november 13, 2009 new unit momentum intro to momentum and impulse work momentum problems ...
TRANSCRIPT
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November 13, 2009New Unit
Momentum Intro to Momentum and ImpulseWork Momentum Problems Homework
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What do you think of …When you hear the word
“Momentum”Remember inertia
Are they related?Think of momentum as
“Inertia in motion”
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Momentum = mass X velocity
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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 = ?
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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
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Impulse = change in momentum Impulse is how long
a force acts on an object.
More time equals more change in momentum.
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Impulse – how long the force acts on the object.
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Impulse = force X time intervalImpulse causes a change in momentum
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Increasing impulse – increases momentum:
Momentum can be increased by either increasing the force or increasing the time interval.
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So… Force X Δ time = mass X Δ velocity
(impulse) (change in momentum)
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Safety gear… Can you think of an
application of using impulse to change momentum?
Share with the person to your left or right.
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Stop here…Work sheet due in class…Homework due next class…
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Affects of Rebounding:
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When rebounding you experience more change in velocity, thus more impulse!!
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Skiing in the trees…Uhhh…
Ouch!
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November 17, 2009
Conservation of momentum, Collision problems, Types of collisions
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Conservation of Momentum
The vector quantity of momentum remains unchanged during a collision.
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Conservation of momentum
Unless some outside force gets involved…
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Net momentum before = net momentum after.
Total (mv) before = Total (mv) after.
=
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Collisions
Since the two balls have equal masses, they will also experience equal accelerations.
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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?
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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.
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Elastic = colliding objects rebound without deformation or generation of heat.
Energy is conserved!
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Collision types
Inelastic = colliding objects
Deform or …
Generation heat
Do you think energy is conserved?
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Collision at Sea
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View from the Crow’s Nest
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Titanic Cruise
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Momentum is Conserved!
Newton’s 3rd Law states:
Force ab = -Force ba
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Proof of conservation of momentum:
The time that the two objects are in contact is the same:
time ab = time ba
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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
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Proof of conservation of momentum:
mavaf - mavai = -(mbvbf - mbvbi)
mavaf + mbvbf = mavai + mbvbi
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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?
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15 kg 5 kg
6 m/s 0 m/s
_____ kg
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10 kg 4 kg
4 m/s 12 m/s
____kg
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6 kg 4 kg
10 m/s4 m/s
8 m/s_____ m/s
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Today’s Plan:
Review Momentum as a vector!Lab
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Homework…
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Homework…
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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”?
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More Review2 types of collisions?Which one generates heat, light or
sound?
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Big Collision
Elastic or…
Inelastic?
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Conservation of Momentum In the absence of
an external force, the momentum of a system remains unchanged.
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momentum before = momentum after.Total (mv) before = Total (mv) after.
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wham
12 m/s 4 m/s
3 kg 3 kg
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wham
10 m/s 4 m/s
7 kg 9 kg
2 m/s ???
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Would you rather…Get hit by a slow large car…
Or a fast small car?
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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…
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Momentum Vectors Used when objects
are not moving in the same straight line.
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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?
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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
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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
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Momentum Review
November 25, 2009
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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!!!
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What is…Momentum ImpulseThe momentum impulse theorem
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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
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If…A banana is moving at 4 m/s and has
momentum of 0.4 kg m/s… What is its mass?
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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?
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An engineer walks into a bar…OUCH!Which received a bigger impulse – the
bar or the engineer?Which received a larger force?
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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?
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Momentum is conservedMomentum initial = momentum finalOnly true when NO EXTERNAL
FORCES act on the objects!!!!
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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