Work and Energy

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Work and Energy

• Chapter 5

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Work

• Work is the product of the net force on an object
  and the distance through which the object is
  moved
• In its simplest case W Fd
• If we lift two loads, we do twice as much work as
  lifting one load the same distance, because the
  force needed is twice as great.
• If we lift one load twice as far, we do twice as
  much work because the distance is twice as great.

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• Ex. Lifting a barbell then holding it steady
• Work is done on the barbell raising it up, but
  once it is held stationary no work is done on the
  barbell
• Work may be done on the muscles by stretching and
  contracting them, which is work on the biological
  scale, but this work is not done on the barbell

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• Work is done only when the component of a force
  is parallel to displacement
• When force is applied at an angle to the
  displacement WFd(cos ?)
• ? 0o , cos 0 1 then WFd (parallel force)
• ? 90o , cos 90 0 then W 0 (perpendicular
  force)
• Appling a Force does not always constitute work

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• Some work is done against another force.
• An archer stretches her bowstring, doing work
  against the elastic forces of the bow.
• When the ram of a pile driver is raised, work is
  required to raise the ram against the force of
  gravity.
• When you do push-ups, you do work against your
  own weight.
• Some work is done to change the speed of an
  object.
• Bringing an automobile up to speed or in slowing
  it down involves work.

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Sign of Work

• Sign of Work is important
• Work is a scalar quantity that is or
• work force and displacement same direction
• - work force and displacement opposite
  directions (kinetic friction)
• Increase speed work
• Decrease speed - work,

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Net Work (5A)

• Wnet Fnet d (cos ?)
• Units Nm J
• A weightlifter lifts a set of weights a vertical
  distance of 2.00 m. If a constant net force of
  350 N is exerted on the weights, what is the net
  work done on the weights?
• Upon arrival at an airport, a passenger picks up
  her suitcase and drags it with a 100.0 N force at
  60.0o for 200.0 m to her car. Work?

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Energy

• Kinetic Energy energy associated with motion
• Kinetic Energy depends on speed and mass
• KE ½ mv2
• Scalar quantity units are Joules (J)
• KE depends more on velocity then mass
• If velocity doubles, KE quadruples, but why?

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Board Work (5B)

• How does the KE of a car change when the velocity
  increases from 22 m/s to 66 m/s?
• A 6.0 kg cat runs after a mouse at 10.0 m/s. KE
  of cat?
• A 24 kg dog runs after the cat with the same KE.
  What is the velocity of dog?

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Work-Kinetic Energy Theorem

• Says Wnet done by a Fnet acting on an object is
  equal to change in KE of object
• When you throw a ball, you do work on it to give
  it speed as it leaves your hand. The moving ball
  can then hit something and push it, doing work on
  what it hits.
• This theorem allows us to think of KE as the work
  that an object can do while the object changes
  speed

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• To increase the kinetic energy of an object, work
  must be done on the object
• The work-energy theorem applies to decreasing
  speed as well.
• The more kinetic energy something has, the more
  work is required to stop it.
• Twice as much kinetic energy means twice as much
  work.
• Include all forces that do work on object when
  calculating Wnet
• Wnet ?KE
• Wnet ½ mvf2 ½mvi2

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When a car brakes, the work is the friction force
supplied by the brakes multiplied by the distance
over which the friction force acts
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• Due to friction, energy is transferred both into
  the floor and into the tire when the bicycle
  skids to a stop.
• An infrared camera reveals the heated tire track
  on the floor.

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Board Work (5C)

• On a frozen pond, a person kicks a 10.0 kg sled,
  giving it an initial speed of 2.2 m/s. How far
  does the sled move if the coefficient of kinetic
  friction between the sled and the ice is 0.10?

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Potential Energy (PE)

• An object may store energy by virtue of its
  position.
• Energy that is stored and held in readiness is
  called potential energy (PE) because in the
  stored state it has the potential for doing work.

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Potential Energy
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• Work is required to elevate objects against
  Earths gravity.
• The potential energy due to elevated positions is
  gravitational potential energy.
• Water in an elevated reservoir and the raised ram
  of a pile driver have gravitational potential
  energy.

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• The amount of gravitational potential energy
  possessed by an elevated object is equal to the
  work done against gravity to lift it.
• The upward force required while moving at
  constant velocity is equal to the weight, mg, of
  the object, so the work done in lifting it
  through a height h is the product mgh.
• gravitational potential energy weight height
• PE mgh
• Note that the height is the distance above some
  chosen reference level, such as the ground or the
  floor of a building.

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• The potential energy of the 100-N boulder with
  respect to the ground below is 200 J in each
  case.
• The boulder is lifted with 100 N of force.
• The boulder is pushed up the 4-m incline with 50
  N of force.
• The boulder is lifted with 100 N of force up each
  0.5-m stair.

