november 13, 2009 new unit momentum intro to momentum and impulse work momentum problems ...
TRANSCRIPT
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