Momentum and Impulse

Momentum

All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.

The amount of momentum which an object has is dependent upon two variables:

how much matter is moving?

how fast the matter is moving?

Momentum

Inertia in motion

Vector quantity

Momentum = mass x velocity

p = mv p is momentum

m is mass

v is velocity

Units will be Kg• m/s

Momentum is a measure of moving inertia. An

object at rest has inertia but no momentum.

Let’s Compare…• A moving truck has more momentum than a car moving at

the same speed because the truck has more mass.

• A fast car can have more momentum than a slow truck.

• A truck at rest has no momentum at all.

• A truck rolling down a hill has more momentum than a

roller skate with the same speed. But if the truck is at rest

and the roller skate moves, then the skate has more

momentum.

Think about…

Which has more momentum…

1200 kg steamroller moving at 1 m/s

or

1 kg bullet moving at 1200 m/s

Think About…

What is the momentum of a 40 kg jogger

running southward at 2 m/s?

What is the momentum of a 60 kg halfback

moving east at 9 m/s?

Think About…

What is the momentum of a 40 kg jogger

running southward at 2 m/s?

80 kg•m/s south

What is the momentum of a 60 kg halfback

moving east at 9 m/s?

540 kg•m/s east

If the boulder and the boy

have the same momentum,

will the boulder crush the

boy?

p = mv

No. The boy has less mass, thus he will need to have a much higher velocity in order to have the same momentum as the boulder with a much greater mass.

Impulse/ DMomentum Theorem

As the force acts upon the object for a given

amount of time, the object's velocity is changed.

Remember Newton’s 2nd law equation: F = ma

& a = Dv/ Dt

F Dt = D(mv)

= mvf – mvi

= m(vf – vi)

•Impulse = change in momentum

IMPULSE – A force applied for a period

of time which results in a change of

momentum.

Impulse = change in momentum

F∆t = ∆p = ∆(mv)

F∆t = mvf - mvi

F∆t = m (vf – vi)

To change the momentum of a body, a

force must be applied to the mass. The

longer this force is applied to the mass, the

greater effect it will have on changing the

momentum.

Impulse Change in momentum

Impulse = ∆ (mv)

Impulse = F• ∆t

Ft = ∆(mv) F is Force

t is time Force is applied

m is mass

v is velocity

Impulse will have the same units as momentum (Kg• m/s) but it is NOT momentum…It is a CHANGE in momentum

Think About…

A hockey player applies an average force of 80 N to a

.25 kg puck for a time of 0.1 seconds. Determine the

impulse experienced by the hockey puck.

Think About…

A hockey player applies an average force of 80 N to a

.25 kg puck for a time of 0.1 seconds. Determine the

impulse experienced by the hockey puck.

imp = F∆t = (80N)(.10s) = 8 N•s or kg•m/s

Increasing Momentum

To increase the momentum of an object, apply the greatest

force possible for as long as possible.

A golfer teeing off and a baseball player trying for a home

run do both of these things when they swing as hard as

possible and follow through with their swing.

Think of rifle vs. hand gun barrel

Decreasing Momentum

Think about riding in an out of control car…would you

prefer hitting a haystack or brick wall?

When hitting either the wall or the haystack and coming to a

stop, the momentum is decreased by the same impulse.

• The same impulse does not mean the same amount of force or

the same amount of time.

• It means the same product of force and time.

• To keep the force small, we extend the time.

Decreasing Momentum

If the change in momentum occurs over a long time, the

force of impact is small.

If the change in momentum occurs over a short time, the

force of impact is large.

Decreasing Momentum

Examples…

• A padded dashboard in a car is safer than a rigid metal one.

• Airbags save lives.

• To catch a fast-moving ball, extend your hand forward and

move it backward after making contact with the ball.

• Egg toss game.

• Jump off roof or fence bend your knees.

• Drop glass on tile/concrete vs. carpet.

• Circus acrobats and net

• Boxer “rides” a punch

• Others?

Conservation of Momentum Remember Newtons 2nd Law…To accelerate an object exert

a force on it.

To change momentum of an object, exert an impulse on it.

Need unbalanced or net impulse

Law of Conservation of Momentum- states that, in the

absence of an external force, the momentum of a system

remains unchanged

The force or impulse that changes momentum must be

exerted on the object by something outside the object.

• Molecular forces within a basketball have no effect on the

momentum of the basketball.

• A push against the dashboard from inside does not affect the

momentum of a car.

These are internal forces. They come in balanced pairs that cancel

within the object.

The momentum before firing is zero. After firing, the net

momentum is still zero because the momentum of the

cannon is equal and opposite to the momentum of the

cannonball. Momentum of cannon and momentum of

cannon ball

Conservation of Momentum

Collisions

Objects collide in absence of external forces

net momentum before = net momentum after

Very short impact so ignore changes from outside forces (ex.

Car crash do not consider rubber on concrete etc.)

Types of Collisions…

Elastic

Inelastic

Break Apart

Collisions Elastic

Objects bounce off each other

Neither deformed permanently

No heat or sound given off

(Ex. Bumper cars, baseball and bat, basket ball and floor, golf

club and ball, billiard balls.)

Collisions Inelastic

Objects become tangled or coupled –They stick!

Distortion happens

Heat and sound given off

(Ex. Sticking car crash, linebacker and running back)

Collisions Break Apart or Explosion

Objects start as one

Objects move in opposite directions

(Ex. Shooting a gun or astronaut throwing something)

Collision Equations

Elastic Collision

m1v1 + m2v2 = m1v1’ + m2v2’

Inelastic Collision

m1v1 + m2v2 = (m1 + m2)vf

Break Apart or Explosion

(m1 + m2)vi = m1v1 + m2v2

Think About…

A 4o kg football player leaps through the air to collide with

and tackle a 60 kg player heading toward him (also in the

air). If the 40 kg player is heading to the right at 7 m/s and

the 60 kg player is heading toward the left at 3 m/s, what is

the speed and direction of the tangled players?

Think About…

1 m/s. Positive so to the right.