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Impulse; Conservation of Momentum

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Title: Impulse; Conservation of Momentum


1
Impulse Conservation of Momentum
2
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
3
  • 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)

4
  • 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).

5
  • 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).

6
  • 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?

7
  • 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?

8
  • 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
9
  • 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
10
  • Ex. C What is the impulse when a force of 35N
    is applied for 1.2 seconds?

11
  • Ex. C What is the impulse when a force of 35N
    is applied for 1.2 seconds?

12
  • 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
13
  • To increase the momentum of an object the most
    you want the greatest force possible over the
    longest time possible

F?t m?v
14
  • 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
15
  • Which car is going to take less time to stop

stops in less time
10 m/s
500kg
A
10 m/s
500kg
B
16
  • 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
17
  • 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
18
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

19
  • 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?

20
  • 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?

21
  • 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.

22
  • 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.

23
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

24
  • 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?

25
  • 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?

26
  • 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?

27
  • 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
.
28
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

29
  • 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
30
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

31
Elastic Collisions
  • Elastic collision- When objects collide without
    being permanently deformed and without generating
    heat.
  • Net momentumbefore collision Net momentumafter
    collision

32
Elastic Collision Equation
  • m1v1o m2v2o m1v1f m2v2f

33
Elastic Collision Example
  • Objects do not stick together

34
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

35
Inelastic collision equation
  • m1v1o m2v2o (m1m2)(vf)
  • If the objects sticking together after the
    collision will have the same combined velocity.

36
Inelastic Collision
  • Both have the same final velocity since they
    stick together

37
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)

38
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
39
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?

40
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?
41
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?
42
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?

43
  • 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?

44
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?

45
  • 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?

46
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
47
  • 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
48
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?

49
  • 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?

50
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?

51
  • 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?

52
  • 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?

53
  • 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?

54
  • 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?

55
  • 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?

56
  • 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?
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