NAME_________________
Collisions in 1D Elastic, Conservation of Momentum and Momentum Bar Charts.
Instructions on editing and saving PDFs:
1. This lab is in pdf format. Use Acrobat Reader to open it. You can then type
your answers in the answer blanks.
2. Predict the bars in each bar chart. A toolbar lies along the right side of the
Acrobat Reader window. Click the ‘Comment’ tool ( ). A ‘Comment’ toolbar
should appear along the top of the window. Click the ‘Drawing Tools’ button (
), then select ‘Rectangle’ to draw the bars of the bar chart.
2. Draw the blocks or Freebody diagrams. Click the ‘Drawing Tools’ button (
),
then select ‘Arrow’ to draw the forces. To label the forces, either click the ‘Use
Drawing Tool’ tool (
), or if you prefer, use the ‘Text Box’ tool ( ). Don’t
worry about making the force subscripts look like subscripts.
3. Draw the correct bar chart using the ‘Use Drawing Tool’ tool (
)
4. If the correct bar chart doesn’t match your prediction, reflect on what
made you predict incorrectly.
5. When you are done with the lab, save it (i.e., save your comments) and
submit it via Canvas.
Introduction
Momentum is defined as: p = mv
For a constant force, impulse is defined as: J = F Δt
Both momentum and impulse are vector quantities. Notice that momentum is defined as the
product of a scalar (the mass) and a vector (the velocity). Since the mass is always positive, the
momentum always has the same direction as the velocity. Similarly, for a constant force, the
direction of the impulse on an object is always the same as the direction of the force acting on
that object since the time interval (t) is always positive.
The relationship between momentum and impulse (called the impulse-momentum theorem) is:
Jnet = pf – pi
→
pi + Jnet = pf
The impulse momentum theorem is applied to a system (i.e., a collection of interacting
objects). In words, the impulse-momentum theorem states that any net impulse delivered to a
system goes directly into changing the linear momentum of that system.
The total momentum of a system is determined by adding the momenta of each of the objects
in the system (vector addition!). The net impulse is determined by inserting the net force acting
on the system into the definition of impulse. The net force on a system is the sum of all external
forces (i.e., the force exerted by objects outside of the system) since internal forces (i.e., forces
exerted by objects inside of the system due to interactions between objects) come in equal and
opposite action-reaction pairs and hence cancel.
Collision problems are often shown as prior and post collisions. Momentum is
conserved, meaning that p = pf – pi = 0, this is related to total initial moment pi (before to the
collision), and final momentum pf (after to the collision).
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Experiment 1 (Elastic Collison)
A red puck (0.5kg) is initially sliding to the right at 1m/s on a frictionless surface and
green puck (1.5kg) is at rest. After the collision, the green puck is moving to the right at 0.5m/s.
The system consists of both pucks. Predict the momentum and velocity of the red puck after
the collision.
The questions below are intended to help you correctly predict your first impulse
momentum bar chart. Ask yourself similar questions in all subsequent experiments. Remember
that since p = mv, the direction of the momentum is always the same as the direction of the
velocity.
1. Initially the red puck is moving to the right. What is the direction of red puck’s initial
momentum vector? ____________ (left, right, or zero momentum).
• This momentum is____________. (positive, negative, or zero).
2. Initially the green puck is not moving. What is the direction of green puck’s initial
momentum vector? ____________ (left, right, or zero momentum).
• This momentum is____________. (positive, negative, or zero).
3. After the collision, the green puck is moving to the right. What is the direction of green
puck’s final momentum vector? ____________ (left, right, or zero momentum).
• This momentum is____________. (positive, negative, or zero).
Draw a Freebody Diagram of the two pucks at the instant when the red puck is impacting the right
side of the green puck.
Red Puck
Green Puck
to test your
4. The total net force in the horizontal direction during the impact is____________.
(positive, negative, or zero).
5. What is the direction of the impulse vector on the red puck + the green puck (which is
the same as the direction of the horizontal component of the net force)? ____________
(left, right, or zero momentum).
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Use your answers from above to draw a predicted
momentum bar chart to the right. Be sure the bars
balance so that momentum is conserved. Note that
your bars don’t have to be exact and are subjective
so you should try to use whole blocks rather than
partial blocks of momentum.
Using your bar chart, predict the direction of the momentum of the red puck after the collision:
6. My bar chart predicted that the red puck’s momentum after the collision
is____________. (positive, negative, or zero).
• Therefore, after the collision, the direction of green puck’s final momentum
vector is ____________ (left, right, or zero momentum).
