Chapter 7 Momentum and Impulse

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Chapter 7Momentum and Impulse
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Collisions

• What happens when there is a rapid change of
  motion, such as a collision? Can we apply
  Newtons Law?

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What happens when a ball bounces?

• Does the velocity change?
• Is there an acceleration?
• Is there a force? If so, what is the direction of
  the force?

• Forces in collision may be difficult to analyze
• Strong forces acting for a very short time that
  may change rapidly during the collision.
• Newtons second law

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Momentum and Impulse

• Impulse the (average) force acting on an object
  multiplied by the time interval over which the
  force acts (Unit Ns)
• Momentum the mass of the object times its
  velocity (Unit kg.m/s).
• Change in momentum
• (Units of Ns and Kg.m/s are actually equivalent)

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Impulse-Momentum Principle
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Momentum
A bowling ball and a tennis ball may have the
same momentum.
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Application of Impulse and Momentum Principle

• Example (Box 7.1)
• A golf club exerts an average force of 500N on a
• 0.1 kg golf ball, but the club is in contact with
  the
• ball for only a hundredth of a second.
• What is the magnitude of the impulse delivered by
  the club?
• What is the change in velocity of the golf ball?

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Impulse-Momentum Principle
Example (E8) A ball traveling with an initial
momentum of 2.5 kg.m/s bounces off a wall and
comes back in the opposite direction with a
momentum of -2.5 kg.m/s. a) What is the change
in momentum of the ball? b) What impulse would
be required to produce this change?
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More Examples
Q9. What is the advantage of an air bag in
reducing injuries during collision? Explain.
Q11. If you catch a baseball or softball with
your bare hand, will the force exerted on your
hand by the ball e reduced if you pull your arm
back during the catch? Explain.
E2. An average force of 300N acts for a time
interval of 0.04 s on a golf ball. What is the
magnitude of the impulse acting on the golf ball?
What is the change of the golf balls momentum?
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Conservation of Momentum

• In collision, does Newtons third law hold?
• For every action, there is an equal but opposite
  reaction.
• The impulse acting on two objects are equal in
  magnitude but opposite in sign.

If the net external force acting on a system of
objects is zero, the total momentum of the system
is conserved.
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Conservation of Momentum

• Two useful simple cases
• Two object stick together after collision.
• The initial velocity is zero for both objects
  before collision (recoil).

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A 100-kg fullback moving straight downfield
collides with a 75-kg defensive back. The
defensive back hangs on to the fullback, and the
two players move together after the collision.
What is the initial momentum of each player? What
is the total momentum of the system?
Example (Box 7.2)
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What is the velocity of the two players
immediately after the collision?
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Recoil

• A brief force between two objects causes the
  objects to move in opposite directions.
• Momentum Conservation Principle applies to the
  system.
• The system includes both objects involved in the
  collision.

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Two skaters of different masses prepare to push
off against one another. Which one will gain the
larger velocity? Why?
Example E11. An ice skater with a mass of 80 kg
pushes off against a second skater with a mass of
32 kg. Both skaters are initially at rest. a)
What is the total momentum of the system after
they push off? b) If the larger skater moves off
with a speed of 3 m/s, what is the corresponding
speed of the smaller skater?
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Is momentum conserved when shooting a shotgun?

• The explosion of the powder causes the shot to
  move very rapidly forward.
• If the gun is free to move, it will recoil
  backward with a momentum equal in magnitude to
  the momentum of the shot.
• If the shotgun is held firmly against your
  shoulder, it doesnt hurt as much. Why?

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Example E 12A rifle with a mass of 1.2 kg
fires a bullet with a mass of 6.g (0.006kg). The
bullet moves with a muzzle velocity of 600 m/s
after the rifle is fired.a) What is the momentum
of the bullet after the rifle is fired?B) If the
external force against the rifle is ignored, what
is the recoil velocity of the rifle?
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How does a rocket accelerate in empty space when
there is nothing to push against?

• The exhaust gases rushing out of the tail of the
  rocket have both mass and velocity and,
  therefore, momentum.
• The momentum gained by the rocket in the forward
  direction is equal (in magnitude) to the momentum
  of the exhaust gases in the opposite direction.
• The rocket and the exhaust gases push against
  each other (Newtons third law applies).

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Elastic and Inelastic Collisions

• Different kinds of collisions
• objects stick together after collision.
• objects bounce apart after collision.
• What is the difference between these types of
  collisions?
• Is energy conserved as well as momentum?

