Download Momentum - WebPhysics

Goal: To understand
momentum
Objectives:
1) To Learn about What momentum is
2) To learn about how to calculate Momentum in 2
dimensions
3) To understand How is momentum changed?
4) To understand the Conservation of momentum
5) To learn about Why momentum is useful to
understand.
6)
In the 2nd hour: To learn about applications to the
conservation of momentum
What is momentum?
• You have probably used the word
momentum tossed out in everyday life –
but not necessarily 100% correctly.
• With a neighbor discuss where you have
heard momentum talked about, and try to
figure out from that what the average
person probably thinks momentum means.
Will the real momentum please
stand up?
• In reality momentum is quite simply a
measure of your mass times your velocity.
• Momentum = mass * velocity
• Anytime you have a collision or separation
it will be a momentum problem
• Lets do some a sample:
• 1) A car with mass of 500 kg moves at a
velocity of 20 m/s. What is the car’s
momentum?
Another example:
• Two cars are headed towards one another.
• The first car has 700 kg of mass and moves at a
velocity of 20 m/s North
• The 2nd car has 1400 kg of mass and moves at a
velocity of 10 m/s South.
• A) How much momentum does each car have in
the North direction (yes momentum has
direction)?
• B) What is the combined momentum of the
cars?
Momentum in 2 dimensions…
Each dimension has momentum.
• So, you have to find the total momentum
for each dimension separately.
• Then at the end you can get a magnitude
if you want, but usually it is more useful to
keep them separate much like you keep a
checking account separate from a savings
account.
Changing momentum
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How do you change momentum?
You use what is called an “impulse”.
Impulse = force * time
Note that force = mass * acceleration
So, Impulse = mass * (acceleration * time)
• What does acceleration * time equal?
Impulse
• Acceleration * time = change in velocity
• So, Impulse = mass * change in velocity in
essence.
• However, you will almost always be given
a force and time to find it.
Example:
• A car runs into a mailbox.
• The mass of the mailbox is 10 kg and the mass of the
car is 800 kg.
• If the car imparts a 2000 N force to the mailbox for 0.4
seconds find:
• A) The impulse on the mailbox
• B) The new velocity of the mailbox (set impulse = to
mass * change in velocity)?
• C) What is the impulse the mailbox imparts on the car?
(What, you have forgotten about Newton’s 3rd law
already?)
• D) How much does the car’s momentum change?
• E) What is the net change in momentum (i.e. if you add
the changes in momentum of the car and mailbox what
do you get)?
Conservation of momentum!
• Momentum is almost always conserved in
a collision.
• In fact it is conserved for each dimension.
• Quick question – will kinetic energy be
conserved?
• KE = 0.5 * mass * velocity * velocity
Energy?
• Sometimes kinetic energy is also
conserved.
• Collisions that conserve kinetic energy are
called elastic collisions.
• Collisions where energy is not conserved
are called inelastic collisions.
• However, what happens to the “lost”
energy for an inelastic collision?
“Oooh, oooh, fender bender”
The pips from that car commercial
• In many collisions energy is transferred.
• Energy is transferred to sound energy, heat
energy, and used to crumple a car.
• These collisions are always inelastic collisions.
• So, if you get hit by a car, you want it to be an
elastic collision!
• You will fly faster and further, but the initial
impact won’t use energy to bend and break
things.
Uses
• Well, using momentum we can better
predict what will happen in many
collisions.
• When might this be useful?
Useful when:
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Playing pool
Bowling
Making safety features for cars or other things
Making a racecar safe (parts fly off at high speed
so that the rest of the car can more safely loose
momentum – protecting the driver).
• Military – bombs ect – especially if you want to
prevent hurting innocent bystanders
• Sports
Conclusion for this hour
• We learned that momentum = mass *
velocity
• Momentum has direction and breaks into
dimensions
• Changing momentum requires impulses
• Momentum is conserved even when
kinetic energy is not
• Knowing about momentum helps
In this hour
• We will apply the conservation of momentum to
some real life problems.
• Example 1 importance of the follow through:
• Two hitters hit a 0.6 kg ball coming at them at 40
m/s South (90 mph).
• The first applies a force of 320 N North for 0.2
seconds.
• The second applies a force of 80 N North for 1.2
seconds (he follows through)
• What will the velocities of the hit balls be for
each hitter and which did a better job of hitting
the ball?
Rear end crash
• A speeding car of mass 800 kg attempting
to elude the police crashes into a 600 kg
car sitting parked at the intersection.
• Ignoring breaks and friction, if the initial
velocity of the speeding car is 50 m/s and
the final velocity of the speeding car is 10
m/s then what will the final velocity of the
other car be?
Head on collision
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Car 1: 25 m/s East and a mass of 800 kg.
Car 2: 30 m/s West and a mass of 900 kg.
A) What is the momentum of each car.
B) What is the net momentum of the two
cars combined.
• C) After the crash Car 1 moves West at a
velocity of 5 m/s. What will the final
velocity of car 2 be?
Ball off a wall
• You bounce a 0.1 kg ball off of the wall.
• The ball hits the wall at 20 m/s and when it bounces it
returns at 80% of the speed of when it hit the wall.
• A) What is the change in velocity for the ball (remember
direction)?
• B) What is the change in momentum?
• C) If the ball is in contact with the wall for 0.6 seconds
then what is the average force that the wall imparts to
the ball?
• D) What is the acceleration the wall gives the ball?
• E) If you ran into the wall and were given that
acceleration what would happen?
Conclusion
• Momentum = mass * velocity
• Momentum is conserved!
• Momentum is conserved in every
direction!
• If you run into something – or it runs into
you – at high velocity – don’t bounce!