Momentum and Collisions

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Momentum and Collisions
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Momentum

• The linear momentum of an object of mass m moving
  with a velocity v is the product of the mass and
  the velocity.
• Momentum mass X velocity
• pmv
• Units kg?m/s

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Momentum Practice

• A 2250 kg pickup truck has a velocity of 25 m/s
  to the east. What is the momentum of the truck?
• Given m2250 kg
• v 25 m/s
• pmv 2250kg x 25 m/s
• 5.6x104 kg?m/s

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Changing Momentum

• A change in momentum takes force and time
• Fm(?v/?t)
• Newtons original formula
• F?p/?t
• ?pmvf-mvi
• Force change in momentum during time interval

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Impulse

• Impulse is the force for the time interval.
• Impulse-momentum theorem is the expression F?t
  ?p
• If you extend the time of impact you reduce the
  amount of force.

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Force and Impulse

• A 1400 kg car moving westward with a velocity of
  15 m/s collides with a utility pole and is
  brought to rest in .30 s. Find the force exerted
  on the car during the collision.
• Given m1400 kg, ?t .30 s
• vf0 m/s vi15 m/s
• What formula can I use?

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Impulse-Momentum

• F?t ?p
• ?pmvf-mvi
• F?tmvf-mv I am looking for force
• Fmvf-mv/ ?t Now I just plug in my numbers
• (14000-1400-15)/.30 7.0104 N to the east

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Stopping Distance

• A 2240 kg car traveling west slows down uniformly
  from 20.0 m/s to 5.0 m/s How long does it take
  the car to decelerate if the force on the car is
  8410 to the east? How far does the car travel
  during the deceleration?

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What am I given?

• M 2240 kg
• vi 20.0 m/s to the west -20.0 m/s
• vf 5.0 m/s to the west -5.0 m/s
• F 8410 N to the east so it stays positive
• Unknown ?t and ?x

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Impulse Momentum Theorem

• F?t ?p
• ?pmvf-mvi
• ?tmvf-mvi /F
• ((2240-5)-(2240-20))/8410
• ?t4.0s

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Displacement of the vehicle

• To find the change in distance
• Average velocity change in d/change in t
• Average velocity (initial final)/2
• Since these are equal I can combine them
• ?x/?t(vf vi)/2
• Solving for x((vf vi)/2) ?t
• x((-20-5)/2)4
• x-50 so it would be 50m to the west

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Conservation Of Momentum

• When I have two objects A and B
• p(Ai)p(Bi)p(Af)p(Bf)
• Total initial momentumtotal final momentum

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Conservation of Momentum

• A 76 kg boater, initially at rest in a stationary
  45 kg boat, steps out of the boat and onto the
  dock. If the boater moves out of the boat with a
  velocity of 2.5 m/s to the right what is the
  final velocity of the boat?
• Given m of person 76 kg vi0 m/s,vf2.5 to the
  right
• m of boat 45 kg vi0 vf?

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• m1v1im2v2im1v1fm2v2f
• Because the boater and the boat are initially at
  rest m1v1i m2v2i0
• Rearrange to solve for final velocity of boat
• v2f (-m1/m2)/v1f
• -76/45 2.54.2 to the right -4.2

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• Two train cars of mass 8000 kg are traveling
  toward each other. One at a speed of 30 m/s to
  the west and the other at a speed of 25 m/s to
  the east. They crash and become entangled, what
  is their final velocity and direction?

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• m1 8000 kg
• m2 8000 kg
• v1-30m/s
• v225 m/s
• m1v1m2v2mtotvtot