Chapter 6

Momentum

1. MOMENTUM

• Momentum - inertia in motion• Momentum = mass times

velocityvmp

Units - kg m/s or sl ft/s

2. IMPULSE

• Collisions involve forces (there is a v).

• Impulse = force times time.

ΔtFI

Units - N s or lb s

3. IMPULSE CHANGES MOMENTUM

Impulse = change in momentum

amF

vmtF

tv

mF

vmtF

pI

)vmvm(tF if

)vv(mtF if

)pp(tF if

I

t

Case 1Increasing Momentum

Follow through

Examples:Long Cannons

Driving a golf ballCan you think of others?

t p

I

F

p

Video ClipVideo Clip

Tennis racquet and ballTennis racquet and ball

tF

Case 2Decreasing Momentum over a

Long Time

Examples:Rolling with the Punch

Bungee JumpingCan you think of others?

Ip

tF

Warning – May be dangerous

Case 3Decreasing Momentum over a

Short Time

Examples:Boxing (leaning into punch)

Head-on collisionsCan you think of others?

tFIp

4. BOUNCING

There is a greater impulse with bouncing.

Example:Pelton Wheel

Demo – Impulse PendulumDemo – Impulse Pendulum

• Consider a hard ball and a clay ball that have +10 units of momentum each just before hitting a wall.

• The clay ball sticks to the wall and the hard ball bounces off with -5 units of momentum.

• Which delivered the most “punch” to the wall?

Initial momentum of the clay ball is 10.Final momentum of clay ball is 0.The change is 0 - 10 = - 10.It received - 10 impulse so itapplied + 10 to the wall.

Initial momentum of the hard ball is 10.Final momentum of hard ball is - 5.The change is - 5 - 10 = - 15.It received - 15 impulse so itapplied + 15 to the wall.

5. CONSERVATION OF MOMENTUM

Example:Rifle and bullet

Demo - Rocket balloons (several)Demo - Clackers Video - Cannon recoilVideo - Rocket scooter

Consider two objects, 1 and 2, and assume that no external forces are acting on the system composed of these two particles.

i11f111 vmvmtF

Impulse applied to object 1

i22f222 vmvmtF

i22f22i11f11 vmvmvmvm0

Impulse applied to object 2

Total impulseappliedto system

f22f11i22i11 vmvmvmvm

or

Apply Newton’s Third Law21 FF

tFtFor 21

•Internal forces cannot cause a change in momentum of the system.

•For conservation of momentum, the external forces must be zero.

Chapter 6 Review Questions

The product of mass times velocity is most appropriately called

(a) impulse

(b) change in momentum

(c) momentum

(d) change in impulse

You jump off a table. When you land on the floor you bend your knees during the landing in order to

(a) make smaller the impulse applied to you by the floor

(b) make smaller the force applied to you by the floor

(c) both (a) and (b)

An egg dropped on carpet has a better chance of surviving than an egg dropped on concrete. The reason why is because on carpet the time of impact is longer than for concrete and thus the force applied to the egg will be smaller.(a) True(b) False

6. COLLISIONS

Collisions involve forces internal to colliding bodies.

Elastic collisions - conserve energy and momentum

Inelastic collisions - conserve momentum

Totally inelastic collisions - conserve momentum and objects stick together

Demos and Videos

Demo – Air track collisions (momentum & Demo – Air track collisions (momentum & energy)energy)Demo - Momentum balls (momentum & energy)Demo - Momentum balls (momentum & energy)Demo - Hovering disks (momentum & energy)Demo - Hovering disks (momentum & energy)Demo - Small ball/large ball dropDemo - Small ball/large ball dropDemo - Funny BallsDemo - Funny BallsVideo - Two Colliding Autos (momentum)Video - Two Colliding Autos (momentum)

Terms in parentheses represent what is conserved.Terms in parentheses represent what is conserved.

Collision between two objects of the same mass. One mass is at rest.

Collision between two objects. One not at rest initially has twice the mass.

Collision between two objects. One at rest initially has twice the mass.

Simple Examples of Head-On Collisions

(Energy and Momentum are Both Conserved)

Head-On Totally Inelastic Collision Example

• Let the mass of the truck be 20 times the mass of the car.

• Using conservation of momentum, we get

mph60vtruck mph60vcar

v)m21()mph60(m)mph60(m20

v21)mph60(19

)mph60(2119

v

mph3.54v

initial momentum of system = final momentum of system

• Remember that the car and the truck exert equal but oppositely directed forces upon each other.

• What about the drivers?• The truck driver undergoes the same

acceleration as the truck, that is

tmph7.5

tmph)603.54(

• The car driver undergoes the same acceleration as the car, that is

tmph3.114

t)mph60(mph3.54

The ratio of the magnitudes of these two accelerations is

207.53.114

Remember to use Newton’s Second Law to see the forces involved.

• For the truck driver his mass times his acceleration gives

F

am

For the car driver his mass times his greater acceleration gives

ma

F

•

• Your danger is of the order of twenty times greater than that of the truck driver.

TRUCKS , big trucks that is.• Don’t mess with T

7. More Complicated Collisions

Vector Addition of Momentum

Collision between two objects of the same mass. One mass is at rest.

Example of Non-Head-On Collisions

(Energy and Momentum are Both Conserved)

If you vector add the total momentum after collision,you get the total momentum before collision.

Examples:Colliding cars

Exploding bombs

Video - Collisions in 2-DVideo - Collisions in 2-D

Chapter 6 Review Questions

In which type of collision is energy conserved?

(a) elastic(b) inelastic(c) totally inelastic(d) All of the above(e) None of the above

A Mack truck and a Volkswagen have a collision head-on. Which driver experiences the greater force?

(a) Mack truck driver(b) Volkswagen driver(c) both experience the same force