Momentum and its Momentum and its ConservationConservation

Chapter 9Chapter 9

MomentumMomentum

•Objects in motion are said Objects in motion are said to have a momentum.to have a momentum.

•Momentum depends on:Momentum depends on:•VelocityVelocity•MassMass

MomentumMomentum

Momentum is a vector. Momentum is a vector. •MagnitudeMagnitude•DirectionDirection

MomentumMomentum

Momentum ( p unit:kg•m/s )A property a moving

object has because of mass and velocity.

MomentumMomentum

p=mv

Momentum of Momentum of SystemsSystems

Momentum of theMomentum of theball changes!!!ball changes!!!

Momentum of Momentum of SystemsSystems

Momentum of theMomentum of thepins change!!pins change!!

Momentum of Momentum of SystemsSystems

Momentum of the ball and Momentum of the ball and pins do not change!!pins do not change!!

ImpulseImpulse

ImpulseImpulse

ImpulseForce applied on an object in a

given amount of time

ImpulseImpulse

FΔt

AccelerationAcceleration

Δv Δt

a=

Newton’s 2Newton’s 2ndnd Law Law

F=ma

Δv Δt

F=m

Impulse / MomentumImpulse / Momentum

FΔt = m Δv

Change in Change in MomentumMomentumImpulse Impulse

Change in MomentumChange in Momentum

ρ = m Δvρ = m (v1-v2)ρ = m v1-mv2

ExampleExample

A 100kg running back is A 100kg running back is moving at a speed of moving at a speed of 12m/s is stopped by a 12m/s is stopped by a linebacker in 0.5s. How linebacker in 0.5s. How

much force did the much force did the linebacker apply to the linebacker apply to the

running back? running back?

ExampleExample

Given: Given: vv11 = 12 m/s = 12 m/s vv22 = 0 m/s = 0 m/s m = 100kg m = 100kg

Δt = 0.5sΔt = 0.5s

Find:Find: F = ?F = ?

Equation: FΔt = m ΔvEquation: FΔt = m Δv F = m F = m ΔvΔv

ΔtΔt F = m F = m vv11 –v –v22

ΔtΔt

F = (100kg)F = (100kg)(12m/s – 0m/s)(12m/s – 0m/s) 0.5s0.5s

F = 2400NF = 2400N

HomeworkHomework

Practice ProblemsPractice Problems2,3,4,13,14 & 152,3,4,13,14 & 15

Pages: 217Pages: 217Due: 1/9/07Due: 1/9/07

Conservation of Conservation of MomentumMomentum

The total momentum of a group of objects does not change unless

outside forces act on the objects.

The momentum before a collision is equal to the momentum

after the collision.

Total Momentum Before = Total Momentum After

Total Momentum Before = Total Momentum After

ExampleExample

A 2000kg car going 25m/s rear ends an 500kg car going 15m/s on ice moving in the same direction. The two cars lock bumpers at collision. How fast does the wreckage move immediately after collision?

ExampleExample

ExampleExample

Given: m1 = 2000kg v1 = 25m/sm2 = 500kg v2 =15m/sm1,2 =2500kg

Find: v1,2= ?

Total Momentum Before = Total Momentum After

ExampleExample

ρbefore = ρafter

ρ1 + ρ2 = ρ1,2

m1v1 + m2v2 = m1,2v1,2

ExampleExample

(2000kg)(25m/s)+(500kg)(15m/s)= v1,2

(2500kg)

m1v1+m2v2= v12

m12

V12 = 23m/s

HomeworkHomework

Practice ProblemsPractice Problems7-127-12

Page: 210Page: 210Due: 1/7/02Due: 1/7/02

ExplosionExplosion

ExplosionExplosion

ρbefore = ρafter

ρbefore = ρcannon+ ρball

ρbefore = 0

ExplosionExplosion

0 = ρcannon+ ρball

ρcannon = ρball

mvcannon = mvball

Explosion - ExampleExplosion - Example

A student, with a mass of 50kg, is standing in a boat, throws a 10kg medicine ball. The ball has a velocity of 10m/s. What is the speed of the student after the throw?

Explosion - ExampleExplosion - Example

Given: ms = 50kgmb = 10kgvb = 10m/s

Find: vs = ?

Explosion - ExampleExplosion - Example

ρbefore = ρafterρbefore = ρstudent+ ρball

ρbefore = 0 ρstudent = ρball

Explosion - ExampleExplosion - Example

msvs = vb mb

vs = mbvb

ms

Explosion - ExampleExplosion - Example

vs =(10kg)(10m/s)

(50kg)

vs = 2m/s

Homework Homework

Page: 217Page: 217Problems: Problems:

34, 35, 36 & 3834, 35, 36 & 38Due: 1/3/07Due: 1/3/07

HomeworkHomework

Practice ProblemsPractice Problems13-1613-16

Page: 214Page: 214Due: 1/7/02Due: 1/7/02