November 13, 2009  New Unit  Momentum  Intro to Momentum and Impulse  Work 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 interval Impulse 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 3 rd 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…m 1 Δv = m 2 Δv

Proof of conservation of momentum:  m a v af - m a v ai = -(m b v bf - m b v bi )  m a v af + m b v bf = m a v ai + m b v bi

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/s 4 m/s 8 m/s _____ m/s

Today’s Plan:  Review  Momentum as a vector!  Lab

Homework…

Quick Review  Momentum = ????  When is momentum conserved?  What is impulse?  What is the impulse momentum theorem?  Why does a bounce cause more force than a “splat”?

More Review  2 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

wham 10 m/s4 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 at 2 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?  a 2 + b 2 = c 2  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/s  The blue car is heading east at 20 m/s  Determine 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  Impulse  The 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 joke  Two 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 conserved  Momentum initial = momentum final  Only 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