Applying a Force
Momentum
Impulse
Momentum
Conservation of Momentum
Collisions
Impulse
The product of force and contact time
Vector quantity, Symbol: J
Direction is the same as the net or
average force applied
Units: N-s, kg-m-s-1
Momentum
Product of mass and velocity
Vector quantity, Symbol: p
Direction is the same as the
velocity
Units: kg-m-s-1
Large Force, Short Contact Time
Can you give
other examples?
Small Force, Long Contact Time
Airbags
Seatbelt
Small Force, Long Contact Time
Catching a baseball
Bungee Jumping
Example
A cricket ball, mass 0.5 kg, was bowled at
50 m s-1 at a batsman who misreads the
ball and the 5 kg bat is knocked out of
his hands, the ball rebounds at 25 ms-1.
What is the change in momentum of the ball?
If the bat was in contact with the ball for 2.0
ms, how much force did the batsman apply on
the ball?
Conservation of Momentum
Total momentum before is equal to
total momentum after
In a closed system (external forces
are negligible)
Inelastic Collision
Only momentum is conserved
Perfectly inelastic collision
(The colliding bodies couple after
the collision)
Example
A railway wagon travelling at 1.0 m s–1
catches up with and becomes coupled
to another wagon travelling at 0.5 m
s–1 in the same direction. The faster
moving wagon has 1.7 times the mass
of the slower one. Immediately after
impact, what is the speed of the
coupled wagons?
Elastic Collision
Momentum is conserved.
Kinetic Energies are conserved.
(Relative Velocities) are conserved.
Analyzing billiard balls
Simulation
Example
A trolley of mass 1 kg rolls along a level,
frictionless ramp at a speed of 6 m s-1. It
collides with a second trolley of mass 2 kg
which is initially at rest. The first trolley
rebounds at a speed of 2 m s-1.
Find, by conservation of momentum, the
velocity of the second trolley after the
collision.
Compare the kinetic energy before and after
the collision. Is the collision elastic?
Example
A ball of mass 0.20 kg is dropped from a
height of 3.2 m onto a flat surface which it
hits at 8.0 m s-1. It rebounds to 1.8 m. (g =
9.8 m s-2)
What is the rebound speed just after impact?
What is the change in energy of the ball?
What momentum change has the ball between
just touching the surface and leaving it?
Your Turn