Momentum

1
Chapter 7

• Momentum

2
Momentum

• Momentum inertia in motion
• the mass of an object multiplied by its velocity
• p mv
• units kgm/s
• A vector quantity
• The faster you move, the more momentum you have
  and the more difficult it is to come to a stop

3
Momentum

• Imagine rolling a bowling ball down a bowling
  lane and rolling a playground ball down another
  lane at the same speed. Which ball has the
  greater momentum?
• The more massive bowling ball has more momentum
  therefore it exerts a more force on the pins at
  the end of the lane
• A large truck and a roller skate have different
  masses and therefore different momenta. Is it
  possible for the roller skate to have more
  momentum than the large truck?
• It all depends on the velocity of the objects.
  If the truck is at rest, it has no momentum, and
  any moving roller skate has momentum. So the
  roller skate will have more momentum than the
  truck

4
Momentum

• A deer with a mass of 146 kg is running head-on
  toward you with a speed of 17 m/s. You are going
  north. Find the momentum of the deer.
• A 2250 kg pickup truck has a velocity of 25 m/s
  to the east. What is the momentum of the truck?
• What velocity must a 1210 kg car have in order to
  have the same momentum of the truck in question
  2?

5
Impulse Changes Momentum

• If the momentum of an object changes, either the
  mass or velocity or both change.
• A change in momentum takes force and time.
• Catching a ball
• A ball moving very fast stings your hands when
  you catch it, while a slow moving ball causes no
  discomfort when you catch it.
• The fast moving ball stings because it exerts
  more force on your hands than the slow moving
  ball does.

6
Impulse Changes Momentum

• To change the momentum, a force must act on the
  systemthe greater the force the greater the
  change in velocity and the greater change in
  momentum
• The amount of time the force acts upon the object
  is important. The longer you apply a force, the
  larger the change in momentum.
• the quantity force time interval impulse
• Impulse change in momentum
• I F?t or Ft ?(mv) mvf - mvo

7
Increasing Momentum

• To increase the momentum of an objectapply the
  greatest force possible for as long as possible
• Forces involved in an impulse usually vary from
  instant to instant
• Think of a golf club hitting a golf ball
• There is no force until ball is initially struck,
  then the force increases rapidly while the ball
  is distorted and the force decreases as the ball
  goes back to its original shape
• Impact is the force on the ball (newtons)
• Impulse is the impact force multiplied by time
  (kgm/s)

8
Decreasing Momentum

• Why is hitting a soft object entirely different
  than hitting a hard object (punch a pillow or a
  concrete wall)?
• Whether you are punching a pillow or a wall your
  impulse is the same, but the same impulse does
  not mean the same amount of force (impact) or the
  same amount of time.
• By hitting the pillow rather than the wall you
  extend the impact time (the time in which the
  momentum of your hand is brought to zero).
• A longer impact time reduces the impact force on
  your hand and decreases the deceleration (caused
  by the impact force)
• Force is reduced when the time interval of an
  impact is increased.

9
Impulse Changes Momentum

• Tiger Woods hits a 0.050 kg golf ball, giving it
  a speed of 75 m/s. What impulse does he impart
  to the ball?
• Wayne hits a stationary 0.12 kg hockey puck with
  a force that lasts for 1.00 x 10-2 s and makes
  the puck shoot across the ice with a speed of
  20.0 m/s, scoring a goal for the team. With what
  force did Wayne hit the puck?

10
Impulse Changes Momentum

• A tennis ball that is traveling 10.0 m/s is
  returned by Venus Williams. It leaves her racket
  with a speed of 36.0 m/s in the opposite
  direction from which it came. (1) What is the
  change in momentum of the 0.060 kg tennis ball?
  (2) If the 0.060 kg tennis ball is in contact
  with the racket for 0.020s, with what average
  force has Venus hit the ball?
• To demonstrate a new high-speed camera, Flash
  performs an experiment in the physics lab in
  which he shoots a pellet gun at a pumpkin to
  record the moment of impact on film. The 1.0g
  pellet travels at 100.m/s until it embeds itself
  2.0cm into the pumpkin. What average force does
  the pumpkin exert to stop the pellet?

11
Bouncing

• Impulses are greater when an object bounces
• The impulse required to bring an object to a stop
  and then throw it again is greater than the
  impulse required to merely stop an object
• The magnitude of an impact force when bouncing
  occurs depends on impact time.
• For an elastic collision, where momentum is
  reversed, and the change in momentum is twice
  that of halting, impulse is doubled!
• Although IMPULSE is greater for bouncing, impact
  may or may not be dependent on time

12
Conservation of Momentum

• An outside (external) force is required to change
  momentum
• Think of pushing on the dashboard of your car
  the force is canceled and therefore has no effect
  on the momentum of your car
• Momentum is a vector quantitylike velocity, it
  can be cancelled
• If no net force or net impulse acts on a system,
  the momentum of that system cannot change
• Think of a cannon and cannonball
• Before the cannon is shot--the momentum (mass x
  velocity) is zero
• The cannonball is shot and the cannon recoils
  (the forces are equal and oppositeNewtons 3rd
  Law)
• The net force on the cannon-cannonball system is
  zero
• The momentum on the cannon-cannonball system is
  also zero

