Momentum

1
Momentum

• The world is filled with objects in motion.
  Objects have many properties such as color, size,
  and composition. One important property of an
  object is its mass.

2
Momentum

• The mass of an object is the amount of matter in
  the object.
• The SI unit for mass in the kilogram (kg),
• The weight of an object is related to the objects
  mass.
• Objects with more mass weigh more than objects
  with less mass.

3
Momentum

• A bowling ball has more mass than a pillow, so it
  weighs more than a pillow.
• A pillow is larger than a bowling ball, but the
  bowling ball has more mass.
• The size of an object is not the same as the mass
  of an object.

4
Momentum

• Objects with different masses are different in
  important ways.
• Think about what happens when you try to stop
  someone who is rushing toward you.

5
Momentum

• A small child is easy to stop.
• A large football player is hard to stop.

6
Inertia

• The more mass an object has, the harder it is to
  start it moving, slow it down, speed it up, or
  turn it.
• This tendency of an object to resist a change in
  motion is called inertia.

7
Inertia

• The more mass an object has, the harder it is to
  start it moving.

8
Inertia

• The more mass an object has, the harder it is to
  slow it down.

9
Inertia

• The more mass an object has, the harder it is to
  speed it up.

10
Inertia

• The more mass an object has, the harder it is to
  turn it.

11
Inertia

• Remember that the tendency of an object to resist
  a change in motion is called inertial.

12
Inertia

• Objects with more mass have more inertia.
• The more mass an object has, the harder it is to
  change its motion.

13
Momentum

• The faster your bicycle moves the harder it is to
  stop
• Increasing the speed or velocity of the object
  makes it harder to stop just like increasing the
  mass does also.

14
Momentum

• Momentum of an object is a measure of how hard it
  is to stop the object.
• Momentum depends upon the objects mass and
  velocity.

15
Momentum

• Momentum Equation
• Momentum is symbolized by p.
• momentum (kg m/s)
• mass (kg) x velocity (m/s)
• p mv

16
Momentum

• p mv
• Mass is measured in kilograms and velocity has
  units of meters per second.
• (kg m/s)
• Velocity includes direction, momentum has a
  direction that is the same as the direction of
  the velocity.

17
Momentum

• Applying Math
• Calculate the momentum of a 14 kg bicycle
  traveling north at 2 m/s.
• Mass m 14 kg
• Velocity v 2 m/s north
• Formula momentum p kg m/s

18
Momentum

• p mv (14 kg) (2 m/s north)

19
Momentum

• Answer
• (14 kg) (2 m/s) 28 kg .m/s north

20
Momentum

• Applying Math
• A 10,000 kg train is traveling east at 15m/s.
• Calculate the momentum of the train.

21
Momentum

• p mv

22
Momentum

• Mass 10,000 kg
• Velocity 15 m/s east

23
Momentum

• p mv
• 10,000 kg X 15 m/s east

24
Momentum

• 150,000 kg m/s east

25
Momentum

• Applying Math
• What is the momentum of a car with a mass of 900
  kg traveling north at 27 m/s.

26
Momentum

• p mv
• 900kg X 27 m/s north

27
Momentum

• 24,300 kg m/s north

28
Momentum

• Conservation of Momentum
• The law of conservation of momentum
• The total momentum of objects that collide is the
  same before and after the collision.

29
Conservation of Momentum

• According to the law of conservation of momentum
  if one ball swings in then how many balls will
  swing out?

30
Conservation of Momentum

• When the cue ball hits another ball, the motion
  of both balls change. The cue ball slows down and
  may change direction, so its momentum increases.

31
Conservation of Momentum

• It seems as if momentum is transferred from the
  cue ball to the other ball.
• In fact, during the collision, the momentum lost
  by the cue ball was gained by the other ball.

32
Conservation of Momentum

• Outside forces, such as gravity and friction are
  almost always acting on objects that are
  colliding.
• Sometimes these forces are small enough that they
  can be ignored.
• Then the law of conservation of momentum allows
  us to predict how motions of objects will change
  after a collision.

33
Conservation of Momentum

• Sometimes objects that collide will bounce off of
  each other.

34
Conservation of Momentum

• In some collisions objects will stick to each
  other after the collision.
• What would be an example of the above?

35
Conservation of Momentum

• In some collisions the objects will stick to each
  other after the collision.

36
Conservation of Momentum

• In both of these types of collisions, the law of
  conservation of momentum enables the speed of the
  objects after the collision to be calculated.

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Conservation of Momentum

• Sticking Together
• Imagine being on skates when someone throws a
  backpack to you.

38
Conservation of Momentum

• When you catch the backpack, you and the
  backpack continue to move in the same direction
  as the backpack was moving before the collision.

39
Conservation of Momentum

• The law of conservation of momentum can be used
  to find your velocity after you catch the
  backpack.

40
Conservation of MomentumProblem

• Suppose a 2 kg backpack is tossed at a speed of 5
  m/s. Your mass is 48 kg and initially you are at
  rest.
• Total momentum momentum of backpack your
  momentum
• 2 kg X 5 m/s 48 kg X 0 m/s
• 10 kg m/s

41
Conservation of MomentumProblem

• After the collision, the total momentum remains
  the same, and only one object is moving. Its mass
  is the sum of your mass and the mass of the
  backpack.
• Use the equation for momentum to find the final
  velocity.

42
Conservation of MomentumProblem

• Total momentum (mass of backpack your mass)
  X velocity
• 10 kg m/s (2 kg 48 kg) X velocity
• 10 kg m/s (50 kg) X velocity
• 0.2 m/s velocity
• This is the velocity right after you catch the
  backpack.

43
Conservation of Momentum

• As you continue to move on your skates, what
  force will act upon you?

44
Conservation of Momentum

• Friction
• The force of friction between the ground and the
  skates slows you down.

45
Conservation of Momentum

• Two objects of the same mass moving at the same
  speed collide head-on.
• What happens?

46
Conservation of Momentum

• Two objects of the same mass moving at the same
  speed collide head-on.
• They will rebound and move with the same speed in
  the opposite direction. The total momentum is
  zero before and after the collision.

47
Conservation of Momentum

• 2. A less massive object strikes a more massive
  object that is at rest.
• What happens?

48
Conservation of Momentum

• . A less massive object strikes a more massive
  object that is at rest.
• After the collision, the smaller object bounces
  off in the opposite direction. The larger object
  moves in the same direction that the small object
  was initially moving.

49
Conservation of Momentum

• 3. A large object strikes a smaller object that
  is at rest. (Lets pretend that the small object
  is at rest.)
• What happens?

50
Conservation of Momentum

• After the collision, both objects move in the
  same direction.
• The less massive object always moves faster than
  the more massive one.

51
Conservation of Momentum

• Colliding and Bouncing Off
• In some collisions, the objects involved, like
  bumper cars bounce off each other.

52
Conservation of Momentum

• The law of conservation of momentum can be used
  to determine how these objects move after they
  collide.
• Two identical objects moving with the same speed
  collide head-on and bounce off.
• Question What is the total momentum before the
  collision?

53
Conservation of Momentum

• Before the collision the momentum of each object
  is the same, but in opposite directions.
• The total momentum before the collision is zero.
• What is the total momentum after the collision?

54
Conservation of Momentum

• After the collision, the total momentum must also
  be zero.
• This means that the two objects must move in
  opposite directions with the same speed after the
  collision
• The total momentum is zero.

55
Conservation of Momentum