Chapter 6 Momentum

Momentum and Collisions This chapter is concerned with inertia and motion. Momentum helps us understand collisions.

Momentum = mass X velocity p = mv Momemtum is a vector

Sample Questions Which has more momentum, a 1-ton car moving at 100 km/hr or a 2-ton truck moving at 50 km/hr? Carp = mv = (1 ton)(100km/hr) Truckp = (2 ton)(50 km/hr)

Large Momentum Examples:  Huge ship moving at a small velocity  High velocity bullet P = m v

Impulse Newton’s Second Law can read  F = ma =m(  v/  t) =(  mv)/(  t) =(  p/  t) Rearranging, Impulse =  p = F  t

Sample Question Does a moving object have impulse? Impulse is not a property of the object, but something that it can give or get from an interaction. Notice that it is not motion that gives us an impulse (v) but a change in motion (  v).

Sample Question Does a moving object have momentum? Yes, but recall that motion is relative, so the momentum depends on having velocity with respect to the standard of rest.

When Force is Limited Apply a force for a long time.  Examples:  Follow through on a golf swing.  Pushing a car. FtFt

Make it Bounce p1p1 p 2 = -p 1  p = p 2 - p 1 = -p 1 - p 1 = -2p 1

Minimize the Force To minimize force …  Increase  t  catching a ball  Bungee jumping FtFt

Maximize Momentum Change Apply a force for a short time.  Examples:  Boxing  Karate FtFt

If  F = 0, then impulse =  p = zero, or Momentum is conserved

Demonstrations Rocket balloon Cannon Rocket Scooter

When can Momentum be Conserved? u Internal forces cannot cause a change in momentum of the system. u For conservation of momentum, the external forces must be zero.

COLLISIONS Collisions involve forces internal to colliding bodies. Inelastic collisions - conserve momentum Totally inelastic collisions - conserve momentum and objects stick together Elastic collisions - conserve energy and momentum

v = 10v = 0 Before Collision MM p = Mv MM After Collision p = 2Mv’ Mv = 2Mv’ v’ = ½ v v’ = 5 v’

Collisions Air Track Link

Conserve Energy and Momentum Case 1: Case 2: Equal masses M > M Case 3: M < M Before Collision