L135. Conservation of Momentum and Kinetic Energy in Collisions

You'll investigate conservation laws in various collisions.

About submitting your work:  Submit your answers in WebAssign assessments L135PL and L135.

 Goal

To determine how nearly momentum and kinetic energy are conserved in inelastic collisions

 Prelab

Do the L135PL WebAssign. You'll need to refer to Solving Conservation of Momentum Problems in One Dimension for the examples presented. 

 Data, Analysis, and Interpretation

Enter all your work for this lab in WebAssign L135.

Part A. Explosions

Copy the following table into a Word file where you can record values in the cells as you watch a video clip. The clip is Momentum and Kinetic Energy in 1-Dimensional Explosions: Streamed / RealPlayer / Flash. Enter the data given in the clip into the first four columns of the table.

The direction of positive displacement is in the direction of vR.
Quantity: mL mR ΔtL ΔtR vL vR pL pR Pi Pf
Units: kg kg s s m/s m/s kgm/s kgm/s kgm/s kgm/s
Run 1                    
Run 2                    
Run 3                    
Run 4                    
  1. After you've watched the clip and recorded the first four columns of data, complete all cells in the table. Review as needed Example 1 of the Guide to Solving Conservation of Momentum Problems, Part I for help in the calculations.) Assume that the direction of positive displacement is in the direction of vR. The velocities, vL and vR, are the velocities of the carts after separating. The momenta, pL and pR, are the corresponding momenta of the carts after separating. They're vectors, too. Piand Pf are the total momenta of the system of carts before and after separation. And, of course, they're also vectors. Don't round intermediate calculations, as this may increase errors. Express momenta to the nearest 0.001 kgm/s.

Enter your results from the last 4 columns of the table in question 1 of WA P14. Then continue with answers to the following questions.  Assume the system to be composed of the two cars only.

  1. List the external forces acting on the system of the two carts.

  2. The final momenta show an interesting trend. The final total momentum for each run is positive. Let's assume that this trend is due to an imbalance in the external forces so that the net, external force on the system isn't 0. Hypothesize about a possible cause for the imbalance. Explain specifically how this could lead to the observed trend. This means you need to explain how the final total momentum could be positive every time.

  3. How can you easily tell that kinetic energy isn't conserved in these explosions? (Hint: Consider the fact that kinetic energy is, by its definition, greater than or equal to 0.)

  4. Let's assume that mechanical energy is conserved for the system; that is, ΔEsys = ΔK + ΔU = 0. (This means we're ignoring the influence of possible external forces.)  From the previous problem, we see that ΔK is positive; therefore, ΔU must be negative. What form of potential energy is involved here and why is it decreasing?

Part B.  Sticking collisions

Next you'll watch a clip on sticking collisions. Copy the following data table first. This time, assume that the direction for positive displacement is to the left in the direction of all velocities. Note the subscripts i and f that have been added to times, velocities, and momenta. These are to help avoid confusion between the initial state (before collision) and the final state (after collision).  The vLi and pLi columns have been filled in to remind you that the left cart has initial velocity and momentum of zero.

The direction of positive displacement is to the left.
Quantity: mL mR ΔtLf ΔtRi vLi vLf vRi pLi pLf pRi Pi Pf % Diff. in P Ki Kf (Kf - Ki)/Ki
Units: kg kg s s m/s m/s m/s kgm/s kgm/s kgm/s kgm/s kgm/s   J J  
Run 1         0.000     0.000                
Run 2         0.000     0.000                
Run 3         0.000     0.000                
Run 4         0.000     0.000                
Run 5         0.000     0.000                

The clip is Momentum and Kinetic Energy in 1-Dimensional Sticking Collisions:  Streamed / RealPlayer / Flash. After you've watched the clip and recorded the data, do the following. Review as needed Example 2 of the Guide to Solving Conservation of Momentum Problems, Part I for help in the calculations.)

    1. Complete the table through the Pf column. Express momenta to the nearest 0.001 kgm/s.
    2. Calculate the percentage differences between the initial and final values of the total momentum using the formula 100(Pf - Pi)/(Pf + Pi). Don't take the absolute value. That way, you can tell by the sign which was larger, Pi or Pf.
    3. Ki and Kf are the total kinetic energies of the system of gliders before and after collision. (Kf - Ki)/Ki is the fractional change in kinetic energy. Fill in these three columns now. Calculate kinetic energies to the nearest 0.001 J.

Do the following to complete WA L135.

  1. Enter your values of Pi, Pf, Ki, and Kf.

  2. The percentage difference between initial and final momenta is a good measure of how nearly momentum was conserved. You should see an obvious trend in the percentage differences. What is the trend and how can you explain it? Give evidence from your viewing of the clips and use good physics in your explanation.

  3. Was kinetic energy conserved in these collisions?  Support your answer with evidence from your table.

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