Impulse

1

• Impulse
• Momentum

2
?

• Both the truck and the bicycle lost their brakes
  on a downhill slope and rolling slowly downwards,
  and the drivers are shouting help! help!.
• Would you be able to stop the truck?
• What it has more compared to the bicycle that you
  would not be able to stop it?

3
?

• Both the truck and the bicycle lost their brakes
  on a downhill slope and rolling slowly downwards,
  and the drivers are shouting help! help!.
• Would you be able to stop the truck?
• What it has more compared to the bicycle that you
  would not be able to stop it?
• Inertia

4
Momentum

• momentum is the inertia in motion.
• More specifically momentum is defined as the
  product of the mass of an object and its
  velocity that is,

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Momentum

• We all know that a heavy truck is harder to stop
  than a small car moving at the same speed.
• We state this fact by saying that the truck has
  more momentum than the car.

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Momentum

• The truck has more momentum than the car moving
  at the same speed because it has a greater mass.
• We can see that a huge ship moving at a small
  speed can have a large momentum, as can a small
  bullet moving at a high speed.
• And, of course, a huge object moving at a high
  speed, such as a massive truck rolling down a
  steep hill with no brakes, has a huge momentum,
  whereas the same truck at rest has no momentum at
  allbecause the v part of mv is zero.

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Change in momentum related to force

• Changes in momentum may occur when there is
  either a change in the mass of an object, a
  change in velocity, or both.
• If momentum changes while the mass remains
  unchanged, as is most often the case, then the
  velocity changes. Acceleration occurs.
• And what produces an acceleration? The answer is
  a force.
• The greater the force that acts on an object, the
  greater will be the change in velocity and,
  hence, the change in momentum.

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Time

• But something else is important in changing
  momentum timehow long a time the force acts.
• Apply a force briefly to a stalled automobile,
  and you produce a small change in its momentum.
• Apply the same force over an extended period of
  time, and a greater change in momentum results.
• A long sustained force produces more change in
  momentum than the same force applied briefly.

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Impulse

• So for changing the momentum of an object, both
  force and the time during which the force acts
  are important.
• We name the product of force and this time
  interval impulse.
• Or, in shorthand notation,
• Whenever you exert a net force on something, you
  also exert an impulse.
• The resulting acceleration depends on the net
  force
• the resulting change in momentum depends on both
  the net force and the time during which that
  force acts.

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Impulse Changes Momentum

• Impulse changes momentum in much the same way
  that force changes velocity.
• The relationship of impulse to change of momentum
  comes from Newton's second law and
• a F/m
• the definition of accelaration
• a ?v/t
• F/m ?v/t
• Ft m ?v
• Ft ?mv
• which reads, force multiplied by the time
  during which it acts equals change in momentum.

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Impulse Changes Momentum

• The impulse-momentum relationship helps us to
  analyze many examples in which forces act and
  motion changes. Sometimes the impulse can be
  considered to be the cause of a change of
  momentum. Sometimes a change of momentum can be
  considered to be the cause of an impulse. It
  doesn't matter which way you think about it. The
  important thing is that impulse and change of
  momentum are always linked. Here we will consider
  some ordinary examples in which impulse is
  related to (1) increasing momentum, (2)
  decreasing momentum over a long time, and (3)
  decreasing momentum over a short time.

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Momentum

1. Which has more momentum, a 1-ton car moving at
   100 km/h or a 2-ton truck moving at 50 km/h?

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Momentum

1. Both have the same momentum.

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Impulse

• 2. Does a moving object have impulse?

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Impulse

• 2. No, impulse is not something an object has,
  like momentum. Impulse is what an object can
  provide or what it can experience when it
  interacts with some other object. An object
  cannot possess impulse just as it cannot possess
  force.

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Momentum

• 3. Does a moving object have momentum?

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Momentum

• 3. Yes, but, like velocity, in a relative
  sensethat is, with respect to a frame of
  reference, often taken to be the Earth's surface.
  
• The momentum possessed by a moving object with
  respect to a stationary point on Earth may be
  quite different from the momentum it possesses
  with respect to another moving object.

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Increasing Momentum

• If you wish to increase the momentum of something
  as much as possible, you not only apply the
  greatest force you can, you also extend the time
  of application as much as possible.
• Hence the different results in pushing briefly on
  a stalled automobile and giving it a sustained
  push.

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Increasing Momentum

• Long-range cannons have long barrels. The longer
  the barrel, the greater the velocity of the
  emerging cannonball or shell.
• The force of exploding gunpowder in a long barrel
  acts on the cannonball for a longer time. This
  increased impulse produces a greater momentum.

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Increasing Momentum

• The force that acts on the golf ball, for
  example, increases rapidly as the ball is
  distorted and then diminishes as the ball comes
  up to speed and returns to its original shape.
• When we speak of impact forces in this chapter,
  we mean the average force of impact.

