Momentum & Impulse Lab
Group: _________________________________
_________________________________
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_________________________________
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Purpose:
1. Examine the result of elastic and inelastic collisions.
2. Test the principle of conservation of momentum.
Introduction:
When objects move, they have momentum. Momentum, p, is simply the product of an object’s
mass m and its velocity v. The unit for momentum is kg∙m/s. During a collision, an object’s
momentum can be transferred to impulse, which is the product of force (N) and time (s) over which
the force acts. This allows us to write the momentum-impulse theorem:
In a totally elastic collision, the total momentum ptotal is the sum of the momenta of each object.
Since according to the conservation of momentum, the total momentum does not change, the
momentum after the collision remains the same:
ptotal = m1v1 + m2v2 = m1v1’ + m2v2’
In a totally inelastic collision, the total momentum is also conserved, but because the two objects
stick together, they may be treated as one object, with a mass equal to the sum of the individual
masses:
ptotal = m1v1 + m2v2 = (m1 + m2)v’
Materials:
Lab computer using PhET simulation, this lab worksheet, calculator
Strategy:
You will observe collisions between two and more objects in one dimension
using the PhET Collision Lab simulation.
Procedure:
Part I – Elastic Collisions
1. Point your web browser to the PhET site and locate the Collision Lab simulation under Physics:
Motion and select
or you may go directly to
http://phet.colorado.edu/sims/collision-lab/collision-lab_en.html.
2. Spend a couple minutes playing with the simulation to get acquainted with
the controls.
3. When ready to start the lab, hit the Reset All button in the green option box
on the right. Then select 1 Dimension, Velocity Vectors, Reflecting Border,
and Momenta Diagram. Make sure Elasticity is set to 1.00 and turn on
sound.
4. Prior to running tests in the sim, complete the table below by calculating the
missing values. Use the equation for elastic collisions, making sure you use
the appropriate sign for the velocity (ie. right is positive, left is negative):
ptotal = m1v1 + m2v2 = m1v1’ + m2v2’
5.
SETUP
ptotal (kg∙m/s)
m1 (kg)
m2 (kg)
v1 (m/s)
v2 (m/s)
v1’ (m/s)
v2’ (m/s)
1
0.5
1.0
1.0
1.0
-0.5
-0.5
1.0
2
0.0
1.0
2.0
2.0
-1.0
-2.0
1.0
3
3.0
1.0
2.0
3.0
0.0
-1.0
2.0
4
7.0
1.0
3.0
4.0
1.0
-0.5
2.5
Now test your predictions using the PhET sim. Hit More Data to bring up the data
table on the bottom of the sim. Enter the masses in the first column, and the initial
velocities in the Vx column. The y and Vy columns should remain zero to keep the motion
in one dimension. The momentum for each ball can be found in the Px column – add them
together to check ptotal. Once the sim is set up, hit play and pause it after the collision and
before either ball bounces off one of the side walls. After confirming the post-collision
velocities, rewind and try the next setup.
Did your experimental results match your calculations? ______
(Hint: They should – if not, go back and check your math!)
6. Now make some predictions:

What happens when a moving ball hits a stationary ball of equal mass? _____________
_______________________________________________________________________

What if the stationary ball is heavier? ________________________________________
_______________________________________________________________________

What if the stationary ball is lighter?
________________________________________
_______________________________________________________________________
7. Set up the sim to test your predictions. Did you confirm or disprove your hypotheses?

Actual results when stationary ball is same? __________________________________
_______________________________________________________________________

Actual results when stationary ball is heavier? __________________________________
_______________________________________________________________________

Actual results when stationary ball is lighter? __________________________________
_______________________________________________________________________
Part II – Inelastic Collisions
1. In an inelastic collision, the balls will “stick together” after impact, as if they were covered in
Velcro. The two masses will move together, essentially becoming one mass. For each of the
four setups from Part I, calculate the final velocity of the combined masses. Note that ptotal
should be the same, so the final velocity should be equal to ptotal/(m1+m2)
SETUP
ptotal (kg∙m/s)
m1 (kg)
m2 (kg)
m1 + m2 (kg)
v' (m/s)
1
0.5
1.0
1.0
2.0
0.25
2
0.0
1.0
2.0
3.0
0.00
3
3.0
1.0
2.0
3.0
1.00
4
7.0
1.0
3.0
4.0
1.75
2. Using the PhET sim, rerun the setups from Part 1 with the elasticity set to 0.00.
Use the same initial velocities, and confirm the final velocity is the same as you
calculated for each setup. Make sure you pause before the balls strike a wall,
since collisions with the wall are also inelastic (ie. they stick!).
3. On the left side of the screen and directly below the impact area, the total kinetic energy of the
system is displayed. Run a couple setups in elastic and inelastic mode and note what happens
to the kinetic energy in the following situations:

Elastic collision: _________________________________________________________

Inelastic collision: ________________________________________________________

Why the difference? ______________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
Part III – Impulse
1. When two object meet in an elastic collision, they each apply the same force to the other over
the short time they are in contact. (Remember Newton’s third law?) This force multiplied by
the time they are in contact is called impulse, and is measured in N∙s. Because N is
equivalent to kg∙m/s2, the units for impulse are the same as for momentum. In fact, the
momentum-impulse theorem states that the impulse is equal to the change in momentum, or
FΔt = Δp = mΔv
2. Since the impulse on each ball is equal and opposite, so is the change in momentum for each:
Δp1 = -Δp2
3. Rerun the four setups with elasticity = 1.00, and record the momentum of
each ball before and after the collision as displayed in the Px column on the
screen.
SETUP
p1 (kg∙m/s)
p1' (kg∙m/s)
Δp1 (kg∙m/s)
p2 (kg∙m/s)
p2' (kg∙m/s)
Δp2 (kg∙m/s)
1
2
3
4
4. Compare Δp1 and Δp2 for each setup. Are they equal and opposite? ________
Part IV – Bonus (time permitting)
1. Rewind the sim and set it up with one dimension, reflecting borders, and elasticity = 1.00. You
may select the other options as desired, though I recommending turning the sound on. Hit the
Add Ball button until you have five balls, and set them up as follows:
ball
mass
x
y
Vx
Vy
1
2
3
4
5
1.0
1.0
1.0
1.0
1.0
0.500
1.300
1.610
1.920
2.230
0.000
0.000
0.000
0.000
0.000
2.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
2. Move the Time Rate slider all the way to the right. Hit play and let the simulation run.

Describe the motion: _____________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________

Where have you seen this motion before? ____________________________________
_______________________________________________________________________
_______________________________________________________________________
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3. See if you can set up the simulation with different numbers of balls moving.