Download Chapter 6: Momentum and Collisions

Section 6–2:
Conservation of
Momentum
Coach Kelsoe
Physics
Pages 205–211
Objectives
• Describe the interaction between two objects
in terms of the change in momentum of each
object.
• Compare the total momentum of two objects
before and after they interact.
• State the law of conservation of momentum.
• Predict the final velocities of objects after
collisions, given the initial velocities.
Momentum is Conserved
• We have already talked about different
quantities that are conserved – quantities like
mass and energy.
• Momentum is another quantity that is
conserved.
• If you consider two billiard balls, one at rest
and another rolling toward the first, then the
momentum that the ball at rest gains would
ideally be equal to the momentum the moving
ball lost.
Momentum is Conserved
• If we wrote the last scenario in an equation, it
would look like this:
– Pa,i + Pb,i = Pa,f + Pb,f
• The sum of the initial momentum for the
objects equals sum of the final momentum.
• The law of conservation of momentum can be
summed up from the following equation:
– m1v1,i + m2v2,i = m1v1,f + m2v2,f
– The total momentum of all objects interacting with
one another remains constant regardless of the
nature of the forces between the objects.
Conserved Momentum in Collisions
• The assumption we made with the billiard
balls was that the surface they were sitting on
was frictionless.
• In your book and in many of the problems we
will work, most conservation of momentum
problems will deal with only two interacting
objects, neglecting friction/air drag.
• Keep in mind, however, that frictional and
drag forces do play a role in the conservation
of momentum.
Objects Pushing Away
• Conservation of momentum also occurs
between two objects pushing away from each
other.
• There is even conservation of momentum
between you and Earth when you jump, but
Earth doesn’t move much because of its
extremely large mass (6 x 1024 kg).
• Momentum is conserved because the
velocities are in opposite directions.
Sample Problem D
• 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?
Sample Problem Solution
• Identify givens and unknowns:
– m1 = 76 kg
– v1,i = 0 m/s
– v1,f = 2.5 m/s to the right
m2 = 45 kg
v2,i = 0 m/s
v2,f = ?
• Choose the correct equation:
– m1v1,i + m2v2,i = m1v1,f + m2v2,f
– m1v1,f + m2v2,f = 0  v2,f = -m1v1,f/m2
• Plug values into the equation
– v2,f = -m1v1,f/m2  -(76 kg)(2.5 m/s)/(45 kg)
– v2,f = -4.2 m/s, or 4.2 m/s to the left
Newton’s Third Law
• Newton’s Third Law of
Motion leads to
conservation of momentum.
• During the collision, the force
exerted on each bumper car
causes a change in
momentum for each car.
• The total momentum is the
same before and after the
collision.