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Decreasing Momentum over a Long Time

• Imagine you are in a car out of control, and you
  have a choice of slamming into either a concrete
  wall or a haystack.
• You needn't know much physics to make the better
  decision, but knowing some physics helps you to
  understand why hitting something soft is entirely
  different from hitting something hard.
• In the case of hitting either the wall or the
  haystack, your momentum will be decreased by the
  same amount, and this means that the impulse
  needed to stop you is the same.
• The same impulse means the same product of force
  and time - not the same force or the same time.

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Decreasing Momentum over a Long Time

• By hitting the haystack instead of the wall, you
  extend the time of impactyou extend the time
  during which your momentum is brought to zero.
• The longer time is compensated by a lesser force.
  
• If you extend the time of impact 100 times, you
  reduce the force of impact by 100.
• So whenever you wish the force of impact to be
  small, extend the time of impact.

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Decreasing Momentum over a Short Time

• When boxing, move into a punch instead of away,
  and you're in trouble.
• Likewise if you catch a high-speed baseball while
  your hand moves toward the ball instead of away
  upon contact.
• Or when out of control in a car, drive it into a
  concrete wall instead of a haystack and you're
  really in trouble.
• In these cases of short impact times, the impact
  forces are large.
• Remember that for an object brought to rest, the
  impulse is the same, no matter how it is stopped.
  But if the time is short, the force will be large.

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Decreasing Momentum over a Short Time

• The idea of short time of contact explains how a
  karate expert can sever a stack of bricks with
  the blow of her bare hand.
• She brings her arm and hand swiftly against the
  bricks with considerable momentum.
• This momentum is quickly reduced when she
  delivers an impulse to the bricks.
• The impulse is the force of her hand against the
  bricks multiplied by the time her hand makes
  contact with the bricks.
• By swift execution she makes the time of contact
  very brief and correspondingly makes the force of
  impact huge.
• If her hand is made to bounce upon impact, the
  force is even greater.

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Bouncing

• You know that if a flower pot falls from a shelf
  onto your head, you may be in trouble. And
  whether you know it or not, if it bounces from
  your head, you may be in more serious trouble.
• Impulses are greater when bouncing takes place.
• This is because the impulse required to bring
  something to a stop and then, in effect, throw
  it back again is greater than the impulse
  required merely to bring something to a stop.
• Suppose, for example, that you catch the falling
  pot with your hands. Then you provide an impulse
  to catch it and reduce its momentum to zero. If
  you were to then throw the pot upward, you would
  have to provide additional impulse.
• So it would take more impulse to catch it and
  throw it back up than merely to catch it.
• The same greater impulse is supplied by your head
  if the pot bounces from it.

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Bouncing

• An interesting application of the greater impulse
  that occurs when bouncing takes place was
  employed with great success in California during
  the gold rush days.
• The water wheels used in gold-mining operations
  were ineffective.
• A man named Lester A. Pelton saw that the problem
  had to do with their flat paddles.
• He designed curved-shape paddles that would cause
  the incident water to make a U-turn upon
  impactto bounce.
• In this way the impulse exerted on the water
  wheels was greatly increased.

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When does impulse equal momentum?

• Impulse equals a change in momentum.
• if an object is brought to rest, impulse
  initial momentum.
• If the initial momentum of an object is zero when
  the impulse is applied, then impulse final
  momentum.

Total impulse initial momentum final
momentum.
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Conservation of Momentum

• Newton's second law tells us If we want to
  accelerate an object, we must apply a force.
• We say much the same thing in this chapter when
  we say that to change the momentum of an object
  we must apply an impulse.
• In any case, the force or impulse must be exerted
  on the object or any system of objects by
  something external to the object or system.
  Internal forces don't count.
• An outside, or external, force acting on the
  baseball or automobile is required for a change
  in momentum.
• If no external force is present, then no change
  in momentum is possible.

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Conservation of Momentum

• When a bullet is fired from a rifle, the forces
  present are internal forces. The total momentum
  of the system comprising the bullet and rifle
  therefore undergoes no net change.
• By Newton's third law of action and reaction, the
  force exerted on the bullet is equal and opposite
  to the force exerted on the rifle.
• The forces acting on the bullet and rifle act for
  the same time, resulting in equal but oppositely
  directed impulses and therefore equal and
  oppositely directed momenta (the plural form of
  momentum).
• Although both the bullet and rifle by themselves
  have gained considerable momentum, the bullet and
  rifle together as a system experience no net
  change in momentum.
• Before firing, the momentum was zero after
  firing, the net momentum is still zero.
• No momentum is gained and no momentum is lost.

