Aim: How can we apply conservation of
momentum to collisions?
 Identify conservation laws that you know.

Conservation of Momentum
In a system, the momentum of the
individual components may change, but
the total momentum of the system remains
constant.
 Law of Conservation of Momentum:

pbefore = pafter (in reference table)
 How is this useful?

Identifying terms
Before Collision
1
2
After Collision
1
pbefore  p after
2
Car Accident

A 1,000-kg car moving at 5 m/s collides
into a 1200-kg car at rest. After the
collision the 1000 kg car comes to rest.
Calculate the velocity of the 1200kg car after
the collision.
 Calculate the total momentum before and
after the collision.

Solution
momentum before
=
momentum after
pbefore = pafter
m1v1  m2v2 
m1v1 'm2v2 '
m
m
m
1000kg(5 )  1200kg(0 ) 1000kg(0 )  1200kg(v2 ' )
s
s
s
5000kgm / s  0
 0  1200kg(v ' )
2
m
v2 '  4.17
s

A 1,000 kg car is moving to the right at 12
m/s. Another 1500kg car is moving to the
left. The cars collide and are brought to
rest. Determine the initial speed of the
1500 kg car.
A 0.005 kg bullet is moving to the right at
200 m/s. The bullet strikes a stationary
block of wood on a frictionless, level
surface. The mass of the wood block is
7.0 kg. The bullet travels right through
the wood and continues out the other side
with a speed of 150 m/s.
 1. Calculate the speed of the block after
the collision.
 2. What is the direction of the block after
the collision?

A 0.26-kg cue ball moving at 1.2 m/s
strikes a stationary 0.17-kg 8 ball. After the
collision the cue ball comes to rest.
 A) Calculate the magnitude of the velocity
of the 8 ball after the collision.


B) Determine the total momentum after the
collision.

A 1.0-kg ball traveling north at 3.0 m/s
collides with a 4.0-kg ball at rest.
Determine the magnitude of the total
momentum after the collision.
Summary
Describe the conservation of momentum.
 Identify the formula for conservation of
momentum.
 A 5-kg bowling ball rolling at 3m/s collides
into a 6.2-kg ball at rest. After the collision
the 5-kg ball comes to rest.

A) Calculate the speed of the 6.2-kg ball after
the collision.
 B) If the time of impact is .23 seconds,
determine the force exerted on the 6.2-kg ball.

Aim: How can we calculate final
velocity after a collision?

A 2-kg object moving at 5 m/s collides with
a 4-kg object at rest. After the collision the
2-kg object comes to rest.
A) Calculate the velocity of the 4-kg object
after the collision.
 B) If the time of impact was .01 seconds then
what is the force exerted on the 4kg object?
 Is the force exerted on the 2-kg object the
same? Why?


A 5.0-kilogram steel block is at rest. A 1.5kilogram lump of clay is propelled at
5.0m/s at the steel block. After the collision
the clay sticks to the steel block. Calculate
the speed after the collision. (hint: sketch a
picture)
Bullet and Block

A 0.1-kilogram bullet is fired horizontally
with a velocity of 400m/s into a 14.6-kg
wooden block at rest. The bullet is
imbedded in the wooden block. Determine
the speed of the block after impact.

A 2.0-kg object is moving at 3m/s to the
right and a 4.0-kg object is moving at 8m/s
to the left on a horizontal frictionless table.
If the two objects collide and stick together
after the collision then what is the final
total momentum?
Summary:
1) How can we describe an inelastic
collision?
 2) Explain what happens to the masses
after the collision.

Aim: How can we apply
conservation of momentum to the
recoil/explosion problem?
A 0.1-kilogram bullet is fired horizontally at
350m/s into a 5-kg wooden block at rest.
The bullet is imbedded in the wooden
block. Determine the speed of the block
after impact.
 http://www.youtube.com/watch?v=x71pa_
YWgbQ


A hunting rifle fires a bullet of mass
0.00953 kg with a velocity of 500 m/s to
the right. The rifle has a mass of 4 kg.
Calculate the recoil speed of the rifle as
the bullet leaves the rifle.

A 62.1-kg male ice skater is facing a 42.8kg female ice skater. They are at rest on
the ice. They push off each other and
move in opposite directions. The female
skater moves backwards with a speed of
3.11 m/s. Determine the speed of the male
skater.

A rock is hammered into two pieces. A 0.25-kg
piece flies to the left at 5 m/s, while the other 0.5
kg piece flies to the right. How fast does the
second piece fly?
Summary
Describe the total momentum before the
explosion/recoil.
 Identify the formula for recoil/explosion
formula.
 Explain conservation of momentum.

Aim: How can we apply
conservation of momentum to
head on collisions?
How can we describe the types of
head on collisions?
Inelastic
 Elastic

A
900kg car traveling west at 20 m/s
collides head on with a 1,000kg car
traveling east. Immediately after the
collisions the cars come to rest.
 Determine
the initial speed of the
1,000kg car.

A 850kg car traveling north at 15 m/s
collides with a 2,000kg car traveling south.
After the collision the 850kg car rolls south
at 4 m/s. The 2,000kg car come to rest.

Determine the initial speed of the 2,000kg car.

A 2,000kg truck traveling at 30m/s east
collides with a 10,000kg bus traveling
west. The vehicles lock at move together
at 7 meters per second west.

Calculate the initial speed of the bus.
Summary:
How do we determine if the collision is
inelastic or elastic?
 Describe the total momentum before and
after a collision.

Aim: How can we apply conservation of
momentum to applications?

A 300 kg motorcycle moving at 15m/s east
collides with a 900 kg car at rest. After the
collision the 900kg car moves at 6m/s east
and the 300 kg motorcycle rolls west.
A) Determine the final speed of the
motorcycle.
 B) If the time of impact was 0.85 seconds then
calculate the force.
 C) Calculate the impulse.
