Conservation of Momentum
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Transcript Conservation of Momentum
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.