Lab 15: Collisions in two dimensions

Collisions in Two Dimensions

I-Shou Lin, Kirk Paderes, Jorge Avalos

4/24/17

To record a two-dimensional collision with two balls and analyze if momentum and energy are conserved through graphical analysis

When collisions occur, they often last for just a small instant in time. However, during the collision, the objects that are being collided experience changes in both kinetic energy and momentum. In the case of a two-dimensional collision with two balls of different masses, a recording device can capture the motion of the two balls before, during, and after the collision. With the help of a logger pro, the position vs time graph for the two balls throughout the entire " journey" can be produced. Then, we verify if the momentum and kinetic energy is conserved in this collision. 

The laboratory procedure consisted of putting a recording device on the top of the stick over the glass table. Then, the balls collide with one another and then the recording is taken and uploaded onto logger pro for further analysis. 


( leveled glass table apparatus) 
Data Table

Experiment 1	Ball 1	Ball 2
Mass	0.005 kg	0.005 kg
Velocity, x ( initial)	0.1137 m/s	0.000 m/s
Velocity, x ( final)	0.04678 m/s	0.0494 m/s
Velocity, Y ( initial)	-0.0041 m/s	0.000 m/s
Velocity, Y ( final)	0.02755 m/s	-0.02964 m/s

experiment 2	Ball 1	Ball 2
Mass	0.005 kg	0.003 kg
Velocity, x ( initial)	0.1179 m/s	0.000 m/s
Velocity, x ( final)	0.05373 m/s	0.05131 m/s
Velocity, Y ( initial)	-0.002279 m/s	0.000 m/s
Velocity, Y ( final)	0.02042 m/s	-0.02275 m/s

( screenshot of experiment 1)

( screenshot of experiment 2) 

               ( Xcm and Ycm vs t, and Vxcm and Vycm vs t)

 ( Experiment 1)

 Xcm and Ycm vs t, and Vxcm and Vycm vs t)

( Experiment 2) 

Conservation of Momentum ( experiment 1)

                    X component

       m(1x1i)+m(2x2i) = m(1x1f)+m(2x2f)

       0.005 kg*0.1137 m/s +0.005 kg*0.00 m/s=0.005 kg*0.04678 m/s+0.005 kg * 0.0494 m/s

       0.1137 m/s+0.000 m/s = 0.04678 m/s+ 0.0494 m/s

        0.1137 m/s = 0.09618 m/s  

          not conserved, but close 

Y-Component

m(1y1i)+ m(2y2i)= m(1y2f)+ m (2y2f)

y1i+y2i= y1f+y2f

-0.0041 m/s+0.000 m/s= 0.02755 m/s+ (-0.02964 m/s)

-0.0041 m/s = -0.00209 m/s

 not conserved

Conservation of kinetic energy ( experiment 2) 

k.e.i=k.e.f

The first two graphs depict the position of the two balls before, during, and after collision in their components for experiment 1 and experiment 2. With the position of their components graphed, it makes the analyzing how the collision affected the position of the two balls. Then, the velocity of the two balls can be determined through the change in position divided by the elapsed time. The last two graphs show the position vs time graph and velocity vs time graph of the x and y components of the center of mass of the two system. The center of mass divided into the x and y components tells us if whether the collision is elastic or not by looking to see the slope of the position vs time graph for acceleration and by looking at the velocity of the center of mass vs time graph to see if there are changes in the slope of the velocity of the center of mass vs time graph. The position of the center of mass can be calculated through the center of mass formula. and the velocity of mass is found by taking the derivative of the center of mass formula with respect to time.

This lab was a fairly straightforward lab in terms of setup and data recording. However, analyzing the data for position vs time and then graphing these for analysis was more time consuming. The two main principles in this experiment are conservation of momentum and conservation of kinetic energy. In an ideal world, momentum and kinetic energy would both be conserved. The results show that momentum and kinetic energy aren't conserved. The momentum values before and after the collision are fairly close, but the kinetic energy values aren't. These may be due to the work done by non-conservative forces such as friction and other forms of energy such as sound energy. When the two balls collided, there was a noticeable sound. This energy came from the initial kinetic energy of the two balls. Therefore, the collision isn't an elastic collision.