Conservation of momentum

Collisions

Homework answers

1a) 23,200 kg m/s eastward

1b) 38.4 km/h eastward, 10.7 m/s eastward

3a) 2.7 m/s same direction as original velocity

3b) 1.3 m/s in the same direction as original velocity

5a) 7,800 N opposite direction of motion

5b) 800 kg (too heavy to lift)

Newton’s Cradle

CONSERVATION OF MOMENTUM

Pool and momentum

What happens to the speed and/or direction of the cue ball after impact?

Conservation of momentum

• If system is closed and isolated:

• Momentum in the system can not be created or destroyed, only transferred

Conservation of momentum

• The total amount of momentum in a isolated system is conserved

• Conserved means that the momentum can be transferred from one object to another, but not lost to the system

• Isolated system: no other factors (forces) play a significant role in the interaction

Closed environment

• No net gain or loss of momentum

• No additional outside forces

Conservation of momentum

• In a closed isolated system, momentum won’t be created or destroyed, but can be transferred

Is this roller coaster a closed system? Is it an isolated system?

A pedal powered roller coaster “Sky Cycle” in Okayama, Japan

Closed systems

• No truly closed, isolated systems

• But lots of systems that are significantly closed and isolated to allow use of the idea of conservation

TYPES OF COLLISIONS

Types

• Elastic: collision where KE and momentum are conserved, nothing sticks together

• Inelastic: collision where only momentum is conserved, nothing sticks together

• Completely Inelastic: collision where only momentum is conserved, objects stick together

Example of Elastic Energy

• There are no examples of large scale perfectly elastic collisions

• Some of the kinetic energy of a moving object is converted into internal (ex. Thermal) energy of the other object involved in the collision, or converted to external TE (heating the surrounding environment)

Most common type of collision is inelastic in nature

EQUATION FOR CONSERVATION OF MOMENTUM

Momentum of all object in system before interaction = Momentum of all objects afterward

Equation for Conservation of Momentum

• Momentum of all objects in system before interaction = Momentum of all objects after the interaction

• pobj1 before + pobj2 before = pobj1after + pobj2 after

Conservation of Momentum equation

• For 2 objects

• (can be expanded by adding a term on each side of equation for each additional object)

m1v1 + m2v2 = m1v1’ +m2v2’

Example problem #1

• Two Car Collision…

• A 1500 kg car was paused at a stop sign, when a 3500 kg truck rammed into it from behind going 15 m/s. If the truck continues forward at 6 m/s after contact, what is the resulting velocity of the car?

• (assume no mass is lost or transferred in either vehicle during the interaction)

Example Problem #2

• A hockey player shots a 1.5 kg puck at 80 m/s that is caught by the opposing team’s 65 kg goalie. What is the resulting velocity of the goalie, who started from rest?

HOCKEY (OCTOPUS ON ICE)Example of conservation of momentum

Using conservation of momentum to solve for mass or velocity

SHOOTING A GUN AND RECOIL

Example of Conservation of momentum

Shooting A Gun

• My experience with a sniper rifle

• What are the action reaction forces

• The amount of momentum in the gun and bullet before pulling the trigger and after

Shooting a artillery piece or a pumpkin

Using conservation of momentum to explain recoil

Example #3

• Mr. Baker shoot a 87g bullet from a 4.8 kg gun. The bullet leaves the gun at 600 m/s If both bullet and gun start from rest, what is the final velocity of the gun.

Another example of conservation of momentumRecoil

• Rifle story

Recoil

• Rifle story

Math behind recoil

• Initial momentum of bullet and gun = 0

• The sum of the momentums of both must total 0

• Momentum of gun = -(Momentum of bullet)

• Stepping on a boat

• Jumping onto a moving hay ride

• Running into someone

Momentum, reaction forces and shooting a gun

Does the gun gain momentum when it fires a bullet?

LAUNCHING A ROCKETExample of conservation of momentum

What force makes the rocket move upward?

How rockets move

• Fuel is ignited, particles move very fast.

• Particles push on the rocket

• Rocket pushes back sending particles down towards Earth

• The upward p of rocket = downward p of exhaust

Conservation in 2 dimensions

• Grenade story

• Car accidents