Transcript File

Lesson 6.2
Conservation of Momentum
Essential Question: What is the
conservation of momentum?
Before we
Think of the relay event in short
track speed skating. One skater
completes a lap and then pushes a
teammate to continue skating. What
happens to the skater who is pushed?
What do you think?
• Two skaters have equal mass and are at rest.
They are pushing away from each other as
• Compare the forces on the two girls.
• Compare their velocities after the push.
• How would your answers change if the girl on
the right had a greater mass than her friend?
• How would your answers change if the girl on
the right was moving toward her friend before
they started pushing apart?
A stationary billiard ball is set into motion by a
collision with a moving billiard ball. Both balls
are on a smooth table and neither ball rotates
before or after the collision.
Momentum During Collisions
• When the bumper cars collide,
F1 = -F2 so F1t = -F2t,
and therefore p1 = -p2 .
• The change in momentum for one object is equal and opposite
to the change in momentum for the other object.
• Total momentum is neither gained not lost during collisions.
What is the law of conservation of
𝑚1 𝑣1,𝑖 + 𝑚2 𝑣2,𝑖 = 𝑚1 𝑣1,𝑓 + 𝑚2 𝑣2,𝑓
Total initial momentum = total final momentum
In general, the total momentum remains constant
for a system of objects that interact with one
Momentum is conserved in collisions.
What about objects pushing away from
each other?
Momentum is still conserved here.
Imagine two skaters
pushing away from each
other. The skaters are both
initially at rest with a
momentum of zero. When
they push away from each
other, they move in
opposite directions with
equal but opposite
momentum so that the
total final momentum is
also zero.
A 76 kg boater, initially at rest in a stationary 45
kg boat, steps out of the boat and onto the dock.
If the boater moves out of the boat with a
velocity of 2.5 m/s to the right, what is the final
velocity of the boat?
A 63.0 kg astronaut is on a spacewalk when the tether
line to the shuttle breaks. The astronaut is able to throw
a spare 10.0 kg oxygen tank in a direction away from
the shuttle with a speed of 12.0 m/s, propelling the
astronaut back to the shuttle. Assuming that the
astronaut starts from rest with respect to the shuttle, find
the astronaut’s final speed with respect to the shuttle
after the tank is thrown.
An 85.0 kg fisherman jumps from a dock into a
135.0 kg rowboat at rest on the west side of the
dock. If the velocity of the fisherman is 4.30 m/s
to the west as he leaves the dock, what is the
final velocity of the fisherman and the boat?
Each croquet ball in a set has a mass of 0.50 kg.
The green ball, traveling at 12.0 m/s, strikes the
blue ball, which is at rest. Assuming that the
balls slide on a frictionless surface and all
collisions are head-on, find the final speed of the
blue ball in each of the following situations:
a. The green ball stops moving after it strikes
the blue ball
b. The green ball continues moving after the
collision at 2.4 m/s in the same direction.
A boy on a 2.0 kg skateboard initially at rest
tosses an 8.0 kg jug of water in the forward
direction. If the jug has a speed of 3.0 m/s
relative to the ground and the boy and skateboard
move in the opposite direction at 0.60 m/s, find
the boy’s mass.
A 44 kg student on in-line skates is playing with
a 22 kg exercise ball. The student is holding the
ball, and both are at rest. The student then throws
the ball horizontally, causing the student to glide
back at 3.5 m/s. What is the final velocity of the
Newton’s third law leads to
conservation of momentum.
The impulse on the mass of
object 1 is equal to and
opposite the impulse on the
mass of object 2.
This relationship is true in
every collision or interaction
between two isolated
In every interaction between two isolated
objects, the change in momentum of the first
object is equal to and opposite the change in
momentum of the second object.
If the momentum of one object increases after a
collision, then the momentum of the other object
in the situation must decrease by an equal
In a real collision, the forces may vary in time in
a complicated way.
The time-averaged force during a collision is
equal to the constant force required to cause the
same change in momentum as the real, changing
A boy stands at one end of a floating raft that is
stationary relative to the shore. He then walks in
a straight line to the opposite end of the raft,
away from the shore.
a. Does the raft move? Explain.
b. What is the total momentum of the boy and
the raft before the boy walks across the raft?
c. What is the total momentum of the boy and
the raft after the boy walks across the raft?
What is the conservation of momentum?