo, Chandler
    Date: 17-Oct-2016

2. Purpose
The purpose of this experiment was to look at two dimensional collisions in order to determine if momentum and energy are conserved. 

3. Introduction
We measured the total momentum of steel ball with glass ball and steel ball with plastic ball after a glancing collision and to find the initial and final momentum and energy. At first, we did the experiment about steel ball with glass ball, then we did experiment about steel ball with plastic ball. 

4. Apparatus/Experimental Produce
At first, we leveled the glass table and put the stationary ball on the leveled glass table. Set up a iPhone as the camera on the top of the glass table in order to take a video form aerial view the position of a ball rolling and hit another ball at rest. Aimed the rolling ball so that it hit that side of the stationary ball. Then balls ideally rolled off at some decent angle from one another. After setting up, we inserted the videos into LogPro to analysis the motion trajectory of two balls. Set origin and added point series to record the motion of two balls. Through the LogPro, we opened the Option Menu, Movie Option, choose Override Frame Rate to 60 fps and Advance the movie 2 Frame after adding a new point. 

5. Measured/Graph of Data
Part 1: Steel Ball and Plastic Ball
1) Used the LogPro to describe the motion trajectory of two balls. The blue line was the motion trajectory of the plastic ball; the red line was the motion trajectory of the steel ball. The center line was the motion trajectory of center of mass. 

2) After we recorded the motion trajectory of two balls, we had a lot of points placed on the graph of distance vs. time. Then, used the linear fit to get each lines. The x-direction and y-direction of the ball as separate lines. 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, with gave us velocity in the x and y directions. 

3) Used Logger Pro to find the position of the center of mass. Created a new formula in Logger Pro (m1*x1+m2*x2)/m1+m2 to produce the graph:

Xcm vs. t And Ycm vs.t

4) Used Logger Pro to find the velocity of the center of mass. Created a new formula in Logger Pro (m1*v1+m2*v2)/m1+m2:

Vx-cm vs.t And Vy-cm vs. t

Part 2: Steel ball with Glass ball

1) Did the same process as part 1 to record the motion trajectory of two balls. The red line was the motion of glass ball, the blue line was the motion of steel ball and the center line was the center of mass of both balls. 

2) It was the same as part 1, through the graph about distance vs. time, we got the velocities before collision and after collision in x and y direction. :

3) Created a new formula in Logger Pro (m1*x1+m2*x2)/m1+m2 to produce the graph about the position of the center of mass:

4) Created a new formula in Logger Pro (m1*v1+m2*v2)/m1+m2 to get the graph about the velocity of the center of mass:

6. Calculated Data

Used the equation for conservation of momentum in x and y direction to see if momentum before the collision was equal to momentum after the collision. 

Part 1: Steel Ball and Plastic Ball

Part 2: Steel Ball with Glass Ball

Used the equation for conservation of kinetic energy in x and y direction to see if kinetic energy before the collision was equal to kinetic energy after the collision. 

Part 1: Steel Ball and Plastic Ball

Part 2: Steel Ball with Glass Ball

7. Explanation/Analysis

Through the equation of conservation of momentum and kinetic energy, we found that the initial and final momentum and kinetic energy were not equal in those collisions. The different percent of initial and final momentum of the steel and plastic ball was 13.6%, and the steel and glass ball was 15.1%. The different percent of initial and final kinetic energy of the steel ball and plastic ball was 11.2%, and the steel and glass ball was 23.3%. And, we found that the initial kinetic energy was bigger than the initial energy.

8. Conclusion

In this experiment, we determined kinetic energy was not conserved because some of kinetic energy was converted to another form of energy, such as heat; therefore, the kinetic energy was not conserved in those collision. But the total energy was conserved because the initial kinetic energy was equal to the final kinetic energy and the energy of heat. Also, the momentum was not conserved because the net external force on a system was not zero. The glass table that the balls were rolling was not friction less; therefore, it caused the velocity slow down and momentum was not conserved.