Momentum and Collisions

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Momentum and Collisions
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Momentum

• Inertia in Motion
• Momentum mass x velocity pmvMomentum is
  doubly dependent Large mass--greater
  momentum--
  
• e.g. train vs. car at same speed Large
  velocity--greater momentum--
  
• baseball pitched by little
• leaguer or major leaguer

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Impulse

• Momentum changes when force is applied
• Force causes acceleration
• Acceleration changes velocity

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Impulse

• Momentum change depends on how long force is
  applied
  
• Time of force is proportional to momentum
  change
  
• Impulse force x time (seconds) change in
  momentum

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Interactions Involving Impulse

• Increasing momentumHit golf ball -- apply
  greatest force and follow through to increase
  timeBaseball hitter--same principle
  
• Impulse is thusly impact force x time and
  measured in newton-seconds

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Impulse

• Decreasing momentum over a long time
• Car out of control-- hit haystack or brick
  wall??
  
• Lengthen collision time with softer landing
  (examples from film)
  
• Airbags in car do the same job--lengthen impact
  time
  
• When jumping down from high place--bend knees
  on contact
  
• In judo or in wrestling, take fall with relaxed
  muscles

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Impulse
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Impulse/Impact

• Decreasing momentum in a short time
• Car hitting concrete wall-- great damage by quick
  change
  
• Karate master-- great momentum of hand causes
  breaking of bricks

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Bouncing

• Impulse is greater in bouncing due to double
  force Force to stop object Force to send it
  back
  
• Pelton water wheel uses the bounce principle to
  make more force for grinding rocks in the
  goldfields

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Conservation of Momentum

• Newtons 3rd Law
• Momentum before interaction is zero--no
  acceleration
  
• Momentum after interaction adds to
  zero Rifle/bullet ---- Mr vr mb Vb
  
• All interactions obey same principle

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Momentum as Vectors

• 0 net internal forces only
• No external force means no change in total
  momentum
  
• Within a system, momentum is conserved. In the
  absence of external forces, the momentum of a
  system remains unchanged

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Collisions

• Elastic Collisions
• Obey conservation of momentum net momentum
  before net momentum after
  
• Billiard balls of the same size and composition
  collide without lasting deformation or generation
  of heat
  
• Elastic collisions perfectly transfer momentum
  between objects

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Elastic Collisions
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Inelastic Collisions

• Obey conservation of momentum just as elastic
  collisions
  
• Inelastic because there is a connection to
  increase mass, as in coupling train cars
  
• Most collisions are not perfect in either case,
  since there is almost always either heat or
  deformation
  
• At molecular level, most collisions are nearly
  perfectly elastic

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Inelastic Collisions
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Momentum Vectors

• Collision-- Vectors before collision add to make
  the resultant momentum
  
• Breakup or explosion-- parts go in directions
  which would add to the original momentum vector
  
• Subatomic particles can be massed by the tracks
  they leave after collision

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Momentum Vectors
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Momentum Vectors
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Homework

• p99-100
• RQ 1,2, 5, 7, 10, 13, 17
• TE 1, 3, 5, 8, 9

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Energy and Work

• Force Times DistanceForce must be appliedObject
  must move
  
• Both are proportionalTwice the force twice the
  workTwice the distance twice the workHolding
  heavy object no work Object not moving has no
  work on it
• Work is happening within muscles, not outside

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Categories of work

• Against another forceArcher pulling bow
  stringPush-ups against gravityPushing object
  against friction
  
• To change speed of an object

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Units of work/energy

• Joule - one Newton times one meter
• Calorie - 4.18 joules, used for heat

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Power

• How fast work is or can be done Power work
  divided by time
  
• Greater power means same work done in less amount
  of time
  
• Unit of power - watt one joule per second
  Electricity measured in KilowattsMotors rated
  in horsepower 750 watts

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Mechanical Energy

• Energy causes work
• Energy of position - potential
• Energy of movement - kinetic

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Potential Energy

• Energy due to gravity and position
• Energy due to state - compressed spring or
  chemicals
  
• Energy which is storedGravitational potential
  energy weight times heightWeight mass times
  gravity P.E. mgh
  
• P.E. same no matter how it gets to its position

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Potential Energy
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Kinetic Energy

• When object is moving - energy is usedK.E. 1/2
  mass times velocity times velocity 1/2 mv2
  
• Moving objects can cause others to move, thus
  causing work to be done
  
• Velocity difference causes greater change in
  K.E.Double V quadruple K.E.Car going 100 km/h
  takes four times as long to stop as a car going
  50 km/h

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K.E. in many forms

• Heat - molecular motion
• Sound -molecular vibration
• Light - photon motion

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Conservation of energy

• Energy transformsSnow melts in mountain
  potential to kineticWater turns turbine in
  powerhouse kinetic straight to kinetic
  radialTurbine turns generator kinetic radial
  to electricityElectricity runs light in class
  electricity to lightLight causes calculator to
  work light to electricity Other pathways
  similar, but always there is less available
  energy after transformation
• Some becoming heatHeat is least useful form
  because it spreads most

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Conservation Law -

• Energy not created or destroyed can be
  transformed but total is constant.Pendulum shows
  this PE -- KE -- PE -- KE -- PE --
  etc.Even mass is considered concentrated energy
  Released by nuclear fission in nuclear
  reactors Released by nuclear fusion in sun and
  stars

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Machines

• Utilizing energy Machines use work equation to
  multiply or redirect forces Machines obey
  conservation of energy work in work out

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Machines

• Lever - rod and pivot (fulcrum) Force x
  distance force x distance Multiplies force,
  but not work Ratio of forces mechanical
  advantage force out M.A. force
  in
• Smaller force over greater distance greater
  force over smaller distance

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Machines

• 3 types of lever

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Machines

• Pulley - change direction of force Single fixed
  - changes direction onlyMovable pulleys
  Number of supporting strands gives M.A. No
  Machine puts out more energy than that put in,
  only changes its form

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Efficiency

• Ideal machines get 100 output of energy
• Real machines lose some output as heatSimple
  lever may put in 100 J, get 98 J out Efficiency
  work out 98 98 work in
  100
• Different systems have different
  efficiencies Pulleys about 60 Auto engines
  about 30

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Life Energy

• Mostly from chemical bonds
• Released greatly by combustion in cells
• Originally stored by the process of
  photosynthesis
  
• Original energy for life from solar nuclear fusion

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Homework

• p117-118
• RQ 3, 5, 7, 9, 12, 13, 14, 15
• TE 2, 5, 10, 11