Momentum

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Momentum and Impulse

• Momentum
• and
• Impulse
• Updated 11/1/06

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Momentum and Impulse

• momentum inertia in motion.
• units are kg m/s.
• the more mass an object has, the more momentum.
  Think of a loaded dump truck.
• the more speed an object has, the more momentum.
  Think of a high-speed bullet.

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Momentum and Impulse

• Momentum mass x velocity
• p mv

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Momentum and Impulse

• impulse a change in momentum caused by applying
  a force for a time period.
• units are kg m/s (same as momentum).
• the more force applied to an object, the bigger
  the impulse. Think of a gunshot.
• the longer the time a force is applied, the
  bigger the impulse will be. Think of a rocket
  launch.

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Momentum and Impulse

• impulse force x time interval
• impulse Ft
• and
• impulse change in momentum
• or
• Ft ?p ?(mv)

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Momentum and Impulse

• Collisions are about change in momentum.
• The longer it takes to stop an object, the
  smaller the force needed to stop it.
• Softer is better Concrete is harder than Wood is
  harder than Grass is harder than Sand is harder
  than Water

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Momentum and Impulse

• Safety devices like boxing gloves, nets, bungee
  cords and airbags are designed to be as soft as
  possible.
• That is, they resist your motion, but give at
  the same time. They slow you down gradually,
  reducing the force that your body feels.

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Momentum and Impulse

• momentum problems calculate the momentum of the
  following.
• a .05 kg bullet traveling at 400 m/s
• a 100 kg football player going 9 m/s
• a 1200 kg car going at 30 m/s.
• a 500,000 kg train going at 30 m/s
• a 20,000 kg shuttle traveling at 10 km/s

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Momentum and Impulse

• impulse problem A 50-kg diver jumps from a 5
  meter platform into a pool.
• How fast is the diver going when he/she enters
  the water?
• What is the divers momentum?
• If it takes .4 seconds to stop, what is the
  average force on the diver after entry?

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Momentum and Impulse

• impulse problem A 50-kg diver jumps from a 5
  meter platform onto concrete.
• How fast is the diver going when he/she hits the
  pad?
• What is the divers momentum?
• If it takes .02 seconds to stop, what is the
  average force on the diver on landing?

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Collisions

• Law of conservation of momentum
• In the absence of an external force, the momentum
  of a system remains unchanged.
• net momentumbefore net momentumafter

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Collisions
Conservation of momentum pBEFORE
pAFTER For 2 objects m1u1 m2u2 m1v1 m2v2
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Collisions
Conservation of momentum can be expanded to
include n objects m1u1 m2u2 m3u3
m1v1 m2v2 m3v3 m mass u initial
velocity (or speed) v final velocity (or speed)
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Collisions

• Elastic collisions
• Mechanical (kinetic) energy is conserved. The
  objects bounce off of each other.
• Inelastic collisions
• Mechanical energy is not conserved. The objects
  may be deformed, objects may stick together,
  energy may be lost as heat.

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Collisions
Inelastic Collisions Momentum is conserved, but
energy is not. For two objects m1u1 m2u2
(m1 m2)v The objects are joined and have a
common velocity.
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Collisions
Elastic Collisions Momentum and mechanical
energy are conserved. For two objects m1u1
m2u2 m1v1 m2v2 Describes how momentum is
conserved.
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Collisions
Elastic Collisions Mechanical energy is also
conserved. For two objects ½m1u12 ½ m2u22
½ m1v12 ½ m2v22 Describes how energy is
conserved.
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Collisions
Web Sites basic collision animations. NTSB
train-truck collision animations. NTSB train-bus
collision animations.
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Momentum and Impulse

• Example calculating momentum
• A 7 kg bowling ball is moving down the lane at 12
  m/s. What is the momentum?
• p mv (7 kg)(12 m/s) 84 kg m/s
• A 4,500 kg truck is driving at 32 m/s. What is
  the momentum of the truck?
• p mv (4,500 kg)(32 m/s) 144,000 kg m/s

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Momentum and Impulse

• Example calculating momentum
• A bowling ball is moving with a momentum of 72 kg
  m/s. What is speed of the 5 kg ball?
• v p/m (72 kg m/s) / (5 kg) 14.4 m/s
• A Harley has 12,000 kg m/s of momentum and is
  moving at 24 m/s. What is its mass?
• m p/v (12,000 kg m/s) / (24 m/s) 500 kg

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Momentum and Impulse

• Example calculating impulse
• A bowling ball is moving with a momentum of 72 kg
  m/s. It stops at the end of the alley. What is
  the impulse?
• impulse ?p (72 kg m/s) - (0) 72 kg m/s
• What impulse is needed to increase the momentum
  of a Harley from 4,600 kg m/s to 12,000 kg m/s of
  momentum?
• ?p (12,000 kg m/s) - (4,600 kg m/s) 7,400 kg
  m/s

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Momentum and Impulse

• Example calculating impulse
• A bowler applies a force of 300N to a bowling
  ball for .24s. What is the impulse?
• impulse Ft (300N)(.24s) 72 kg m/s
• Note Ft (300 kg m/s2)(.24s) 72 kg m/s
• If the same momentum is generated in .08s, what
  is the force?
• F ?p/t (72 kg m/s) / (.08 s) 900 N

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Momentum and Impulse

• Example calculating momentum

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Momentum and Impulse

• Example calculating impulse

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Momentum and Impulse

• End of
• Momentum
• and
• Impulse