Momentum

And its

Conservation

Momentum

Momentum is defined as mass times

velocity.

Momentum is represented by the

symbol p, and is a vector quantity.

p = mvmomentum = (mass)( velocity)

the SI units are mass & velocity combined

(kg x m/s)

Bowling ball or basketball?

Picture two lanes at a bowling alley.

One with a bowling ball the other with a

basketball going at the same speed.

Which will exert more force on the pins?

Why?More momentum

Momentum

Example

A 2250 kg pickup truck has a velocity of

25 m/s to the east. What is the momentum of the truck?

p = mv

p = (2250 kg)(25 m/s east)

p = 5.6 x 104 kg x m/s to the east

Momentum

2) A deer with a mass of 146 kg is running head-on toward you at a speed of 17 m/s. You are going north find the momentum of the deer.

p = 2482 kg*m/s south

3) A 21 kg child on a 5.9 kg bike is riding with a velocity of 4.5 m/s to the northwest.

a) What is the total momentum of the child and the bike together?

b) What is the momentum of the child?

c) What is the momentum of the bike?

Conservation ofMomentum

So far we only have considered the momentum

of only one object at a time.Now we will look at two or more objects

interacting with each other.Picture this. . .You are playing pool. You

strike the cue ball it hits the 8 ball. The 8 ball had no momentum before they

collided.During the collision the cue ball loses

momentum and the 8 ball gains momentum.

The momentum the cue ball loses is the same amount that the 8 ball gained.

Conservation ofMomentum

The Law of Conservation of Momentum:The total momentum of all objects

interacting with one another remainsconstant regardless of the nature of the

forces between the objects.total initial momentum = total final momentum

p1i + p2i = p1f + p2f

m1v1,i + m2v2,i = m1v1,f + m2v2,f

Momentum is Conserved

The total momentum of all objects interacting with one another remains

constant regardless of the nature of the forces between the objects.

Go back to the pool table example.

The cue ball and the 8 ball do not have a constant momentum, but the total

momentum is constant.

Momentum is Conserved

Picture this . . .Two people on skates

facing one another. They push away from one another. Initially, they are both at rest with a momentum of 0. When the push away, they move in opposite directions with equal but opposite momentum, so that the total momentum is unchanged and still 0.

Little Problem

A 76 kg boater, initially A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?

Impulse

In a collision of two ordinary objects, both objects are deformed, often considerably, due to the large forces involved.

ImpulseWhen the collision

occurs, the force usually

jumps from zero at the moment of contact to

a very large value within a very short periodof time, and then abruptly returns to

zero again.

Impulse

From Newton’s second law, the net force

on an object is equal to the rate of change

of momentum:

Multiplying both sides by t gives:

Impulse = F x t = ρ = m x v

tmaF

ImpulseImpulse helps us when dealing with forces

that occur over a short period of time. A golf ball being hit A water balloon catching contest ?

It should be noted that Impulse I = F x t

Can be represented by the area under a graph of force vs time.