Momentum

1
Momentum

• Momentum can be defined as
• "mass in motion."
• All objects have mass so if an object is moving,
  then it has momentum
• it has its mass in motion.

2
Momentum

• The amount of momentum which an object has is
  dependent upon two variables
• How much stuff is moving and
• how fast the stuff is moving.
• Momentum depends upon the variables mass and
  velocity.

3
Momentum

• In terms of an equation, the momentum of an
  object is equal to the mass of the object times
  the velocity of the object.
• Momentum mass velocity
• In physics, the symbol for the quantity momentum
  is the small case "p" thus, the above equation
  can be rewritten as
• p m v

4
Momentum

• In terms of an equation, the momentum of an
  object is equal to the mass of the object times
  the velocity of the object.
• Momentum mass velocity
• In physics, the symbol for the quantity momentum
  is the small case "p" thus, the above equation
  can be rewritten as
• p m v
• The units for momentum would be mass units times
  velocity units. The standard metric unit of
  momentum is the kgm/s.

5
Momentum

• It is not enough to say that a ball has
• 10 kgm/s of momentum the momentum of the ball
  is not fully described until information about
  its direction is given.
• The direction of the momentum vector is the same
  as the direction of the velocity of the ball.

6
Momentum

• From the definition of momentum, it becomes
  obvious that an object has a large momentum if
  either its mass or its velocity is large.
• Both variables are of equal importance in
  determining the momentum of an object.
• Objects at rest do not have momentum - they do
  not have any "mass in motion.
• Both variables - mass and velocity - are
  important in comparing the momentum of two
  objects.

7
Momentum

• The more momentum which an object has, the harder
  that it is to stop.

8
Law of Conservation of Momentum

• According to Newton, whenever objects A and B
  interact with each other, they exert forces upon
  each other. When you sit in your chair, your body
  exerts a downward force on the chair and the
  chair exerts an upward force on your body. There
  are two forces resulting from this interaction -
  a force on the chair and a force on your body.
  These two forces are called action and reaction
  forces and are the subject of Newton's third law
  of motion.

9
Law of Conservation of Momentum

• Formally stated, Newton's third law is
• "For every action, there is an equal and opposite
  reaction."

10
Law of Conservation of Momentum

• The statement means that in every interaction,
  there is a pair of forces acting on the two
  interacting objects.
• The size of the forces on the first object equals
  the size of the force on the second object.
• The direction of the force on the first object is
  opposite to the direction of the force on the
  second object.
• Forces always come in pairs - equal and opposite
  action-reaction force pairs.

11
Law of Conservation of Momentum

• Consider the motion of a car on the way to
  school. A car is equipped with wheels which spin
  backwards. As the wheels spin backwards, they
  grip the road and push the road backwards. In
  turn, the road reacts by pushing the wheels
  forward. The size of the force on the road equals
  the size of the force on the wheels (or car) the
  direction of the force on the road (backwards) is
  opposite the direction of the force on the wheels
  (forwards). For every action, there is an equal
  (in size) and opposite (in direction) reaction.

12
Law of Conservation of Momentum

• Newton's third law of motion is naturally applied
  to collisions between two objects.
• In a collision between two objects, both objects
  experience forces which are equal in magnitude
  and opposite in direction.
• Such forces cause one object to speed up (gain
  momentum) and the other object to slow down (lose
  momentum).

13
Law of Conservation of Momentum

• One of the most powerful laws in physics is the
  law of momentum conservation.
• The law of momentum conservation can be stated as
  follows
• For a collision occurring between object 1 and
  object 2 the total momentum of the two objects
  before the collision is equal to the total
  momentum of the two objects after the collision.
• That is, the momentum lost by object 1 is equal
  to the momentum gained by object 2.

14
Law of Conservation of Momentum
15
Law of Conservation of Momentum
16
Law of Conservation of Momentum

• In a collision, the momentum change of object 1
  is equal and opposite to the momentum change of
  object 2.
• That is, the momentum lost by object 1 is equal
  to the momentum gained by object 2.
• In a collision between two objects, one object
  slows down and loses momentum while the other
  object speeds up and gains momentum.

17
Law of Conservation of Momentum

• The animation below portrays the collision
  between a 1.0-kg cart and a 2-kg dropped brick.

18
Law of Conservation of Momentum

• In the collision between the cart and the dropped
  brick, total system momentum is conserved.
• Before the collision, the momentum of the cart is
  60 kgcm/s and the momentum of the dropped brick
  is 0 kgcm/s the total system momentum is 60
  kgcm/s.
• After the collision, the momentum of the cart is
  20.0 kgcm/s and the momentum of the dropped
  brick is 40.0 kgcm/s the total system momentum
  is 60 kgcm/s.
• The momentum of the loaded cart-dropped brick
  system is conserved.

19
Law of Conservation of Momentum

• Imagine that you are hovering next to the space
  shuttle in earth-orbit and your buddy of equal
  mass who is moving 4 m/s (with respect to the
  ship) bumps into you. If she holds onto you, then
  how fast do the two of you move after the
  collision?

20
Law of Conservation of Momentum

• Since there is twice as much mass in motion after
  the collision, it must be moving at one-half the
  velocity. Thus, the two astronauts move together
  with a velocity of 2 m/s after the collision.

21
Law of Conservation of Momentum
22
Law of Conservation of Momentum
23
Law of Conservation of Momentum
24
Law of Conservation of Momentum

• A gun recoils when it is fired. The recoil is the
  result of action-reaction force pairs. As the
  gases from the gunpowder explosion expand, the
  gun pushes the bullet forwards and the bullet
  pushes the gun backwards. The acceleration of the
  recoiling gun is ...

a. greater than the acceleration of the
bullet. b. smaller than the acceleration of the
bullet. c. the same size as the acceleration of
the bullet.
25
Law of Conservation of Momentum

• Would it be a good idea to jump from a rowboat to
  a dock that seems within jumping distance?
  Explain.

26
Law of Conservation of Momentum

• Miles Tugo and Ben Travlun are riding in a bus at
  highway speed on a nice summer day when an
  unlucky bug splatters onto the windshield. Miles
  suggests that the momentum change of the bug is
  much greater than that of the bus. After all,
  argues Miles, there was no noticeable change in
  the speed of the bus compared to the obvious
  change in the speed of the bug. Ben disagrees
  entirely, arguing that that both bug and bus
  encounter the same force, momentum change, and
  impulse. Who do you agree with? Support your
  answer.