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Conservation of Momentum

• The forces acting on the bullet and rifle act for
  the same time, resulting in equal but oppositely
  directed impulses and therefore equal and
  oppositely directed momenta (the plural form of
  momentum).
• Although both the bullet and rifle by themselves
  have gained considerable momentum, the bullet and
  rifle together as a system experience no net
  change in momentum.
• Before firing, the momentum was zero after
  firing, the net momentum is still zero.
• No momentum is gained and no momentum is lost.

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Vector

• Two important ideas are to be learned from the
  rifle-and-bullet example.
• The first is that momentum, like velocity, is a
  quantity that is described by both magnitude and
  direction we measure both how much and which
  direction. Momentum is a vector quantity.
  Therefore, when momenta act in the same
  direction, they are simply added when they act
  in opposite directions, they are subtracted.
• The second important idea to be taken from the
  rifle-and-bullet example is the idea of
  conservation. The momentum before and after
  firing is the same. For the system of rifle and
  bullet, no momentum was gained none was lost.
  When a physical quantity remains unchanged during
  a process, that quantity is said to be conserved.
  We say momentum is conserved.

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Collisions

• Momentum is conserved in collisionsthat is, the
  net momentum of a system of colliding objects is
  unchanged before, during, and after the
  collision.
• This is because the forces that act during the
  collision are internal forcesforces acting and
  reacting within the system itself. There is only
  a redistribution or sharing of whatever momentum
  exists before the collision.In any collision,
  we can say
• Net momentum before collision net momentum
  after collision.
• This is true no matter how the objects might be
  moving before they collide.

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elastic collision

• When a moving billiard ball makes a head-on
  collision with another billiard ball at rest, the
  moving ball comes to rest and the other ball
  moves with the speed of the colliding ball.
• We call this an elastic collision
• ideally the colliding objects rebound without
  lasting deformation or the generation of heat.

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inelastic collision

• But momentum is conserved even when the colliding
  objects become entangled during the collision.
• This is an inelastic collision,
• characterized by deformation or the generation of
  heat or both. In a perfectly inelastic collision,
  both objects stick together.
• Consider, for example, the case of a freight car
  moving along a track and colliding with another
  freight car at rest.
• If the freight cars are of equal mass and are
  coupled by the collision, can we predict the
  velocity of the coupled cars after impact?

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conservation of momentum

• Suppose the single car is moving at 10 m/s, and
  we consider the mass of each car to be m.
• Then, from the conservation of momentum, by
  simple algebra, V 5 m/s.
• This makes sense, for since twice as much mass is
  moving after the collision, the velocity must be
  half as much as the velocity before collision.

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inelastic collision

• The net momentum of the trucks before and after
  collision is the same.
• Note the inelastic collisions shown in Figure.
• If A and B are moving with equal momenta in
  opposite directions (A and B colliding head-on),
  then one of these is considered to be negative,
  and the momenta add algebraically to zero. After
  collision, the coupled wreck remains at the point
  of impact, with zero momentum.

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inelastic collision

• If, on the other hand, A and B are moving in the
  same direction (A catching up with B), the net
  momentum is simply the addition of their
  individual momenta.

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momentum conservation

• For a numerical example of momentum conservation,
  consider a fish that swims toward and swallows a
  smaller fish at rest.
• If the larger fish has a mass of 5 kg and swims 1
  m/s toward a 1kg fish, what is the velocity of
  the larger fish immediately after lunch?
• We will neglect the effects of water resistance.

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momentum conservation

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momentum conservation

• Suppose the small fish in the preceding example
  is not at rest, but swims toward the left at a
  velocity of 4 m/s.
• It swims in a direction opposite that of the
  larger fisha negative direction, if the
  direction of the larger fish is considered
  positive. In this case,

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momentum conservation

• Suppose the small fish in the preceding example
  is not at rest, but swims toward the left at a
  velocity of 8 m/s.
• It swims in a direction opposite that of the
  larger fisha negative direction, if the
  direction of the larger fish is considered
  positive. In this case,

The final velocity is -1/2 m/s. What is the
significance of the minus sign? It means that the
final velocity is opposite to the initial
velocity of the larger fish.
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Complicated Collisions

• The net momentum remains unchanged in any
  collision, regardless of the angle between the
  tracks of the colliding objects.
• Expressing the net momentum when different
  directions are involved can be achieved with the
  parallelogram rule of vector addition.
• Car A has a momentum directed due east, and car
  B's momentum is directed due north.
• If their individual momenta are equal in
  magnitude, then their combined momentum is in a
  northeast direction.

Diagonal is v2 times the length of the side of a
square.
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Component momenta

• A firecracker exploding into two pieces.
• The momenta of the fragments combine by vector
  addition to equal the original momentum of the
  falling firecracker.

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Learn from Collisions

• Whatever the nature of a collision or however
  complicated it is, the total momentum before,
  during, and after remains unchanged.
• This extremely useful law enables us to learn
  much from collisions without knowing any details
  about the interaction forces that act in the
  collision.