Conservation of Momentum

Momentum must be conserved. This fact means that the momentum in a specific direction before a

collision must be equal to the momentum in that same direction after the collision.

Consider the two identical pucks to the right. In the first collision, momentum is conserved because the first puck

completely stops and the second puck departs with the same initial momentum as the first puck in the same direction as the first puck.

In the second collision, momentum is conserved because both pucks move off with one half the speed of the first puck before the collision and in the same direction as the first puck.

Why isn’t the momentum conserved in the collision to follow? The second puck moved with the same speed but in a different

dimension. Therefore, momentum was not conserved in this collision.

Type of Collision

Momentum is Conserved

Kinetic Energy is Conserved

Elastic Yes Yes

Inelastic Yes No

Perfectly Inelastic Yes No

Momentum – Elastic Collisions Elastic Collision – a collision in which the colliding bodies do not stick

together. The equation used for elastic collisions is as follows.

FFII vmvmvmvm 22112211

Momentum – Inelastic Collisions Inelastic Collision – a collision in which the colliding bodies stick

together. The equation used for elastic collisions is as follows.

1 1 2 2 Fm v m v MV

Momentum

Identify the number and types of collisions in the animation below.

FFII vmvmvmvm 22112211 FII MVVmvm 2211

Momentum

Identify the number and types of collisions in the animation below.

Momentum

Identify the number and types of collisions in the animation below.

Momentum

Identify the number and types of collisions in the animation below.

Momentum – Elastic Collisions What type of collision is depicted in the collision of the offensive

paddle and the hockey puck? What about the collision with the defensive paddle? If the offensive paddle (m = 0.5 kg) was traveling at 0.75 m/s before

the collision and 0.25 m/s after the collision, then how fast was the puck ( m = 0.2 kg) moving after the collision?

FFII vmvmvmvm 22112211 FII MVVmvm 2211

Momentum – Elastic Recoil Collisions Recoil can be understood by considering the result of the explosion of

the gun powder on a gun. The bullet flies in one direction while the gun recoils in the other

direction.

Momentum – Inelastic Collisions An explosive bowling ball (m1 = 10 kg, v1I = 10.0 m/s) rolls towards a

gun as shown. The gunman hopes to keep the ball away by shooting

a bullet (m2 = 1.1 kg, v2I = 95.0 m/s) into the ball.

What type of a collision is the one depicted here?

What is the final velocity of the bowling ball?FFII vmvmvmvm 22112211 1 1 2 2 Fm v m V MV

Momentum – Inelastic Collisions

FFII vmvmvmvm 22112211 FII MVVmvm 2211

Two Dimensional Elastic Collision

Elastic Collision: A q-ball (m = 0.6 kg) collides with an eight ball (m = 0.7 kg) that was initially at rest. The initial velocity of the q-ball was V1I = 1.2 m/s. After the collision, the q-ball moves away with a velocity V1F = 0.6 m/s at an angle of 45. Determine the velocity, V2F, of the eight ball after the collision.

1IP

1FP

2 0IP 2FP

Two Dimensional Elastic Collision Draw vector diagrams showing the

resultant velocities of the colliding bodies.

This procedure is the same one used when solving force problems using free body diagrams.

1 1 2 2 1 1 2 2I I F Fm v m v m v m v

1 1 2 2 1 1 2 2Iy Iy Fy Fym v m v m v m v

1 1 2 2 1 1 2 2Ix Ix Fx Fxm v m v m v m v

1FxP

1FP1FyP

1IP

2 0IP

2FP

2FxP 2FyP

Two Dimensional Inelastic Collision Inelastic Collision: A bullet (m = 0.15 kg) collides with a bowling

ball (m = 6.0 kg) that was initially moving at a velocity of v2I = 0.75 m/s due left. The initial velocity of the bullet was v1I = 145 m/s at an angle of 35. The bullet sticks inside of the ball. Determine the velocity, VF, after the collision.

FP

2 IP

1IP

Two Dimensional Inelastic Collision Draw vector diagrams showing

the resultant velocities of the colliding bodies.

This procedure is the same one used when solving force problems using free body diagrams.

1 1 2 2I I Fm v m v MV

1 1 2 2Ix Ix Fxm v m v MV

1 1 2 2Iy Iy Fym v m v MV

FP

2 IxP1IP FxP

2 IyPFyP

2 IP

Momentum A bowling ball (m = 8.50 kg, v = 4.00 m/s @ 12.5) strikes a bowling pin (m = 1.80

kg) initially at rest. After the collision, the pin has a velocity of 9.85 m/s @ 45.0. What is the final velocity of the bowling ball?

Momentum – Elastic Collision Example

Three identical hockey pucks on a frictionless air table have repelling magnets attached.

They are initially held together and then released.

What is the initial momentum of this system?

Each has the same speed at any instant.

One puck moves due North. In which directions do the

other two pucks move?

1 1 2 2 1 1 2 2I I F Fm v m v m v m v

1 1 2 2I I Fm v m v MV

Intersection Collision Problems

Two cars approach an intersection with a malfunctioning stop light.

The red car (m = 2000.00 kg) approaches the intersection from the North.

The blue car (m = 2250.00 kg) approaches the intersection from the West at the speed limit (40.0 km/hr) on both roads.

Cars are designed to collide in-elastically in order to minimize injury to passengers.

After the collision, the cars move at a velocity of 31.7 km/hr @ -48.01.

If you were the police officer investigating the accident, then would you write one of the drivers a citation? Explain your answer.

Momentum – Elastic Collisions The defender below tries to stop the puck by pushing his paddle (m

= 0.50 kg) across the table at a velocity of 0.60 m/s at 88.55. After the collision, the paddle moves at a velocity of 0.25 m/s at -

85.98, and the puck (m = 0.20 kg) moves at a velocity of 3.05 m/s at 44.00.

Is the puck speed shown on the laser speed detector correct? Justify/explain your answer.

Momentum While climbing a cliff, a super model (m = 51.0 kg)

slips and falls. She falls 35.00 m before she is rescued by Super

Doctor Physics (m = 63.0 kg, v = 27.85 m/s @ 130). What was their velocity immediately after the

collision?