November 13, 2009New Unit

Momentum Intro to Momentum and ImpulseWork Momentum Problems Homework

What do you think of …When you hear the word

“Momentum”Remember inertia

Are they related?Think of momentum as

“Inertia in motion”

Momentum = mass X velocity

Simple calculation… A car moving at 5 m/s with a mass of 2,000

kg Momentum = 5 x 2,000 = 10,000 kg m/s

A donkey with a mass of 450 kg has momentum of 900 kg m/s. Velocity = ?

A rabbit with a momentum of 5 kg m/s is running at 4 m/s. Mass = ?

Impulse – Momentum Theorem

Remember this equation? a = Δv/Δt

And this one? F = ma… Or… a = F/m

If we rearrange these…F Δt = m Δv

Impulse = change in momentum Impulse is how long

a force acts on an object.

More time equals more change in momentum.

Impulse – how long the force acts on the object.

Impulse = force X time intervalImpulse causes a change in momentum

Increasing impulse – increases momentum:

Momentum can be increased by either increasing the force or increasing the time interval.

So… Force X Δ time = mass X Δ velocity

(impulse) (change in momentum)

Safety gear… Can you think of an

application of using impulse to change momentum?

Share with the person to your left or right.

Stop here…Work sheet due in class…Homework due next class…

Affects of Rebounding:

When rebounding you experience more change in velocity, thus more impulse!!

Skiing in the trees…Uhhh…

Ouch!

November 17, 2009

Conservation of momentum, Collision problems, Types of collisions

Conservation of Momentum

The vector quantity of momentum remains unchanged during a collision.

Conservation of momentum

Unless some outside force gets involved…

Net momentum before = net momentum after.

Total (mv) before = Total (mv) after.

=

Collisions

Since the two balls have equal masses, they will also experience equal accelerations.

More collisions… Imagine that you are

hovering next to the space shuttle

Your buddy of equal mass who is moving 4 m/s bumps into you.

If she holds onto you, then how fast do the two of you move after the collision?

And after the collision… Twice as much mass

it must be moving at one-half the velocity.

Thus, the two astronauts move together with a velocity of 2 m/s after the collision.

Elastic = colliding objects rebound without deformation or generation of heat.

Energy is conserved!

Collision types

Inelastic = colliding objects

Deform or …

Generation heat

Do you think energy is conserved?

Collision at Sea

View from the Crow’s Nest

Titanic Cruise

Momentum is Conserved!

Newton’s 3rd Law states:

Force ab = -Force ba

Proof of conservation of momentum:

The time that the two objects are in contact is the same:

time ab = time ba

Proof of conservation of momentum:

So therefore, impulse (force X time) must be the same on each object.

Impulse ab = -Impulse ba

Or…m1Δv = m2Δv

Proof of conservation of momentum:

mavaf - mavai = -(mbvbf - mbvbi)

mavaf + mbvbf = mavai + mbvbi

Jocko the Clown Jocko the clown, who

has a mass of 60.0 kg and stands at rest on the ice, catches a 15.0-kg ball that is thrown to him at 20.0 km/hr.

How fast does Jocko (and the ball) move across the ice after the collision?

15 kg 5 kg

6 m/s 0 m/s

_____ kg

10 kg 4 kg

4 m/s 12 m/s

____kg

6 kg 4 kg

10 m/s4 m/s

8 m/s_____ m/s

Today’s Plan:

Review Momentum as a vector!Lab

Homework…

Homework…

Quick ReviewMomentum = ????When is momentum conserved?What is impulse?What is the impulse momentum

theorem?Why does a bounce cause more force

than a “splat”?

More Review2 types of collisions?Which one generates heat, light or

sound?

Big Collision

Elastic or…

Inelastic?

Conservation of Momentum In the absence of

an external force, the momentum of a system remains unchanged.

momentum before = momentum after.Total (mv) before = Total (mv) after.

wham

12 m/s 4 m/s

3 kg 3 kg

wham

10 m/s 4 m/s

7 kg 9 kg

2 m/s ???

Would you rather…Get hit by a slow large car…

Or a fast small car?

Lab Prep…Remember how to calculate the time for

a dropped object to hit the ground?• Δy = ½ at2 or…

Which lands first?• An object dropped or one thrown

horizontally From the same height…

Momentum Vectors Used when objects

are not moving in the same straight line.

Momentum is conserved… In each direction! North and south…

Equal after and before

East and west Equal after and before

Total momentum? a2 + b2 = c2

Remember?

Look out for the tree… John (120 kg) is cutting

across the run at a velocity of 4 m/s

Jan (60 kg) going downhill at 15 m/s.

They “stick together” after the crash…

Determine their final momentum

Another one for you…2 cars – each 1000 kg mass collide

“inelastically”The red car is heading north at 10 m/sThe blue car is heading east at 20 m/sDetermine the final momentum and

velocity of both cars

Momentum Review

November 25, 2009

Today’s Plan Mass your apparatus Put finishing touches on it (10 minutes) “Let the Eggs Smash” Turn in your egg-celleration lab Go over homework Answer any questions before test Work on review sheet – due next time.

Test on Friday!!!

What is…Momentum ImpulseThe momentum impulse theorem

Which has more momentum…A 10 kg dog…

Or a 2 kg cat?Ok…

The dog is moving at 5 m/s and the cat at 24 m/s

If…A banana is moving at 4 m/s and has

momentum of 0.4 kg m/s… What is its mass?

Impulsively speaking…Which has more impulse

A rock that is hit with a force of 10N for 2 seconds, or

A rock that is hit with a force of 7 N for 3 seconds?

An engineer walks into a bar…OUCH!Which received a bigger impulse – the

bar or the engineer?Which received a larger force?

Same jokeTwo engineers walk into a bar

One bounces off… The other just falls to the floor.

Which one received a larger impulse?Which one received a larger change in

momentum?

Momentum is conservedMomentum initial = momentum finalOnly true when NO EXTERNAL

FORCES act on the objects!!!!

Sam and Sally Sam –

mass = 75 kg Velocity = 2 m/s east

Sally Mass = 60 kg Velocity = 4.5 m/s south

Collide inelastically Calculate total momentum and speed Estimate (using graph paper) direction