Impulse; Conservation of Momentum

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Impulse Conservation of Momentum
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Intro Which Train has more momentum?

1. While stopped?
2. When moving at the same velocity?

Both have no velocity no momentum
The larger has more mass more momentum
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• Momentum (?)- (inertia in motion) the product of
  mass and velocity of an object
• Momentum equation
• ? mv
• Momentum mass x velocity
• The SI unit for momentum is kgm/s
• Change in momentum equation
• ?? m?v or ?? m(vf vo)

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• Ex A An airplane is launched from an aircraft
  carrier. The plane is going from south to north.
  If the airplanes launch velocity is 7.0 x 101
  m/s in the direction the ship was sailing and its
  mass is 2.5 x 104 kg, what is its momentum
  immediately after the launch (include direction
  since momentum is a vector).

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• Ex A An airplane is launched from an aircraft
  carrier. The plane is going from south to north.
  If the airplanes launch velocity is 7.0 x 101
  m/s in the direction the ship was sailing and its
  mass is 2.5 x 104 kg, what is its momentum
  immediately after the launch (include direction
  since momentum is a vector).

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• Ex. B A 0.060kg tennis ball traveling at 10.0
  m/s is returned in the opposite direction with a
  speed of 36.0 m/s. What is the change in
  momentum of the ball?

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• Ex. B A 0.060kg tennis ball traveling at 10.0
  m/s is returned in the opposite direction with a
  speed of 36.0 m/s. What is the change in
  momentum of the ball?

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• A moving object can have a large momentum if it
  has a large mass, a lot of speed, or both.

A truck traveling the same velocity of a truck
would have less velocity
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• Impulse (J) is a force applied over a period of
  time
• The SI unit for impulse is Ns
• Impulse F?t

The man is applying an impulse to the car
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• Ex. C What is the impulse when a force of 35N
  is applied for 1.2 seconds?

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• Ex. C What is the impulse when a force of 35N
  is applied for 1.2 seconds?

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• An impulse causes a change in momentum
• F?t m?v
• Impulse change in momentum
• The unit for impulse and momentum are equivalent
• Ns kgm/s

The man in the picture is causing an impulse and
changing the cars momentum
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• To increase the momentum of an object the most
  you want the greatest force possible over the
  longest time possible

F?t m?v
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• Two cars of equal mass are traveling the same
  speed. What do we know about their momentum?

They have the same momentum pmv
10 m/s
500kg
A
10 m/s
500kg
B
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• Which car is going to take less time to stop

stops in less time
10 m/s
500kg
A
10 m/s
500kg
B
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• Which car is going to take less time to stop
• Look at the equation and determine what this
  means F?t m?v

stops in less time
A
B
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• Which car is going to take less time to stop
• F?t m?v
• F?t m?v
• F?t m?v

with the same momentum
less time more force
A
more time less force
B
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Back to Newtons 2nd Law

• Fma
• If there is a greater force on the same object
  you will get a greater acceleration, or
  deceleration.
• Force causes acceleration

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• Ex. D A 0.060kg tennis ball traveling at 10.0
  m/s is returned in the opposite direction with a
  speed of 36.0 m/s. If the ball is in contact
  with the racket for 0.020s, with what average
  force is the ball hit?

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• Ex. D A 0.060kg tennis ball traveling at 10.0
  m/s is returned in the opposite direction with a
  speed of 36.0 m/s. If the ball is in contact
  with the racket for 0.020s, with what average
  force is the ball hit?

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• Ex. E Two identical cars, each traveling 20 m/s,
  are brought to a stop. Car a stops by applying
  its breaks the normal way. Car B stops as a
  result of running into an unmovable concrete
  wall. Which of the following statements is TRUE?
  (explain why the incorrect statements are false)
• Car A has the greatest change in momentum.
• Car B experiences the greatest impulse.
• Car B has the greatest change in momentum.
• Car B has the greatest force applied to it.

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• Ex. E Two identical cars, each traveling 20 m/s,
  are brought to a stop. Car a stops by applying
  its breaks the normal way. Car B stops as a
  result of running into an unmovable concrete
  wall. Which of the following statements is TRUE?
  (explain why the incorrect statements are false)
• Car A has the greatest change in momentum.
• Car B experiences the greatest impulse.
• Car B has the greatest change in momentum.
• Car B has the greatest force applied to it.

