Momentum• Read Your Textbook: Introduction to Physical Science

– Chapter 3.5– Chapter 4

• Practice Homework Exercises

Motion ReviewVelocity = change in displacement = x Speed

change in time t

Acceleration = change in velocity = v How fast are you

change in time t getting faster.

Force = mass x acceleration = m v a = F/m

t

A look at the two definitions of acceleration….

Force and Acceleration F = m v = m a

t

If a Force acts occurs over a short time,

a small acceleration results.

If a Force acts over a long time,

a large acceleration results.

Cannon Ball!

F t = m v

For the same Force (amount of powder), why is the speed of

a cannon ball greater when fired from a longer cannon barrel?

F = m v

t

Interaction Time

F t = m v

The longer cannon barrel gives the cannon ball a larger

impulse and therefore more momentum. The Force (F) is

allowed to act for a longer time t to build up velocity (v).

F t = m v

Impulse and Momentumacceleration = acceleration

a = a

F = v F t = m v

m t

Impulse Momentum

Impulse and Momentum F = v F t = m v

m t

Impulse Momentum

If a change in velocity (momentum) occurs over a short time,

a large force must act.

If the change in velocity (momentum) occurs over an extended

time, a small force is acting. • Recall the Egg Toss Game

• A Boxer Bobs and Weaves His Head

• Bending Legs Upon a Parachute Landing

Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated

system, the total momentum remains unchanged.

Momentum = mass x velocity P = m v

Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated

system, the total momentum remains unchanged.

Momentum = mass x velocity P = m v

Consider the following collision:

Before After

mMV

v

Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated

system, the total momentum remains unchanged.

Momentum = mass x velocity P = m v

Consider the following collision:

Before After

m M mMV

v

v’

V’

Conservation of MomentumMomentum is a conserved quantity, that is, for any isolated

system, the total momentum remains unchanged.

Momentum = mass x velocity P = m v

Consider the following collision:

Before After

Total Momentum

MV + mv = total momentum = MV’ + mv’

m M mMV

v

v’

V’

v

M

m

Total Momentum Before:

M V + m v

60 kg ( 0 km/hr) + 20 kg (10 km/hr) = 200

Ice Ball Toss

Momentum After (must be identical to momentum before)

= 200

= (M+m) v’

200 = (M+m) v’

200 = (60+20) v’

v’ = 200/80 = 2.5 km/hr

Ice Toss

What is the total momentum of the debris from a firecracker?

Before After

M V = 0 = total momentum before

Total Momentum After = m1v1 + m2v2 + m3v3 + …

Conservation of Momentum

m1

m2

m4

m3

What is the total momentum of the debris from a firecracker?

Before After

M V = 0 = total momentum before

Total Momentum After = m1v1 + m2v2 + m3v3 + …

= 0

Conservation of Momentum

m1

m2

m4

m3

Rifle ShotLet mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s

mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle

0 = 0.3 kg (370 m/s) + 5kgVrifle

Rifle ShotIf momentum is conserved, why doesn’t a rifle kill you upon

recoil after firing a bullet?

Before: mbulletvbullet + MrifleVrifle = 0

Rifle ShotIf momentum is conserved, why doesn’t a rifle kill you upon

recoil after firing a bullet?

Before: mbulletvbullet + MrifleVrifle = 0

After: = 0

Let mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s

Rifle ShotLet mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s

mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle

0 = 0.3 kg (370 m/s) + 5kgVrifle

-0.3(370) = 5 kg Vrifle

Vrifle = - 0.3(370)/5 = - 2.2 m/s

Rifle ShotLet mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s

mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle

0 = 0.3 kg (370 m/s) + 5kgVrifle

-0.3(370) = 5 kg Vrifle

Vrifle = - 0.3(370)/5 = - 2.2 m/s

Shoulder aches, BUT your alive!

Mriflevrecoil = mbulletVbullet

Now you try:• What is the velocity of a bullet (m = 0.15 kg) after being fired from a 10 kg rifle (NOTE: rifle recoils with a velocity of 3 m/s).

A. 30 m/sB. 1.5 m/sC. 200 m/sD. 310 m/sE. none of these

mbulletvbullet + MrifleVrifle = 0.15 kg (vbullet) + 10kg (3 m/s)

0 = 0.15 kg (vbullet) + 30 kg m/s

-30 kg m/s = 0.15 kg vbullet

vbullet = - 30 kg m/s /(0.15 kg) = - 200 m/s

Train LinkAn train engine runs into a stationary box car

weighing 4x more than itself to link up. If the engine

was traveling 10 mph before link up, how fast does

the train move after?

Train LinkAn train engine runs into a stationary box car

weighing 4x more than itself to link up. If the engine

was traveling 10 mph before link up, how fast does

the train move after?

MOMENTUM BEFORE = MOMENTUM AFTER

MVBC + 0 = (M + 4M) VAC

Train LinkAn train engine runs into a stationary box car

weighing 4x more than itself to link up. If the engine

was traveling 10 mph before link up, how fast does

the train move after?

MOMENTUM BEFORE = MOMENTUM AFTER

MVBC + 0 = (M + 4M) VAC

M(10) = (5M) VAC

10 = 5 VAC

2 = VAC

Angular MomentumL Angular Momentum: A combination of...

m Mass

v Speed of Rotation

r Mass Position (with respect to rotational axis)

L = m v r

• Conservation Examples:– Spins of Dancers or Ice Skaters– Those Funky Coin Vortexes in Stores– Tops and Gyroscopes– Riding a Bicycle

Precession and the Earth

• 1 complete cycle takes 26,000 years

Orbit ApplicationAngular Momentum L,

is the product of a planet's mass (m),

orbital velocity (v)

and distance from the Sun (R).

The formula is simple: L = m v R,

where R = a function of e the eccentricity.

Faster, CloserConservation of Angular Momentum:

L = L

m V r m v R

Summary• Impulse and Momentum

– F t = m v

• Conservation of Momentum– Total Momentum (P = M V)

• Angular Momentum– L = m v r