1. Elastic Collisions

2. 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

3. 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

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

5. 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:

6. 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

7. Striking a Light Mass
Let m1 >> m2, when a golf club strikes a ball.
The ball is at rest.
v2i = 0
The final velocity is equal and opposite the initial velocity
momentum:
kinetic energy:
combined:
v2f m2
v1i

8. Impact Parameter
When collisions are not head on, the objects can come out at an angle.
The masses come out at equal angles.
The distance of the center of the ball to the center of line between them is the impact parameter.
v1f m1 m1
v1i
v2i m2 m2
v2f
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