Theory

This week we’re going to do a lab based on the conservation of momentum and coefficient of resititution. We’re going to let objects collide, see how their momenta change, and examine the effects of elastic collisions. There won’t be any graphs this week, but there will be quite a few tables.

Set-Up and Results

Go to the collisions experiment on the PHET website. Go to the Intro tag here.

  1. Check the box Kinetic Energy on the right and the box More Data on the left. Adjust the Elasticity slider to read 0%.
    Record the Kinetic Energy (0.44J here) and all the values in the More Data box (the Mass, Position, Velocity, and Momentum).
    Press Play.



2. Once the collision has ocurred, press the Pause button. Record the new values for the Kinetic Energy and the values in the More Data box. When you have done this, refresh the demo by pressing the blue button to the bottom right of the collision screen.



  1. Readjust the Elasticity slider to 20%. Repeat the measurements from steps 1 and 2 above. Do this again for Elasticity set to 40%, 60%, 80%, and 100%.



Data

Fill out a series of tables, one for each setting of Elasticity. For the values seen above, this is shown here:

Results for Elasticity = 0%
Mass (kg) V0 (m/s) Momentum0 (kg m/s) KE0 (J) Vfinal (m/s) Momentumfinal (kg m/s) KEfinal (J)
mass_1 0.5 1.0 0.50 0.251 -0.13 -0.06 0.0041
mass_2 1.5 -0.5 -0.75 0.191 -0.13 -0.19 0.0131
Total NA 1.52 -0.25 0.44 0.002 -0.25 0.020

1 Calculated using ½mv2

2 Calculated by the difference between the velocity of mass1 and mass2



Analysis

For each table, calculate the Coefficient of Restitution by dividing the velocity of separation after the collision by the velocity of approach before the collision. For the table above, this is done by:

\[COR\:=\: \frac{velocity\;of\;separation}{velocity\;of\;approach}\:=\: \frac{0}{1.5}\:=\: 0.0\]
Calculate the amount of kinetic energy lost in the collision by subtracting the \(KE_{final}\) from \(KE_0\). For the table above this would be:

\[Kinetic\:Energy\:Lost\:=\:KE_0\:-\:KE_{final}\:=\:0.44\:-\:0.02\:=\:0.42\:J\]

Discussion

Make a table of your results, filling it out as below:

Overall Results
Elasticity (%) Coeff. of Restitution Kinetic Energy Lost (J)
0 0 0.42
20
40
60
80
100


For this lab, we can’t really discuss inaccuracies, but your discussion section should include a discussion of how our results relate to momentum conservation and energy loss in inelastic collisions.