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• Hydroelectric power stations use gravitational
  potential energy.
• Water from an upper reservoir flows through a
  long tunnel to an electric generator.
• Gravitational potential energy of the water is
  converted to electrical energy.
• Power stations buy electricity at night, when
  there is much less demand, and pump water from a
  lower reservoir back up to the upper reservoir.
  This process is called pumped storage.
• The pumped storage system helps to smooth out
  differences between energy demand and supply.

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Elastic Potential Energy

• A stretched or compressed spring has a potential
  for doing work.
• When a bow is drawn back, energy is stored in the
  bow. The bow can do work on the arrow.
• A stretched rubber band has potential energy
  because of its position.
• These types of potential energy are elastic
  potential energy.

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• Energy of a stretched or compressed elastic
  object
• Depends on the distance of the compression or
  stretch
• PEelastic ½ kx2
• PEtotal PEg PEelastic
• K spring constant parameter that expresses how
  resistant a spring is to being compressed or
  stretched
• Flexible spring small k
• Stiff spring large k

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Elastic Potential Energy
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Board Work (5D)

• When a 2.00 kg mass is attached to a vertical
  spring, the spring is stretched 10.0 cm so that
  the mass is 50.0 cm above the table.
• What is the PEg ? PEelastic ? (k900.0 N/m)
  PEtotal ?

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Board Work (5D)

• A 70.0 kg stuntman is attached to a bungee cord
  with an unstretched length of 15.0 m. He jumps
  off a bridge spanning a river from a height of
  50.0 m. When he finally stops, the cord has a
  stretched length of 44.0 m. Treat the stuntman
  as a point mass, disregard the weight of the
  bungee cord. Assuming the spring constant of the
  cord is 71.8 N/m, what is the PEt relative to the
  water when the man stops falling?

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Conservation of Energy

• The study of the forms of energy and the
  transformations from one form into another is the
  law of conservation of energy.
• For any system in its entiretyas simple as a
  swinging pendulum or as complex as an exploding
  galaxythere is one quantity that does not
  change energy.
• Energy may change form, but the total energy
  stays the same

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Conservation of Energy

• The property of an object or system that enables
  it to do work is energy. Like work, energy is
  measured in joules.
• Mechanical energy is the energy due to the
  position of something or the movement of
  something.
• Mechanical Energy (ME) description of motion of
  many objects that involves a combination of KE
  and PE

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• Energy conservation occurs even when acceleration
  varies, assume no friction
• ME is not conserved in the presence of friction
• Nonmechanical energy is no longer negligible
• ME is the sum of kinetic and all forms of
  potential energy
• ME KE ?PE
• ME is often conserved (neglect friction)
• MEi MEf

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Board Work (5E)

• A 75 kg diver jumps off a diving board with an
  initial speed of 1.5 m/s. If the diving board is
  10.0 m above the water, what is the divers speed
  just before hitting the water?

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Board Work

• A 50.0 kg diver steps off a diving board and
  drops straight down into the water. The water
  provides an average net force of resistance of
  1500 N to the divers fall. If the diver comes
  to rest 5.0 m below the waters surface.
• What is the velocity of the diver at the water?
• What is the total distance between the diving
  board and the divers stopping point underwater?

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Board Work (5E)

• A small 10.0 g ball is held in a sling shot that
  is stretched 6.0 cm. K2.0x102 N/m
• What is PEelastic?
• KE after released?
• Balls speed?
• How high will it go if shot upward?

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Power

• When carrying a load up some stairs, you do the
  same amount of work whether you walk or run up
  the stairs.
• Power is the rate at which work is done
• Machines with different power ratings do the same
  work in different time intervals

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• High-power engine does work rapidly.
• An engine that delivers twice the power of
  another engine does not necessarily produce twice
  as much work or go twice as fast.
• Twice the power means the engine can do twice the
  work in the same amount of time or the same
  amount of work in half the time.
• A powerful engine can get an automobile up to a
  given speed in less time than a less powerful
  engine can.

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• The three main engines of the space shuttle can
  develop 33,000 MW of power when fuel is burned at
  the enormous rate of 3400 kg/s

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• The unit of power is the joule per second, also
  known as the watt.
• One watt (W) of power is expended when one joule
  of work is done in one second.
• One kilowatt (kW) equals 1000 watts.
• One megawatt (MW) equals one million watts

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• In the United States, we customarily rate engines
  in units of horsepower and electricity in
  kilowatts, but either may be used.
• In the metric system of units, automobiles are
  rated in kilowatts. One horsepower (hp) is the
  same as 0.75 kW, so an engine rated at 134 hp is
  a 100-kW engine.
• 1 horsepower 746 W
• P W/t Fd/t Fv

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Board Work (5F)

• A 1000.0 kg elevator carries an 800.0 kg load. A
  constant frictional force of 4000.0 N impedes the
  elevators motion upward. What minimum power, in
  kilowatts, must the motor deliver to lift the
  elevator at a constant speed of 3.0 m/s?