22-APR-2015 Collision In Two Dimensions

Collisions In Two Dimensions

(Is Momentum & Energy Conserved?)

Purpose:  In this lab, we're to determine whether or not momentum and energy are conserved in a two dimensional collision.

Procedure:  In order to easily collect data for this experiment, we observed a collision between two balls (metal v. metal / metal v. aluminum) on an ideal surface while recording the collision from an overhead camera.  This is shown below:

(Experiment Apparatus)

(Ideal surface for experiment)

We measured the mass of each steel ball and the aluminum ball:

m1 = m(steel ball #1) = 66.5 g

m2 = m(steel ball #2) = 66.8 g

m3 = m(alum. ball)   = 10.1 g

We then proceeded to video capture the collision from the overhead camera.  This video was manipulated within LoggerPro in order to capture the motion BEFORE and AFTER the collision.  An example of this is shown below.

(Screenshot of Video Capture from Overhead Camera)

By plotting points throughout the length of the video, LoggerPro can display these motions graphically!!  The manner in which it does this, is that LoggerPro displays the changes in position  in both the x and y directions for EACH particle it is tracking (the balls).  By performing linear fits upon these graphs, we can determine the slope of each, which gives us the velocity of each ball in x and y component forms!

Below are the graphs for the Hit-Er ball before and after the collision, followed by the Hit-Ee ball after the collision.

(Hit-er before collision)

This is the motion of m2; from this, we have:

Vox = - 0.06285 m/s

Voy =    0.3800 m/s

(Hit-er after collision)

This gives us:

Vfx = - 0.1643 m/s

Vfy =   0.2183 m/s

(Hit-ee after collision)

This graph represents the change in position vs. time of m1; which reveals:

Vfx = 0.1029  m/s

Vfy = 0.1783  m/s

We now have all we need to determine whether or not momentum and energy have been conserved!  This analysis is depicted below:

(Momentum Calculations in x and y Directions)

(Energy Calculation)

What the first photo above displays, is that (for the most part) momentum is conserved after the collision in both the x and y directions.  The reason the value are not EXACTLY equal is due to sources of uncertainty (as momentum should ALWAYS be conserved).  These sources of uncertainty include such things as the "fish-eyed" camera which recorded the interaction (upon which all of our position v. time data is built), user error in plotting points during the video analysis, an improperly leveled surface, or incorrect mass readings during measurements.

The Energy calculation percent difference is much more interesting.  Energy is lost within the system, which explains the larger deficit between the two calculated values on either side of the equation.  Energy was lost in the form of sound (when the two objects collided) as well as some heat (miniscule as it may be, it contributes to energy lost in the system).