As we begin we need to place this information

somewhere we have been.

So we can make an association with what we have

learned.

Momentum and its relation to force

By definition linear momentum is the mass times

the velocity.

UNITS

This is saying that if I have net force

acting on an object for a period of time

then it will have a change in momentum.

Lets solve this equation for momentum.

What is momentum?

(not just inertia)

Momentum can be thought

of as 'moving' inertia

Review

Think inertia

Think 2 thing

1 Think mass

2 Motion and force (f=ma)

How much Momentum does a 100 kg

bear have moving at 8 m/s?

A. 200 kg(m/s)

B. 400 kg(m/s)

C. 600 kg(m/s)

D. 800 kg(m/s)

How much momentum does it lose

if it slows down to 2 m/s?

For my bear problem, something happened to slow the bear down.

Just like matter it can't just disappear.

This says that some force acting

in a given amount of time, will change

my momentum.

consider a

tennis ball

and racket

When the ball first hits the racket

not a lot of force happens

then it grows, and starts to move away

and the force shrinks

this force looks like this:

This force happening over a period of time is special.

We call it an impulse

impulse-momentum theorem

"I cannot for the life of me figure out the stop and think from 11.1"

"Can we please go over the conservation of momentum please?"

"I didn't understand how and why we are using integrals in some formulas.. can we review them?"

**If an average Force of 500 N acts on a stationary mass for a duration of 0.002 s**

What is the momentum of the mass after the collision?

A. 0.1 N s

B. 1.0 N s

C. 10 N s

What is the momentum of the mass after the collision?

A. 0.1 N s

B. 1.0 N s

C. 10 N s

**Conservation**

**Consider the following collision**

mv

mv

mv'

mv'

A

A

A

A

A

A

A

B

B

B

B

B

B

B

F

F

A from B

B from A

This says that initial

Momentum equals final

momentum

Stated nicely:

The total momentum of an isolated

system of objects remains constant.

Now this was a nice example of linear

system. The text then jumps into a nice

discussion on multiple dimensions.

Which then proves that:

The total momentum of an isolated

system is constant, and interactions inside

the system do not change to total momentum.

no change when multiple dimensions are

considered.

When doing these type of problems

remember to:

choose an isolated system (if possible)

if not, choose a section of the problem that is isolated and break it into parts

think of the problem as before and after parts

REMEMBER vectors

Consider the following examples.

There are two main types of collisions

Elastic & Inelastic

We will address only inelastic in this

chapter and get to elastic after we have

discussed energy.

Inelastic collisions

When we looked at the tennis ball and racket

we noted that the ball and the springs were

compressed.

In all collisions there is a compression of atoms.

And as we have mentioned before atoms

are bound to each other through electromagnetic

interactions, that act like little springs

or elastics.

demo

If a collision is elastic these springs bounce back.

If it is inelastic the springs do not.

A perfectly inelastic collision is when the objects

'stick' together after the collision.

We usually consider clay balls, or snow balls, or

car crashes, or trains coupling, etc

When they collide they stick to each other and

gain a common final velocity.

**If equal masses of clay are considered**

and initially they are moving at

the same speed in a head on collision

what will there final velocities be?

A. the negative of their initial speeds

B. depends on the time of the collision

C. Zero

and initially they are moving at

the same speed in a head on collision

what will there final velocities be?

A. the negative of their initial speeds

B. depends on the time of the collision

C. Zero

An explosion is the opposite of a collision.

Maybe a bit better, it is the opposite of an

inelastic collision.

Instead of a few masses sticking together into

one mass

It is one mass breaking apart into many masses.

Again if the system is isolated,

(no external forces)

then the momentum will be conserved.

This is true even though there is an

extremely large force when it explodes.

because this force is an internal one.

In most explosions, the initial momentum is zero

so because momentum is conserved the final momentum

must be zero too.

If the problem is linear, and there are just 2 objects, then

the two momentum are equal and opposite.

Demo

http://media.pearsoncmg.com/aw/aw_0media_physics/vtd/video16.html

Momentum in multiple dimensions

Well, what can we say, momentum is a vector quantity, thus it can be broken down into parts.

If the total momentum is conserved,

each component will be too.

overview

Momentum and impulse

Rockets

2D Momentum

Explosions

Collisions

Conservation

Break the momentum down into the components.

Rockets