Physics 160 Biomechanics

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Physics 160 Biomechanics

• Impulse and Momentum

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Questions to think about

• If two football players collide head-on, which
  direction will they travel after the collision?
• Why would a catcher want to pull her hand back as
  she catches the ball?
• Why can you hit a baseball farther with an
  aluminum bat than with a wood bat?

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Momentum

• Momentum is the product of an objects velocity
  and its mass
• Momentum is a vector quantity that points in the
  same direction as the velocity vector.

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Example

• Which has more momentum, a 90 kg hockey player
  traveling at 6 m/s or a 70 kg hockey player
  traveling at 8 m/s?

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Conservation of Momentum

• In the absence of external forces, the total
  momentum of a given system remains constant.
• Before collision After collision
• (m1v1) - (m2v2)
  ( m1 m2)V

m1
m2
v1
v2
V
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Example

• A 90 kg running back is diving towards the end
  zone with a horizontal velocity of 6 m/s. He is
  hit in midair by a 120 kg linebacker who is
  diving in the opposite direction with a
  horizontal velocity of 4 m/s. What is their
  combined velocity after the collision?

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Example

• A medicine ball with a mass of 8 kg is thrown
  with a velocity of 10 m/s at a 45 kg boy who has
  jumped up into the air to catch the ball. What is
  the backwards velocity of the boy after catching
  the ball?

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Impulse

• Impulse is the product of force and time over
  which the force acts

The impulse due to a net external force causes
the momentum of a system to change.
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Example

• A volleyball player blocks a 0.5 kg ball at the
  net. The ball is approaching with a velocity of
  13 m/s horizontally. During the block she applies
  a force of 200N to the ball for 50 ms. What is
  the velocity of the ball after the block?

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Example

• A 50 kg gymnast performs a vault. At landing,
  the downward velocity of his center of mass is
  5.4 m/s. What impulse is required to stop the
  downward motion of his center of mass? If he
  keeps his knees stiff, he can stop his downward
  motion in 0.25 s, if he bends his knees, he can
  stop his downward motion in 0.5 s. What average
  vertical force from the ground will he experience
  in each case?

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Impulse as an Area

• The area between the line and the x axis of a
  force versus time graph between two instants in
  time equals the impulse due to the force over
  that period.

Anteroposterior ground reaction force
illustrating the braking and propulsion impulses
during running.
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Example

• Consider an individual with a mass of 65 kg
  performing high (A) and low (B) vertical jumps
  whose force time graphs are shown below. What is
  the approximate impulse produced by the GRF in A)
  between 100 ms and 230 ms? What was the takeoff
  velocity of the persons center of mass?
  
  
  
  
  
  
  

Force (BW)
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Impact

• A collision in which a large force acts over a
  small time
• The force acting during impact has two effects
• Energy absorbed and lost through deformation
• Remaining force changes the objects direction
• Total momentum before and after impact are equal

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Types of Impacts

• Perfectly Elastic No energy lost. The relative
  velocities of the two bodies after impact are the
  same as their relative velocities before impact
• Perfectly Plastic Objects deform and stick
  together
• Most impacts are somewhere in between

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Coefficient of Restitution

• Measures the elasticity of an impact (e1 for
  perfectly elastic, e0 for perfectly plastic)
• Determined by the properties of the materials
  making up both objects
• Important consideration where bouncing occurs

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Example

• A basketball is dropped from a height of 2 m
  onto a gymnasium floor. If the coefficient of
  restitution between ball and floor is 0.9, how
  high will the ball bounce? Given