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Bouncing

• The impulse needed to bring an object to a stop
  and throw it back again is greater than the
  impulse required to just bring an object to a
  stop.
• To produce a stop you reduce momentum to 0 since
  v0
• To bounce you need a negative momentum since the
  direction of velocity changed

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• Problem Set 1 ?mv J F?t F?t
  m?v
• Bernie, whose mass is 70.0 kg, leaves a ski jump
  with the velocity of 21.0 m/s. What is Bernies
  momentum as he leaves the ski jump?
• Mark squishes a spider by applying a 20N force
  for 0.1s. What is the impulse of this action?
• Ethel hits a 0.20 kg ball at rest causing it to
  go 20 m/s. What average force is applied if the
  ball is in contact for 0.4s?

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• Problem Set 1 ?mv J F?t
  F?t m?v
• Bernie, whose mass is 70.0 kg, leaves a ski jump
  with the velocity of 21.0 m/s. What is Bernies
  momentum as he leaves the ski jump?

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• Problem Set 1 ?mv J F?t
  F?t m?v
• 2. Mark squishes a spider by applying a 20N force
  for 0.1s. What is the impulse of this action?

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• Problem Set 1 ?mv J F?t
  F?t m?v
• 3. Ethel hits a 0.20 kg ball at rest causing it
  to go 20 m/s. What average force is applied if
  the ball is in contact for 0.4s?

0.2
(0.2
.
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Law of Conservation of Momentum

• Momentum is neither gained nor lost in the
  absence of an external force
• All momentum before all momentum after
• p1before p2before p1after p2after
• expanded as
• m1v1o m2v2o m1v1f m2v2f

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• Net momentum before firing is 0 and net momentum
  after is still 0
• The cannon and the cannonball cancel each other
  out

pcannon before pcannonball before 0
before
after
pcannon after pcannonball after 0
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Collisions

• Collisions follow the conservation of momentum
• When two objects collide the net momentum before
  the collision equals the net momentum of both
  objects after the collision
• Net momentumbefore collision Net momentumafter
  collision

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Elastic Collisions

• Elastic collision- When objects collide without
  being permanently deformed and without generating
  heat.
• Net momentumbefore collision Net momentumafter
  collision

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Elastic Collision Equation

• m1v1o m2v2o m1v1f m2v2f

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Elastic Collision Example

• Objects do not stick together

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Inelastic Collisions

• Inelastic collision- collision where the objects
  become distorted or generate heat.
• m1v1o m2v2o (m1m2)(vf)
• If the two objects stick together there is one
  final velocity

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Inelastic collision equation

• m1v1o m2v2o (m1m2)(vf)
• If the objects sticking together after the
  collision will have the same combined velocity.

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Inelastic Collision

• Both have the same final velocity since they
  stick together

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Types of collisions/conservation of momentum
problems

• 1. Both objects start at rest (conservation of
  momentum)
• 2. One object moving other at rest (elastic
  collision)
• 3. Both objects moving same direction (elastic
  collision)
• 4. Both objects moving opposite directions
  (elastic collision)
• 5. One object moving other at rest (inelastic
  collision)
• 6. Both objects moving same direction (inelastic
  collision)
• 7. Both objects moving opposite directions
  (inelastic collision)

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Conservation of momentum

• 1. Both objects start at rest (conservation of
  momentum)
• Ex. F A baseball player standing on a
  frictionless surface with a mass of 50 kg throws
  a 0.25 kg ball forward at a velocity of 25 m/s.
  What is his final velocity and in what direction?

Vo 0 for both objects
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Conservation of momentum

• Ex. F A baseball player standing on a
  frictionless surface with a mass of 50 kg throws
  a 0.25 kg ball forward at a velocity of 25 m/s.
  What is his final velocity and in what direction?

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Types of collisions

• 2. One object moving other at rest (elastic
  collision)

Ex. G A 1000 kg car traveling at 20.0 m/s hits
a 3000 kg truck at rest. If the truck is
traveling 10 m/s forward after the elastic
collision, what is the cars final velocity?
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Ex. G A 1000 kg car traveling at 20.0 m/s hits
a 3000 kg truck at rest. If the truck is
traveling 10 m/s forward after the elastic
collision, what is the cars final velocity?
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Types of collisions

• 3. Both objects moving same direction (elastic
  collision)
• Ex. H A 1000 kg car traveling at 20.0 m/s
  forward hits a 3000 kg truck at 10 m/s in the
  same direction. If the truck is traveling 15 m/s
  forward after the elastic collision, what Is the
  cars final velocity?

