EnergyEnergy

Momentum, Momentum, Collisions, Impulse Collisions, Impulse

MomentumMomentum

A measure of how A measure of how hard it is to stop a hard it is to stop a moving objectmoving object

Momentum = Momentum = (MASS) (MASS)

(VELOCITY)(VELOCITY)

MomentumMomentum

EquationEquation

p= m vp= m vUnits Units

p= mv = p= mv = (kg)(meter(kg)(meter) = ) = kgkg·m·m secondsecond s s

Momentum animationsMomentum animations

http://physics.weber.edu/amiri/http://physics.weber.edu/amiri/director/Momentum.htmldirector/Momentum.html

Momentum Example 1Momentum Example 1

What is the momentum of an What is the momentum of an orange with a mass of 0.5kg orange with a mass of 0.5kg

thrown with a velocity of 5.0 thrown with a velocity of 5.0 m/s?m/s?

m = 0.5kgm = 0.5kgv = 5.0 m/sv = 5.0 m/sp = mv = (0.5kg)(5.0 m/s) = p = mv = (0.5kg)(5.0 m/s) =

2.5 2.5 kgkg··mm ss

Momentum Example 2Momentum Example 2

An object with a mass of 3.0 kg is An object with a mass of 3.0 kg is traveling at a velocity of 4.0 m/s . traveling at a velocity of 4.0 m/s .

What is its momentum?What is its momentum?

More momentum examplesMore momentum examples

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Conservation of MomentumConservation of Momentum

Newton’s Third LawNewton’s Third Law

For every action there is an For every action there is an equal and opposite reaction!equal and opposite reaction!

To accelerate an object, we To accelerate an object, we must apply forcemust apply force

Conservation of MomentumConservation of Momentum

Force(s) must be externalForce(s) must be externalInternal forces do not applyInternal forces do not apply

E.g. to accelerate a car, E.g. to accelerate a car,

do you push do you push

on the dashboard?on the dashboard?

Conservation of MomentumConservation of Momentum

http://id.mind.net/~zona/mstm/http://id.mind.net/~zona/mstm/physics/mechanics/momentum/physics/mechanics/momentum/introductoryProblems/introductoryProblems/momentumSummary3.htmlmomentumSummary3.html

CollisionsCollisions

Net momentum before collision Net momentum before collision ==

Net momentum after the Net momentum after the collisioncollision

Elastic CollisionsElastic Collisions

http://id.mind.net/~zona/mstm/http://id.mind.net/~zona/mstm/physics/mechanics/momentum/physics/mechanics/momentum/solvers/momentumSolvers1.htmsolvers/momentumSolvers1.htm

Inelastic CollisionsInelastic Collisions

http://id.mind.net/~zona/mstm/http://id.mind.net/~zona/mstm/physics/mechanics/momentum/physics/mechanics/momentum/solvers/momentumSolvers1.htmsolvers/momentumSolvers1.htm

ImpulseImpulse

= force exerted over time= force exerted over time

Impulse changes momentumImpulse changes momentum

ImpulseImpulse

EquationEquation

J = (Force) (time)J = (Force) (time)J = Ft = mJ = Ft = mΔΔv = v = ΔΔp = p = m (vm (v22-v-v11) = ) = ΔΔp p

(mass)(change in velocity) =(mass)(change in velocity) = change in momentumchange in momentum

ImpulseImpulse

UnitsUnits

J= (Newton) (seconds)J= (Newton) (seconds)

J = NJ = N··ssForce is in NewtonsForce is in NewtonsTime is in secondsTime is in seconds

Impulse ExampleImpulse Example

An 8N force acts on a 5 kg object An 8N force acts on a 5 kg object for 3 seconds. If the initial for 3 seconds. If the initial velocity of the object was 25 velocity of the object was 25 m/s, what is its final velocity?m/s, what is its final velocity?

F= 8 NF= 8 N m= 5 kg m= 5 kg t= 3 st= 3 s

vv11 = 25 m/s = 25 m/s vv22 = ?= ?J = Ft =(8N)(3s) = 24 NJ = Ft =(8N)(3s) = 24 N··ss BUT we need to find BUT we need to find vv22 ……… ………

Impulse ExampleImpulse Example

J = mJ = mΔΔv = m (vv = m (v22-v-v11) =) =

24 N24 N··s = 5 kg(s = 5 kg(vv2 2 - - 25 m/s) =25 m/s) =

24 = 5 24 = 5 vv22 - 125 m/s =- 125 m/s =

125+24= 5 v125+24= 5 v2 2 = 149/5 = v= 149/5 = v2 2 ==

29.8 m/s29.8 m/s

Impulse problemsImpulse problems

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