13
Conservation of Momentum

• Law of Conservation of Momentum
• In the absence of an external force, the momentum
  of a system remains unchanged.
• If a system undergoes changes wherein all forces
  are internal, the net momentum of the system
  before and after the event is the same

14
Collisions

• Momentum is conserved in collisions
• net momentumbefore collision net momentumafter
  collision
• There are two types of collisions
• Momentum is conserved in both types of collisions
• Elastic Collision (bouncy) a collision in which
  two objects collide and bounce apart with no
  energy loss (no deformation or generation of
  heat) (energy is also conserved in perfectly
  inelastic collisions)
• m1v1o m2v2o m1v1f m2v2f
• Inelastic Collision (sticky) a collision in
  which two objects collide and become distorted
  and generate heat during the collision (objects
  become tangled or coupled together) (energy is
  not conserved in inelastic collisions)
• m1v1o m2v2o (m1 m2)vf

15
Collisions

• most collisions usually involve some type of
  external force
• billiard balls do not move on foreverbecause
  they experience friction from the table and the
  air
• these factors are usually negligible during a
  collision so the net momentum does not change
  during the collision
• perfectly elastic collisions are not common in
  everyday life
• there is most often times some heat generated by
  the collision

16
Elastic Collisions

• An elastic collision between a 1000-kg car and a
  3000-kg truck. The before- and after-collision
  velocities and momentum are shown in the data
  tables.
• http//www.physicsclassroom.com/mmedia/momentum/cr
  ete.gif
• An elastic collision between a 3000-kg truck and
  a 1000-kg car. The before- and after-collision
  velocities and momentum are shown in the data
  tables.
• http//www.physicsclassroom.com/mmedia/momentum/tr
  ece.gif
• In the second collision, the truck has more
  initial momentum than the car did in the first
  collision The resulting velocity of the car (in
  the second collision) is much greater than the
  resulting velocity of the truck (in the first
  collision)

17
Inelastic Collisions

• An inelastic collision between a 1000-kg car and
  a 3000-kg truck. The before- and after-collision
  velocities and momentum are shown in the data
  tables.
• http//www.physicsclassroom.com/mmedia/momentum/cr
  eti.gif
• An inelastic collision between a 3000-kg truck
  and a 1000-kg car. The before- and
  after-collision velocities and momentum are shown
  in the data tables.
• http//www.physicsclassroom.com/mmedia/momentum/tr
  eci.gif

18
Conservation of Momentum Bar Graphs

• Conservation of momentum bar graphs are used to
  organize information about a collision so that
  properties such as initial velocity, final
  velocity or mass of the interacting objects can
  be found.
• 1. The first step in using the bar graphs to
  solve a problem is to identify the event (such as
  a collision or bounce) that separates the initial
  situation from the final situation by writing it
  at the top of the graphs.
• 2. The objects that are part of the system are
  listed to the left of each graph. Once you have
  identified the objects, record their mass and
  velocity right next to each object's name for
  both of the final and initial situations. Choose
  variables for any unknown quantities.
• 3. Sketch bars representing each object's
  momentum (mass x velocity). The bars start at the
  center of the graph and extend to the left or the
  right according to the direction of the object's
  motion. Any change in the length of a bar from
  the initial to final situation represents impulse
  (change in momentum.)
• 4. Write the conservation of momentum bar graph
  below the bars algebraically solve for the
  unknown variable substitute known values with
  their units then finish the computations.

19
Conservation of Momentum Bar Graphs

• A 90kg hockey player makes an illegal check by
  ramming an 80kg player at 6 m/s and slows to 4m/s
  after the collision. The 80kg player had been
  traveling at 2 m/s toward the 90 kg player before
  the collision. Find the velocity of the 80 kg
  player after the collision. We will assume that
  the frictional forces on the players are small
  enough that the only net force on the players is
  due to the collision.
• Conservation of momentum equation
• mi90vi90 mi80vi80 mf90vf90 mf80vf80

20
Collisions

• Tubby and his twin brother Chubby have a combined
  mass of 200.0 kg and are zooming along in a 100.0
  kg amusement park bumper car at 10.0 m/s. They
  bump Melindas car, which is sitting still.
  Melinda has a mass of 25.0 kg. After the elastic
  collision, the twins continue ahead with a speed
  of 4.12 m/s. How fast is Melindas car bumped
  across the floor?

21
Collisions

• A grocery shopper tosses a 9.0 kg bag of rice
  into a stationary 18.0 kg grocery cart. The bag
  hits the car with a horizontal speed of 5.5 m/s
  toward the front of the cart. What is the final
  speed of the cart and the bag?
• A 16.0 kg canoe moving to the left at 12.5 m/s
  makes an elastic head on collision with a 14.0 kg
  raft moving to the right at 16.0 m/s. After the
  collision, the raft moves to the left at 14.4
  m/s. Disregard any affects of the water. Find
  the velocity of the canoe after the collision.

22
Momentum Vectors

• Momentum is conserved even when interacting
  objects dont move along the same direction
• Use vector techniques in previous chapters (trig
  Pythagorean theorem)
• Think of a car traveling North that is struck by
  a car traveling East
• the momentum of the wreck is equal to the vector
  sum of the momentum of the car traveling north
  and the car traveling east
• http//www.physicsclassroom.com/mmedia/momentum/2d
  i.gif