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• Ex. H A 1000 kg car traveling at 20.0 m/s
  forward hits a 3000 kg truck at 10 m/s in the
  same direction. If the truck is traveling 15 m/s
  forward after the elastic collision, what Is the
  cars final velocity?

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Types of collisions

• 4. Both objects moving opposite directions
  (elastic collision)
• Ex. I What is the initial velocity of a 1000 kg
  car traveling to the right that hits a 3000 kg
  truck traveling at 20 m/s to the left. After the
  elastic collision, the truck is traveling 10 m/s
  and the car is traveling 15 m/s both to the left?

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• Ex. I What is the initial velocity of a 1000 kg
  car traveling to the right that hits a 3000 kg
  truck traveling at 20 m/s to the left. After the
  elastic collision, the truck is traveling 10 m/s
  and the car is traveling 15 m/s both to the left?

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Types of collisions

• 5. One object moving other at rest (inelastic
  collision)
• Ex. J In an experiment, a toy wooden car with a
  mass of 300g, initially at rest, is struck in the
  rear by a 30g dart traveling at 15 m/s as shown.
  With what speed does the car with the dart stuck
  in it move after the collision?

V 15 m/s
V 0 m/s
V ?
300g
30g
300g
30g
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• Ex. J In an experiment, a toy wooden car with a
  mass of 300g, initially at rest, is struck in the
  rear by a 30g dart traveling at 15 m/s as shown.
  With what speed does the car with the dart stuck
  in it move after the collision?

V 15 m/s
V 0 m/s
V ?
300g
30g
300g
30g
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Types of collisions

• 6. Both objects moving same direction (inelastic
  collision)
• Ex. K A 50 kg astronaut traveling at 8 m/s to
  the left catches a 10 kg meteor traveling at 20
  m/s to the left. What is the final velocity of
  the astronaut holding the meteor?

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• Ex. K A 50 kg astronaut traveling at 8 m/s to
  the left catches a 10 kg meteor traveling at 20
  m/s to the left. What is the final velocity of
  the astronaut holding the meteor?

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Types of collisions

• 7. Both objects moving opposite directions
  (inelastic collision)
• Ex. L A 50 kg astronaut traveling at 8 m/s to
  the right catches a 10 kg meteor traveling at 20
  m/s to the left. What is the final velocity of
  the astronaut holding the meteor?

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• Ex. L A 50 kg astronaut traveling at 8 m/s to
  the right catches a 10 kg meteor traveling at 20
  m/s to the left. What is the final velocity of
  the astronaut holding the meteor?

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• Problem Set 2
• A 35 kg child runs across a store at 4.0 m/s and
  jumps onto a 35 kg shopping cart initially at
  rest. At what speed will the shopping cart and
  the child move together across the store assuming
  negligible friction?
• Bruno throws a 0.20kg football and knocks over a
  0.88kg vase at rest. After the collision the
  football bounces straight back with a speed of
  3.9 m/s while the vase is moving at 2.6 m/s in
  the opposite direction. How fast did Bruno throw
  the football?
• Martha tosses a 1.5kg ball at a 0.8kg milk jug
  initially at rest. The ball is thrown to the
  right at 7.8 m/s and continues to move to the
  right at 3.0 m/s after the collision. What is
  the velocity of the jug after the collision?
• Sam, who is 85kg, jumps into a 300 kg rowboat
  initially at rest. His initial velocity was 5
  m/s forward. What is the velocity of Sam in the
  boat after he lands?

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• Problem Set 2
• A 35 kg child runs across a store at 4.0 m/s and
  jumps onto a 35 kg shopping cart initially at
  rest. At what speed will the shopping cart and
  the child move together across the store assuming
  negligible friction?

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• Problem Set 2
• 2. Bruno throws a 0.20kg football and knocks
  over a 0.88kg vase at rest. After the collision
  the football bounces straight back with a speed
  of 3.9 m/s while the vase is moving at 2.6 m/s in
  the opposite direction. How fast did Bruno throw
  the football?

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• Problem Set 2
• 3. Martha tosses a 1.5kg ball at a 0.8kg milk
  jug initially at rest. The ball is thrown to the
  right at 7.8 m/s and continues to move to the
  right at 3.0 m/s after the collision. What is
  the velocity of the jug after the collision?

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• Problem Set 2
• 4. Sam, who is 85kg, jumps into a 300 kg rowboat
  initially at rest. His initial velocity was 5
  m/s forward. What is the velocity of Sam in the
  boat after he lands?