Momentum

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

Momentum Inertia in motion mass => quantity of matter in an object inertia => an object's resistance to change in motion

Momentum Defined The quantity of motion, momentum, as being directly proportional to the object's mass and velocity. Momentum is a vector quantity……. ……..because it is a scalar (mass) of the vector velocity.

p = Mv

Momentum = mass X velocity

Momentum Defined  = m  v where  is momentum with units kg  m/s m is the mass with units kg v is the velocity with units m/s

Momentum Defined Very Fast objects have Greeeeat momentum Very Massive Objects have Greeeat momentum

Momentum If Direction Not Important……….. …….Momentum = mass x speed Therefore……..p = ms

A large truck has more momentum than a car moving at the same speed because it has a greater mass. Which is more difficult to slow down? The car or the large truck?

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

Impulse In order to change the momentum of an object you must apply a force over some time interval. Impulse = Force  time interval  p= F  t

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

Impulse When force is limited... –increase  t (Follow through!) –make it bounce (Pelton wheel)

Impulse and Momentum Impulse = Change in Momentum = Final (mv) - Initial (mv) F  t = m  v

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

Case 1: Increasing Momentum –Apply a force for a long time. –Examples: Follow through on a golf swing. Pushing a car. FtFt

Case 2: Decreasing Momentum –Apply a force for a long time. –Examples: Air bags in cars. Catching an egg. Boxing, Figure 5.6 Soft collisions, Figure 5.3. FtFt

Case 3: Decreasing Momentum –Apply a force for a short time. –Examples: Boxing Karate FtFt

Minimize the Force To minimize force … –Increase  t catching a ball Bungee jumping

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

Conservation of Momentum This means that the momentum doesn’t change. Recall that F t =  mv) In this equation, F is the "external force". Internal forces cannot cause a change in momentum.

Examples Conservation of Momentum: If there are no external forces, the total momentum for a system remains unchanged. Example 1: a person sitting inside a car pushing against the dashboard Example 2: a bullet fired from a rifle Example 3: a rocket is space

Conservation of Momentum

In any "closed system" the total momentum does not change.

Conservation of Momentum ……..(Total momentum) before event = (Total momentum) after event (m b v b + m r v r ) before = (m b v b + m r v r ) after

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.

Momentum and Collisions Elastic Collisions –objects rebound –e.g. superball Inelastic Collisions –object stick together an usually become distorted and generate heat –e.g. clay ball

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

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

Momentum = Mass x Velocity p = mv

v

Elastic and inelastic collision

MM M M V1V2 V1’ V2’ Before Collision After Collision

Types of Collisions 1. Elastic 2. Inelastic collisions 3. Completely Inelastic collisions

Elastic Collisions Momentum…. is conserved in every collision Kinetic Energy…..is conserved……. …..No sound or heat is produced

Elastic Collisions Examples….. Subatomic particles repelling magnets a “perfect”super ball

Elastic Collisions M 1 v 1o + m 2 v 2o = m 1 v 1f +m 2 v 2f

Inelastic Collisions Momentum…... is conserved Kinetic Energy……. is not conserved lost in form of heat or sound Contains almost all types of collisions

Inelastic Collisions M 1 v 1o + m 2 v 2o = (m 1 +m 2 )v f

Perfectly Inelastic Collisions More…. Kinetic energy is lost as heat or sound Colliding objects stick together

Example Problems...