Let’s test your prediction by using the same simulation that we used in the 4.0 Momentum and
Impulse Virtual Lab. Start up the simulation by clicking on the link below:
https://phet.colorado.edu/en/simulation/legacy/collision-lab
Starting the simulation:
• Click on the play button on the simulation
• If warned about Flash 8 or better, hit the Attempt to view the simulation anyways
•
If a warning states that adobe flash is blocked, click block button
to add an exception. Then reload the simulation, and it should start.
Setting up the simulation:
• Start the simulation then keep it on the Introduction Tab.
• Expand the simulation to full screen
• On the right-hand side green area
o Check ‘Velocity Vectors’.
o Check ‘Momentum Vectors’.
o Check ‘Kinetic Energy’.
o Elasticity set to 100%
o Leave all other boxes unchecked for now.
•
•
in the upper right
o Hit the Reset All button.
Once you set up your predictions to test, you can restart, play, pause, and step by a
timeframe using the buttons below the simulation.
Further below the simulation, click the more data button
o This area should turn into a table as shown below:
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o This table can be used to alter a puck’s mass, position, and velocity. It also
displays each puck’s current velocity and momentum. Use the current table
setup to go through the next part of the lab.
Adjust the simulation table for mass and velocity for
each puck, then run the simulation to test your
prediction. After you have run the simulation, use the
data and numbers under the momentum area of the
table to adjust your chart in the corrected momentum
bar chart to the right.
Use the area below to create equations from your
corrected momentum bar chart above. Try and verify the simulation’s final velocity of the red
puck after the collision. All equations should be in terms of mass subscripted with R (red) and G
(green) and velocity subscripted with R (red) and G (green), as well as, initial (i) and final (f). For
example, the initial momentum of the red puck in equation form would be piR = mR ViR:
to
Experiment 2 (Elastic Collison)
A red puck (0.5kg) is initially sliding to the right at 3m/s on a frictionless surface and
green puck (1.5kg) is sliding the left at 1m/s. After the collision, the green puck is moving to the
right at 1m/s. The system consists of both pucks. Predict the momentum and velocity of the
red puck after the collision. Answer the following questions:
7. Initially the red puck is moving to the right. The direction of red puck’s initial
momentum is ____________ (positive, negative, or zero).
8. Initially the green puck is moving to the left. The direction of green puck’s initial
momentum is ____________ (positive, negative, or zero).
9. After the collision, the green puck is moving to the right. The direction of green puck’s
final momentum is ____________ (positive, negative, or zero).
4
Use your answers from above to draw a predicted
momentum bar chart to the right. Be sure the bars
balance so that momentum is conserved. Note that
your bars don’t have to be exact and are subjective
so you should try to use whole blocks rather than
partial blocks of momentum.
Use the area below to create equations from your
predicted momentum bar chart above. Try and predict the simulation’s final velocity of the
red puck after the collision. All equations should be in terms of mass subscripted with R (red)
and G (green) and velocity subscripted with R (red) and G (green), as well as, initial (i) and final
(f). For example, the initial momentum of the red puck in equation form would be piR = mR ViR:
I predict the final velocity of the red puck after the collision to be __________m/s.
Adjust the simulation table for mass and velocity for
each puck, then run the simulation to test your
prediction. After you have run the simulation, use the
data and numbers under the momentum area of the
table to adjust your chart in the corrected bar chart
to the right.
Was your predicted final velocity for the red puck after the collisions correct? Did you have to
adjust you bar chart?
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While we are here, lets try and predict the
kinetic energies before and after the collision,
then use the simulation to verify our
calculations. Use the energy bar chart below
to predict kinetic energy. Please fill out the
predicted energy bar chart to the right:
Use the area below to create equations from
your predicted energy bar chart above. Try and predict the simulation’s final velocity of the
red puck after the collision. All equations should be in terms of mass subscripted with R (red)
and G (green) and velocity subscripted with R (red) and G (green), as well as, initial (i) and final
(f). For example, the initial momentum of the red puck in equation form would be KiR = ½ mR
ViR2:
I predict the final velocity of the red puck after the collision using KE to be __________m/s.
Hit the reset button on the simulation then check to make sure ‘kinetic energy’ check box is
checked. Now, run the simulation making note of the total kinetic energy just above the
simulation. After you have run the simulation, use the data and numbers of the kinetic energy
and momentum tables to answer the following statements about elastic collisions.