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Perfect Inelastic Collisions

• A collision in which the objects stick together
  after collision is called a perfectly inelastic
  collision.
• The objects do not bounce at all.
• If we know the total momentum before the
  collision, we can calculate the final momentum
  and velocity of the now-joined objects.
• For example
• The football players who stay together after
  colliding.
• Coupling railroad cars.

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Four railroad cars, all with the same mass of
20,000 kg, sit on a track. A fifth car of
identical mass approaches them with a velocity of
15 m/s. This car collides and couples with the
other four cars. a) What is the initial
momentum of the system? b) What is the velocity
of the five coupled cars after the collision? c)
Is the kinetic energy after the railroad cars
collide equal to the original kinetic energy of
the cars ?
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Elastic and Inelastic Collisions

• Energy is not conserved in a perfectly inelastic
  collision.
• If the objects bounce apart instead of sticking
  together, the collision is either elastic or
  partially inelastic.
• An elastic collision is one in which no energy is
  lost.
• A partially inelastic collision is one in which
  some energy is lost, but the objects do not stick
  together.
• The greatest portion of energy is lost in the
  perfectly inelastic collision, when the objects
  stick.

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• A ball bouncing off a floor or wall with no
  decrease in the magnitude of its velocity is an
  elastic collision.
• The kinetic energy does not decrease.
• No energy has been lost.
• A ball sticking to the wall is a perfectly
  inelastic collision.
• The velocity of the ball after the collision is
  zero.
• Its kinetic energy is then zero.
• All of the kinetic energy has been lost.
• Most collisions involve some energy loss, even if
  the objects do not stick, because the collisions
  are not perfectly elastic.
• Heat is generated, the objects may be deformed,
  and sound waves are created.
• These would be partially inelastic collisions.

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What happens when billiard balls bounce?

• Simplest case a head-on collision between the
  white cue ball and the eleven ball initially at
  rest.
• If spin is not a factor, the cue ball stops and
  the eleven ball moves forward with a velocity
  equal to the initial velocity of the cue ball.
• The eleven balls final momentum is equal to the
  cue balls initial momentum (Momentum is
  conserved).
• The eleven ball also has a final kinetic energy
• equal to the cue balls initial kinetic energy
  (Energy is conserved).
• For equal masses, the only way for momentum and
  energy to both be conserved is for the cue ball
  to stop and the eleven ball to move forward with
  all the velocity.

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What happens to the swing-ball toy?

• The swinging-ball toy has a row of steel balls
  hanging by threads from a frame.
• If one ball is pulled back and released, the
  collision with the other balls results in a
  single ball from the other end flying off with
  the same velocity as the first ball just before
  the collision.
• Both momentum and kinetic
• energy are conserved.
• If two balls on one side are
• pulled back and released, two
• balls fly off from the opposite
• side.
• Why doesnt one ball
• fly off with twice the
• velocity?

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Collisions at an Angle

• Two football players traveling at right angles to
  one another collide and stick together.
• What will be their direction of motion after the
  collision?

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Collisions at an Angle

• The total momentum of the two football players
  prior to the collision is the vector sum of their
  individual momentums.
• The key is that momentum is a vector
  quantity

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Two lumps of clay of equal mass are traveling at
right angles with equal speeds as shown, when
they collide and stick together. Is it possible
that their final velocity vector is in the
direction shown?
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Two cars of equal mass Collide at right angles to
one another in an intersection. Their direction
of motion after the collision is as shown. Which
car had the greater velocity before the
collision?
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On a perfectly still day, a sailboat enthusiast
brings a battery-operated fan to provide an air
current for his sail. A) What are the
directions of the change in momentum of the air
at the fan and at the sail? B) What are the
directions of the forces acting on the fan and on
the sail due to these changes in momentum? C)
Would the sailor be better off with the sail
furled (down) or unfurled (up)?
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1. Suppose you are out on a frozen lake, where
there is no friction. Which of the following
would start you moving towards the shore?a)
Shouting at someone on the shore.b) Removing a
shoe and throwing it towards the shore.c)
Removing a shoe and throwing it away from the
shore.d) None of these would work.  
Conceptual Question
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 Suppose two boys are trapped on the ice atop a
frozen pond, and that the ice is completely
frictionless. The boys are initially at rest,
but they do have a baseball. They begin to play
catch with the ball. Which of these is true?a)
This will not help the boys get to shore.b)
They will get to shore more quickly if they hold
hands.c) If the first boy to catch the ball
doesnt throw it back, both will reach shore more
quickly.d) Each boy will speed up as he throws
the ball, and slow down as he catches it.e) If
at least one catch is made, both should make it
to shore. 
Conceptual Question