You'll investigate conservation laws in various collisions. 
About submitting your work: Submit your answers in WebAssign
assessments L135PL and L135.
To determine how nearly momentum and kinetic energy are conserved in inelastic collisions
Do the L135PL WebAssign. You'll need to refer to Solving
Conservation of Momentum Problems in One Dimension for the examples presented.
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 1Dimensional 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 v_{R}. 
Quantity: 
m_{L} 
m_{R} 
Δt_{L} 
Δt_{R} 
v_{L} 
v_{R} 
p_{L} 
p_{R} 
P_{i} 
P_{f} 
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 










 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 v_{R}. The velocities, v_{L} and v_{R}, are the velocities of the carts after
separating. The momenta, p_{L} and p_{R},
are the corresponding momenta of the carts after separating. They're
vectors, too. P_{i}and P_{f} 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.

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

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.

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.)

Let's assume that mechanical energy is conserved for the system;
that is, ΔE_{sys} =
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 v_{Li} and p_{Li} 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: 
m_{L} 
m_{R} 
Δt_{Lf} 
Δt_{Ri} 
v_{Li} 
v_{Lf} 
v_{Ri} 
p_{Li} 
p_{Lf} 
p_{Ri} 
P_{i} 
P_{f} 
% Diff. in P 
K_{i} 
K_{f} 
(K_{f } K_{i})/K_{i} 
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 1Dimensional 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.)
 Complete the table through the P_{f }column.
Express momenta to the nearest 0.001 kgm/s.
 Calculate the percentage differences between the initial
and final values of the total momentum using the formula 100(P_{f}  P_{i})/(P_{f}_{ }+ P_{i}).
Don't take the absolute value. That way, you can tell by the sign which
was larger, P_{i} or P_{f}.
 K_{i} and K_{f} are the total kinetic
energies of the system of gliders before and after collision. (K_{f}  K_{i})/K_{i} 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.

Enter your values of P_{i}, P_{f}, K_{i},
and K_{f}.

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.

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