Lab 8: Conservation of Momentum
Name: __________________________
Goals:
- Compute momentum, impulse and average force in collisions.
- Use conservation of momentum to predict the outcome of a collision between two objects.
Momentum and Impulse:
The momentum of an object is defined as the product of its mass and velocity: p  mv . You should note that this is a vector
quantity, so momentum always includes a direction. In this class, we will only analyze one-dimensional problems, so we can use “+”
and “–“ to indicate direction.
Impulse is defined as a change of momentum: p  p f  pi . This is a vector pointing in the direction of the momentum change.
The average force during a collision is given by Fnet 
p
, which is really just a new way of saying Fnet  ma (see text or your notes
t
for the derivation).
Conservation of Momentum:
When two objects collide, they exert forces on each other that are equal in magnitude but opposite in direction for the entire contact
period (Newton’s third law). This implies that the change in momentum for one object is the opposite as the change in momentum for
the other object; in other words, the total momentum of the system is constant. Thus, conservation of momentum is just a new way of
expressing Newton’s third law.
We are assuming that there is no net outside force acting on the system, so we can summarize as follows:
If
F
ext
 0 , then pnet  0 ; i.e., pnetinitial  pnet final .
In order to solve collision problems, we usually start by making a picture of the initial and final states of the system. Then we write
down pi  p f . Then we plug in the total momentum before and after the collision in terms of the masses and velocities in the
problem – usually the unknowns are just the final velocities of the objects in the collision.
Elastic and Inelastic Collisions:
In an elastic collision, the kinetic energy is conserved. We can model an elastic collision by using the magnetic bumpers on our carts.
During the collision, the magnetic fields absorb some amount of kinetic energy and store it as spring potential energy (just like a
spring), but this energy is given back to the carts in the form of kinetic energy magnets push away from each other again.
In an inelastic collision, the participants stick together and the combined mass moves as one unit after the collision. We model
inelastic collisions by using velcro bumpers on our carts. During the collision, some kinetic energy is actually lost (and dissipated as
heat).
In reality, all collisions are somewhere between perfectly elastic and perfectly inelastic. For example, a car crash usually involves a
loss of kinetic energy due to the deformation of metal (this is an inelastic property), but the cars also bounce off each other (this is an
elastic property). The two types of collisions should be viewed as two extremes of a continuum.
For each of the following collisions, it is fine to assume that each basic cart has a mass of 0.5 kg and that each additional weight
(iron bar) has a mass of 0.5 kg . Rounding these values helps to simplify the algebra.
Collision I: An inelastic collision.
m1  0.5 kg
v0
m2  0.5 kg
Initial State
m1  0.5 kg m2  0.5 kg
vf
Final State
r
r
1. Write down the equation for conservation of momentum. Start with pi = p f , then put the known masses and unknown
velocities into the equation.
Equation expressing momentum conservation: ____________________________________
2. Now perform the experiment, and print the velocity graphs. Determine the value of v0 from your data:
v0 = __________ m/s
3. Now compute the expected final velocity of the carts:
v f predicted  ________________ m/s
4. Determine the actual final velocity from your data:
v fmeasured = ________________ m/s
5. Now use your velocity-time graphs to find the impulse experienced by each cart.
p1  p1 f  p1i _________________
p2  p2 f  p2i ___________________
6. Finally, find the average force experienced by each cart during the collision.
F1  _________________
F2  ___________________
7. Aside from experimental error, these forces should differ only by a minus sign. Why?
Collision II: Elastic collision #1: equal masses.
m1  0.5 kg
v0
m2  0.5 kg
Initial State
m1  0.5 kg
v1 f
m2  0.5 kg
v2 f
Final State
r
r
1. Write down the equation for conservation of momentum. Start with pi = p f , then put the known masses and unknown
velocities into the equation.
Equation expressing momentum conservation: ____________________________________
2. Write down the equation for conservation of kinetic energy. Start with KEi = KE f , then put the known masses and unknown
velocities into the equation.
Equation expressing kinetic energy conservation: __________________________________
3. Now perform the experiment, and print the velocity graphs. Determine the value of v0 from your data:
v0 = __________ m/s
4. Now compute the expected final velocities of the carts:
v1 f predicted  ___________ ______ m/s
v2 f predicted  ___________ ______ m/s
5. Determine the actual final velocities from your data:
v1fmeasured = __________________ m/s
v2fmeasured = __________________ m/s
6. Now find the impulse experienced by each cart.
p1  p1 f  p1i _________________
p2  p2 f  p2i ___________________
7. Finally, find the average force experienced by each cart during the collision.
F1  _________________
F2  ___________________
Collision III: Elastic collision #2: light mass hitting a heavy mass.
m1  0.5 kg
v0
m2  1.5 kg
Initial State
m1  0.5 kg
v1 f
m2  1.5 kg
v2 f
Final State
r
r
1. Write down the equation for conservation of momentum. Start with pi = p f , then put the known masses and unknown
velocities into the equation.
Equation expressing momentum conservation: ____________________________________
2. Write down the equation for conservation of kinetic energy. Start with KEi = KE f , then put the known masses and unknown
velocities into the equation.
Equation expressing kinetic energy conservation: __________________________________
3. Now perform the experiment, and print the velocity graphs. Determine the value of v0 from your data:
v0 = __________ m/s
4. Now compute the expected final velocities of the carts:
v1 f predicted  ___________ ______ m/s
v2 f predicted  ___________ ______ m/s
5. Determine the actual final velocities from your data:
v1fmeasured = __________________ m/s
v2fmeasured = __________________ m/s
6. Now find the impulse experienced by each cart.
p1  p1 f  p1i _________________
p2  p2 f  p2i ___________________
7. Finally, find the average force experienced by each cart during the collision.
F1  _________________
F2  ___________________
Collision IV: Elastic collision #3: heavy mass hitting a light mass.
m1  1.5 kg
v0
m2  0.5 kg
Initial State
m1  1.5 kg
v1 f
m2  0.5 kg
v2 f
Final State
r
r
1. Write down the equation for conservation of momentum. Start with pi = p f , then put the known masses and unknown
velocities into the equation.
Equation expressing momentum conservation: ____________________________________
2. Write down the equation for conservation of kinetic energy. Start with KEi = KE f , then put the known masses and unknown
velocities into the equation.
Equation expressing kinetic energy conservation: __________________________________
3. Now perform the experiment, and print the velocity graphs. Determine the value of v0 from your data:
v0 = __________ m/s
4. Now compute the expected final velocities of the carts:
v1 f predicted  ___________ ______ m/s
v2 f predicted  ___________ ______ m/s
5. Determine the actual final velocities from your data:
v1fmeasured = __________________ m/s
v2fmeasured = __________________ m/s
6. Now find the impulse experienced by each cart.
p1  p1 f  p1i _________________
p2  p2 f  p2i ___________________
7. Finally, find the average force experienced by each cart during the collision.
F1  _________________
F2  ___________________