? Momentum ?

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? Momentum ?
A.K.A. The difference between moving and
standing still.
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Definition

• Mathematical
• Momentum Mass (kg) x Velocity (m/s)
• Or
• pmvThe units for momentum are kgm/s

• Verbal
• Momentum is inertia in motion.
• Remember Newtons 1st law. Its analogous to
  Inertia.

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Momentum mass x velocity

• Momentum is a true measure of how difficult it is
  to stop something.
• A charging hippo can do some damage, a hippo
  charging twice as fast can do twice the damage.
• Calculating momentum is easy, just find the mass
  and the velocity and multiply.
• p mv
• Notice that mass and velocity both affect
  momentum equally.

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Momentum

• How much momentum does Hulk Hogan have if he has
  a mass of 120 kg and runs at you with a velocity
  of 18 m/s?
• 6.67 kgm/s
• 2160 kgm/s
• 138 kgm/s
• 0 momentums

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Momentum

• A train has a mass of 7.22x107 kg and a momentum
  of 2.7x108 kgm/s. What is the velocity of the
  train?
• 0.267 m/s
• 3.42x108 m/s
• 3.74 m/s
• 0 m/s

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Impulse where momentum comes from!

• Only a force can give something momentum (or
  take it away).
• Lets say you are a member of a bobsled team. You
  push the sled to speed it up. The longer the you
  push the sled the greater the velocity and the
  greater the momentum you give it so time is also
  a factor.
• Or think about the airbags in your car. They give
  you more time to slow down so less force is
  applied to your body.
• So a force applied for a certain time leads to
  a change in momentum.
• ?p (Force) x (time) This is called an impulse
  (I)
• I Ft
• Impulse is a change in momentum (?mV) ?mV
  Ft I m?V Ft
• The units for impulse are the same as momentum
  (kgm/s)

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Impulse
A stuntman jumps off a building while shooting
Die Hard VIII Die Already! If the airbag he
lands on is able to catch him by applying a force
of 1,500 N over 2.5 seconds, what is the impulse
applied to the stuntman (how much does it change
his momentum)?
I Ft
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Impulse
Jack throws a 0.5 kg basketball at Jill with a
velocity of 12 m/s. How much force would Jill
need to apply to stop the ball in 1.2 seconds?
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Momentum is Conserved!
Meaning Once an object has momentum it is going
to keep it OR give it to something else! IT does
not just disappear! Conservation of momentumThe
total amount of momentum in a system does not
change!!! pi pf
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Collisions and Conservation of Momentum!

• A.K.A problems!
• By finding the momentum of the system we can
  calculate the speeds (velocity) of the 2 objects
  after the collision.
• Remember to GUESS!

Conservation of momentum For collisions pi
pfp1i p2i p1f p2fm1v1 m2v2 m1v3
m2v4(V3 is the final velocity of m1 and V4 is
the final velocity of m2)
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Collisions!

• 2 types of collisions
• Elastic collision
• 2 objects collide and then they bounce off of
  each other with no loss of Kinetic Energy.
• Inelastic collision
• 2 objects collide and then they bounce off of
  each other, but there is a loss of Kinetic
  Energy.
• Whats another example?
• Remember In both situations momentum is always
  conserved!

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Example 1

• You are playing pool with a friend and kicking
  butt. You hit the cue ball at 2.5 m/s towards the
  8 ball which is at rest. After they collide
  elastically the cue ball continues at a velocity
  of 0.6 m/s. If the mass of both balls is 1.5 kg,
  what is the final velocity of the 8 ball?
• 1.9 m/s
• 0.6 m/s
• 2.5 m/s
• 0 m/s

m1 m2 V1 V2 V3 V4
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Example 2

• Bill is out cruising in his brand new Kia until
  he hits some crazy traffic on IH-35. Ohh no! He
  just got rear-ended (in an elastic collision) by
  some jerk in a giant 2000 kg truck with an
  initial velocity of 17 m/s! Bills Kia has a mass
  of 850 kg and he was initially traveling at 0.75
  m/s. If the jerks truck continued with a
  velocity of 10 m/s after the collision, what is
  his final velocity after the collision?

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Momentum is a vector Victor!!

• Direction is important!
• 2 vectors in the opposite direction will
  subtract.
• 2 vectors in the same direction add together.
• Think about the velocities of the objects.
  Positive is to the right (or east), negative is
  to the left (or west).
• Example 2 identical lumps of clay fly toward
  each other. They each have a mass of 2 kg. One
  is moving at 5 m/s and the other at 8 m/s.
• What is the total momentum of the system?
• A) 26 kgm/s B) 6 kgm/s C) 10 kgm/s

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Example 3

• Jimmy is playing with his Hotwheel cars! He has a
  truck that has a mass of 1.1 kg, and a sports car
  that has a mass of 0.75 kg. Jimmy wants them to
  crash in an elastic collision, so he gives the
  truck a velocity of 5.6 m/s to the right, and
  gives the car a velocity of 3.9 m/s to the left.
  If the velocity of the truck is 1.2 m/s to the
  right after the crash, what is the final velocity
  of the car after the collision?