Was your predicted final velocity for the red puck after the collisions correct using kinetic
energy equations the same as your velocity calculations using momentum? Was it the same as
the simulation? What do you think this means? Explain.
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Summary of elastic collsions:
Make some general conclusions about elastic collisions based on what you have learned:
10. The total kinetic energy before the elastic collision is_________ after the total kinetic
energy after the collision. (greater than, less than, or equal to).
11. With elastic collisions, kinetic energy________ conserved. (is or is not).
12. The total momentum before the elastic collision is_________ after the total momentum
after the collision. (greater than, less than, or equal to).
13. With elastic collisions, momentum________ conserved. (is or is not).
Experiment 3 (Inelastic Collison)
A red puck (0.5kg) is initially sliding to the right at 1m/s on a frictionless surface and
green puck (1.5kg) is at rest. After the collision, the green puck and red puck are stuck together
and moving. The system consists of both pucks. Predict the momentum and velocity of the
red-green puck stuck together after the collision. Answer the following questions:
14. Initially the red puck is moving to the right. The red puck’s initial momentum is
____________ (positive, negative, or zero).
15. Initially the green puck is not moving. The green puck’s initial momentum is
____________ (positive, negative, or zero).
16. After the collision, the green puck and red puck are connected and moving together.
Their final momentum is ____________ (positive, negative, or zero).
Use your answers from above to draw a predicted
momentum bar chart to the right. Be sure the bars
balance so that momentum is conserved. Note
that your bars don’t have to be exact and are
subjective so you should try to use whole blocks
rather than partial blocks of momentum.
Use the area below to create equations from your
predicted momentum bar chart above. Try and
predict the simulation’s final velocity of the red
puck after the collision. All equations should be in terms of mass subscripted with R (red) and G
(green) and velocity subscripted with R (red) and G (green), as well as, initial (i) and final (f). For
example, the initial momentum of the red puck in equation form would be piR = mR ViR:
I predict the final velocity of the red puck after the collision using momentum to be ______m/s.
7
While we are here, let’s again try and predict the
kinetic energies before and after the collision,
then use the simulation to verify our
calculations. Use the energy bar chart below to
predict kinetic energy. Please fill out the
predicted energy bar chart to the right:
Use the area below to create equations from
your predicted energy bar chart above. Try and predict the simulation’s final velocity of the
red puck after the collision. All equations should be in terms of mass subscripted with R (red)
and G (green) and velocity subscripted with R (red) and G (green), as well as, initial (i) and final
(f). For example, the initial momentum of the red puck in equation form would be KiR = ½ mR
ViR2:
I predict the final velocity of the red puck after the collision using KE to be __________m/s.
Compare the final velocity calculated by KE to you final velocity using momentum. Is there a
difference between the two? Why or why not? Explain.
8
Setting up the simulation:
• Start the simulation then keep it on the Introduction Tab.
• Expand the simulation to full screen
• On the right-hand side green area
o Check ‘Velocity Vectors’.
o Check ‘Momentum Vectors’.
o Check ‘Kinetic Energy’.
o Elasticity set to 0%
o Leave all other boxes unchecked for now.
•
•
o Hit the Reset All button.
Once you set up your predictions to test, you can restart, play, pause, and step by a
timeframe using the buttons below the simulation.
Further below the simulation, click the more data button
o This area should turn into a table as shown below:
o This table can be used to alter a puck’s mass, position, and velocity. It also
displays each puck’s current velocity and momentum. Use the current table
setup to go through the next part of the lab.
Adjust the simulation table for mass and velocity
for each puck, and make sure the simulation’s
Elasticity is set to 0%. Run the simulation to test
your prediction. After you have run the simulation,
use the data and numbers under the momentum
area of the table to adjust your chart in the
corrected momentum bar chart to the right.
After running the simulation, what was the final velocity of both pucks stuck together after the
collision? Which method was able to predict final velocity accurately? Why do you think one
method did not work? Think about Eint energy.
to
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If you need to, re-run the simulation making note of the total kinetic energy just above the
simulation before and after the collision.
Summary of elastic collsions:
Make some general conclusions about inelastic collisions based on what you have learned.
1. The total kinetic energy before the collision is_________ after the total kinetic energy
after the collision. (greater than, less than, or equal to).
2. With inelastic collisions, kinetic energy________ conserved. (is or is not).
3. The total momentum before the inelastic collision is_________ after the total
momentum after the collision. (greater than, less than, or equal to).
4. With inelastic collisions, momentum________ conserved. (is or is not).
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