Impulse

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Impulse Momentum
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What is momentum?

• Momentum is a commonly used term in sports. A
  team that has the momentum is on the move and is
  going to take some effort to stop.
• 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.

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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. 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 x
velocity In physics, the symbol for the quantity
momentum is the small case "p" thus, the above
equation can be rewritten as
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p m x v
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Momentum is a vector quantity. As discussed in an
earlier unit, a vector quantity is a quantity
which is fully described by both magnitude and
direction. To fully describe the momentum of a
moving object, you must include information about
the direction of the object.
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From the definition of momentum, it becomes
obvious that an object has a large momentum if
either its mass or its velocity is large. The
momentum equation (p m x v) can help us to
think about how a change in one of the two
variables might effect the momentum of an object.
The momentum is directly proportional to the
mass and velocity. The mass is inversely
proportional to the velocity.
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Using the equation determine the momentum of
A) 60 kg halfback moving at 9 m/s.
540 kg-m/s
B) 1000 kg car moving south at 20 m/s.
20000 kg-m/s.
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A car has 20000 units of momentum. What will
happen to the momentum if
A) The velocity was doubled?
40000 units.
B) The mass was tripled?
60000 units
C) The mass and velocity were doubled?
80000 units
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• A force acting over time will change an object's
  momentum.
• If the force acts opposite the object's motion,
  it slows the object. If a force acts in the same
  direction as the object's motion, then the force
  speeds the object up.

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Newtons first law states an object in straight
line motion will remain in motion unless acted on
by an outside force. Since this force will
change the objects velocity, it will change the
objects momentum. The change in momentum caused
by a force is called an impulse. Impulse is a
vector quantity like momentum. The impulse acts
in the same direction as the force. The strength
of the impulse depends on two factors The
strength of the force and the time the force is
applied.
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Mathematically impulse force x time. More
importantly impulse is the change in momentum
therefore force x time mass x change in
velocity. Mathematically F x t m x
?v Simply put, you apply a force to a moving
object you will change its velocity.
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Observe the above picture. What exerts the force
providing an impulse to the car?
From Newtons Third Law, the tree exerts a force
on the car equal to the force the car exerted on
the tree.
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The large force exerted by the tree brings the
car to a quick stop. The result is the crushing
of the cars front end. The tree provided the
impulse to stop the car by exerting a large force
over a short time. Is there another option?
Force and time are inversely proportional to each
other. If you increase one the other decreases.
If you increase the time of contact for a
collision the force is reduced.
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Notice what happens to the force as the time
increases.

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The boxer rides the punch, which increases the
contact time of the punch which reduces the force
of the punch.
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Another example is the use of air bags in cars.
When the air bag deploys they extend the time
required to stop the momentum of the driver and
passenger. When lacrosse players catch the ball
the ball is "cradled" when caught i.e., the
lacrosse player reaches out for the ball and
carries it inward toward his body as if he were
cradling a baby. The effect of this strategy is
to lengthen the time over which the collision
occurs and so reduce the force on the lacrosse
ball.
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Which case has the greatest change in velocity?
Case A 10 m/s (-5 m/s) 10 5 15 m/s
Case B 30 m/s (-28 m/s) 30 28 58 m/s
This type of collision is called a rebound.
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A rebound is a collision involving a direction
change in addition to a speed change. The result
of the direction change is a large velocity
change. In a rebound collision, an object will
have the same or nearly the same speed as it had
before the collision. Collisions in which objects
rebound with the same speed (and thus, the same
momentum and kinetic energy) as they had prior to
the collision are known as elastic collisions.
Elastic collisions are characterized by a large
velocity change, a large momentum change, a large
impulse, and a large force.
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F x t m x ?v is the equation which connects the
impulse to the change in velocity.
Force (N) Time (s) Imp ?p m (kg) ?v
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Conservation of Momentum
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• What is the effect of a collision on objects?
  According to Newtons Third Law colliding objects
  exert equal forces on each other. Unless the
  masses of the objects are equal, the colliding
  objects will have different accelerations. Equal
  forces mean equal impulses therefore equal
  changes in momentum, and then the total momentum
  of the system will remain constant.

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• The rightward moving seven-ball experiences a
  leftward force which causes it to slow down the
  eight-ball experiences a rightward force which
  causes it to speed up. Since the two balls have
  equal masses, they will also experience equal
  accelerations. In a collision, there is a force
  on both objects which causes an acceleration of
  both objects the forces are equal in magnitude
  and opposite in direction.

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m1 ?v - m2 ?v

• The above equation is one statement of the law of
  momentum conservation. 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.

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Money Conservation
Before After Change
Jack 100 50 -50
Jill 100 150 50
Total 200 200 0
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The following link connects to a video of
illusionist Chris Angel performing a stunt in
which he survives being hit by a car while he is
standing against a brick wall.

• Chris Angel

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• A hockey player applies an average force of 80.0
  N to a 0.25 kg hockey puck for a time of 0.10
  seconds. Determine the impulse experienced by the
  hockey puck.

.80 N-s Impulse Force x time
If a 5-kg object experiences a 10 N force for a
duration of 0.1-second, then what is the momentum
change of the object?
.1 N-s Impulse equals the change in momentum. If
you calculate the impulse you are calculating the
change in momentum.
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• A 120 kg lineman moving west at 2 m/s tackles an
  80 kg football fullback moving east at 8 m/s.
  After the collision, both players move east at 2
  m/s. In which case is the momentum greater?
• Before the collision
• After the collision
• Neither case, the momentum is the same before and
  after the collision.

Neither case, the momentum is the same before and
after the collision.
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What is the velocity of the grandmother after she
grabs and holds on to him while rollerskating?
80v 40v 480 120v 480 v 4 m/s
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What is the velocity of the truck after colliding
with the stationary car?
3000v 15 000 30 0003000v 15 000v 5.0 m/s