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Perfectly Inelastic Collisions and Conservation
of Momentum!

• Now we are also going to work problems with
  perfectly inelastic collisions.
• Remember in perfectly inelastic collisions two
  objects collide and stick together, due to this
  kinetic energy is lost.
• You can look at the momentum of the system to
  figure out how fast they will be traveling after
  they collide!
• Also, explosions are considered inelastic
  collisions, just backwards. So, reverse the
  formula!

Conservation of momentum For inelastic
collisions pi pfm1v1 m2v2 (m1
m2)v3 (V3 is the final velocity of the system)
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Example 1

• The flash (100 kg) collides with the Blob (500
  kg) at a velocity of 150 m/s and gets wedged into
  some of the Blobs bellyfat so that they stick
  together. What will the new velocity of the
  blob/flash system be if the blob was initially at
  rest?
• 9,000,000 m/s
• 0.04 m/s
• 25 m/s
• 0 m/s

m1v1 m2v2 (m1 m2)v3
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Example 2

• Bill is out cruising in his new Mercedes until he
  hits some crazy traffic on Loop 360. Ohh no! He
  just got rear-ended again (in an inelastic
  collision) by the same jerk in 1000 kg corvette
  with an initial velocity of 17 m/s! If Bills
  Mercedes has a mass of 850 kg and he was
  initially traveling at 0.75 m/s, what is his
  final velocity after the collision?

m1v1 m2v2 (m1 m2)v3
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Explosions!

• Explosions are another type of perfectly
  inelastic collision.
• They are simular to the types of inelastic
  collisions we have seen, but just backwards.
  Kinetic Energy is gained.
• Two objects start as one mass, and after the
  collision, become two different masses.
• Formulapi pf(m1 m2)V3 m1V1 m2V2
  0 m1V1 m2V2
• (The initial momentum of the system is nearly
  always zero when the object starts from rest.)

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Explosions!

• Problem A hand grenade is at rest when it
  explodes into two pieces that go flying in
  opposite directions. The mass of one piece is 2.3
  kg and it flies to the right with a velocity of
  54.9 m/s. What is the mass of the second piece if
  it flies to the left with at 78.1 m/s?

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Unit 3 Momentumformulas!

• Momentum mass x velocity
• p mv
• Conservation of Momentum (CoM)
• pi pf
• Inelastic and Elastic Collisions objects
  bounce off each other.
• m1v1 m2v2 m1v3 m2v4
• Perfectly Inelastic Collisions objects stick
  to each other.
• m1v1 m2v2 (m1 m2)v3
• For explosions, reverse this formula!
• Impulse Change in momentum
• I ?p Ft

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Hammer time

• Thor enjoys performing physics experiments when
  fighting evil. He sees Dr. Doom (mass of 95 kg)
  approaching at a pace of 35 m/s. Thor wants to
  hit Doom in the face with his hammer (30 kg) with
  exactly the same momentum that Doom is charging
  at him with. To do this what should the velocity
  of Thors hammer be at impact?
• 3325 kgm/s
• 35 m/s
• 111 m/s
• 99750 kgm/s

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Hammer time

• Thor successfully hits Doom in the chest with
  exactly the same amount of momentum that Doom had
  (but in the opposite direction). If the hammer
  sticks to Doom (inelastic collision) what must
  Doom and the hammer be doing after the collision?
• Moving to the right.
• Moving to the left.
• They Stopped moving!
• Could be any of the above.

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Hammer time

• Thor successfully hits Doom in the chest with
  exactly the same amount of momentum that Doom had
  (but in the opposite direction). If the hammer
  sticks to Doom (inelastic collision) what must
  Doom and the hammer be doing after the collision?
• Moving to the right.
• Moving to the left.
• They Stopped moving!
• Could be any of the above.

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Hammer time

• Lets say that Doom stops Thors hammer in a very
  short amount of time (0.1 seconds). What is the
  magnitude of the Force that doom must apply to
  generate the impulse that stops the hammer?
  (remember the hammer has a mass of 30 kg and was
  traveling at 111 m/s).
• 33300 N
• 3330 N
• 333 N
• 33 N

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Hammer time

• 4. Thor successfully hits Doom in the chest with
  exactly the same amount of momentum that Doom had
  (but in the opposite direction). If the hammer
  sticks to Doom (inelastic collision) which
  experiences an larger impulse?
• Dr. Doom
• The hammer
• Both have the same
• Depends on the velocity of the hammer

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Two astronauts are floating at rest in space. One
astronaut throws a tool to the other one, who
catches it. What is their motion after
transferring the tool?

1. Both at still at rest
2. They are now floating away from each other
3. They are now floating toward each other
4. The first astronaut is floating away while the
   second is at rest

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