1. Elastic Collisions

2. Momentum and Kinetic Energy
An object in motion has a momentum based on its mass and velocity.
p = mv
The object also has kinetic energy.
K = ½ mv2 = p2 / 2m

3. Kinetic Energy at Collision
Energy is conserved only for conservative forces.
Internal forces may be nonconservative.
The force at the collision is not always conservative. m1 m2
v1i
v2i
Before:
energy lost to heat
v1f
v2f
After:

4. Elastic Collision Elastic
For conservative forces the energy is conserved.
After the collision of contact the potential energy is zero.
The total kinetic energy is conserved – equal before and after the collision.
This an elastic collision.
Elastic

5. Double Conservation
Elastic collisions conserve both momentum and kinetic energy.
Two equations govern all elastic collisions. m1
v1i
v1f m1 m2
v2i m2
v2f
before
after

6. Head-on Collision
An elastic head-on collision takes place in one dimension.
If the collision is not head-on, the force pair is in a different direction.
v1i
v2i
v1i
v2i m1 m2 m1 m2
force and velocity in a line
force and velocity on different lines

7. Related Velocities momentum in a line solve for velocities
v1i
v2i
kinetic energy conservation m1 m2

8. Equal Masses A 150 g ball moves at 1.4 m/s.
The momentum is 0.21 kg m/s
It strikes an equal mass ball at rest.
v1i = 1.4 m/s
v2i = 0
Therefore, v1f = 0
and v2f = v1i
v1i m1 m2
v2f m1 m2
momentum:
kinetic energy:

9. Striking a Heavy Mass
Let m1 << m2, when a golf ball bounces off the floor.
The floor is at rest.
v2i = 0
The final velocity is equal and opposite the initial velocity
momentum:
kinetic energy:
combined:
v1f m1
v1i

10. Striking a Light Mass Let m1 >> m2, when a car strikes a ball.
The ball is at rest.
v2i = 0
For a very heavy m1 , the final velocity of m2 is twice the initial velocity of m1 .
momentum:
kinetic energy:
combined:
v2f m2
v1i