Chapter 5: Work and Energy

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Chapter 5 Work and Energy
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Work

• Work is done on an object when some forces causes
  a displacement of the object (a change in
  position).
• Imagine that your car runs out of gas, and you
  need to push it to the side of the road. You
  exert some force on the car to change its
  position. That means that you are doing work on
  the car. The work that you do on the car is
  equal to the magnitude of the force times the
  magnitude of the displacement of the car.
• W Fd
• The unit for work is the joule (J) named after
  James Joule. 1 J 1 Nm

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Work

• Work is done only when the force is parallel to
  the displacement.
• If the force is perpendicular to the displacement
  of an object, work is not done on the object.
• When the force on an object and the objects
  displacement are in different directions, only
  the component of the force that is parallel to
  the objects displacement does work.
• If ? is the angle between the displacement and
  your applied force, we can calculate the work
  done on the object by using the equation
• W Fdcos?

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Net Work (Wnet)

• If a many forces are applied to an object, we can
  find the net work being done on the object by
  using the equation
• Wnet Fnet d cos ?
• To calculate work, use the following equations
• W Fd
• W Fdcos?
• Wnet Fnet d cos ?

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Do Now 2/18

• Decide whether any work is being done in each
  situation. If so, identify the object (s) on
  which work is being done.
• 1.) A chicken scratching the ground
• 2.) A person reading a sign
• 3.) A crane lifting a bucket of concrete
• 4.) Walking down the hallway with books in your
  hand.

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Kinetic Energy

• Kinetic energy is the energy associated with an
  object in motion.
• Kinetic energy depends on the speed and mass of
  an object.
• To find the kinetic energy of an object, we use
  the equation
• KE ½ mv2
• (kinetic energy is measured in joules (J), like
  work)

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Work-Kinetic Energy Theorem

• ?KE Wnet
• KEf KEi Wnet
• ½ mvf2 ½ mvi2 Wnet
• The Work-Kinetic Energy Theorem tells us the work
  that is done on an object while the object
  changes speed.
• When net work gt 0, speed is increasing
• When net work lt 0, speed is decreasing

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Do Now 2/19

• 1.) A weightlifter lifts a set of weights a
  vertical distance of 1.8 m. If a constant net
  force of 400 N is exerted on the weights, what is
  the net work done on the weights?
• 2.) A crate is pushed with a force of 42 N
  directed at an angle of 20 downward from the
  horizontal. If the crate moves a distance of 30
  m, how much work is done on the crate?
• 3.) Furniture movers wish to load a truck using a
  ramp from the ground to the rear of the truck.
  One of the movers claims that less work would be
  required if the ramps angle with the horizontal
  was reduced. Is this claim valid? Explain.

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Wnet ½ mvf2 ½ mvi2

• A 4550 N forward force is applied to a 950 kg
  boat in order for it to accelerate from rest.
  1120 N of fluid friction from the water also acts
  on the boat. Use the work-kinetic energy theorem
  to determine how far the boat must travel for its
  speed to reach 10 m/s.

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Potential Energy

• The stored energy of an object is called
  potential energy.
• Gravitational potential energy is the potential
  energy due to an objects elevated position. The
  amount of gravitational potential energy
  possessed by an object is equal to the work done
  against gravity in lifting it.
• PE mgh
• Where h is the height - the distance above some
  chosen reference level, such as the ground or the
  floor of a building

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PEg mgh

• 1.) A 2 kg ball is raised 5 meters from the
  ground. If the ground is considered the zero
  level, what is the gravitational potential energy
  of the ball?
• 2.) A 30 kg boulder sits at the top of a
  mountain. If the top of the mountain is
  considered the zero level, what is the
  gravitational potential energy of the boulder?

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Elastic Potential Energy

• The potential energy stored in a compressed or
  stretched object is called elastic potential
  energy.
• PEelastic ½ kx2
• When an external force compresses or stretches
  the spring, elastic potential energy is stored in
  the spring.
• x is the distance that the spring is stretched
  or compressed units for x is meters (m). The
  amount of energy depends on the distance that the
  spring is compressed or stretched from its
  natural length.
• k is the spring constant, which is the springs
  resistance to being stretched or compressed
  units for k are Newtons per meter (N/m)

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Do Now 2/20

• A pinball bangs against a bumper, giving the
  ball a speed of 42 cm/s. If the ball has a mass
  of 50g, what is the balls kinetic energy in
  joules?

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Mechanical Energy

• Conserved quantity
• Mechanical energy is the sum of the kinetic
  energy and all the forms of potential energy in
  an object (remember that an object can have
  elastic potential energy and gravitational
  potential energy).
• ME KE SPE

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Conservation of Mechanical Energy

• When friction is absent, the amount of mechanical
  energy remains constant, or is conserved.
• The initial amount of mechanical energy will
  equal the final amount of mechanical energy.
• MEi MEf
• KEi SPEi KEf SPEf
• KEi PEelastic, i PEg, i KEf PEelastic, f
  PEg, f
• ½ mvi2 ½ kxi2 mghi ½ mvf2 ½ kxf2 mghf

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Do Now 2/23

• A pinball bangs against a bumper, giving the
  ball a speed of 42 cm/s. If the ball has a mass
  of 50g, what is the balls kinetic energy in
  joules?

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Do Now 2/24

• 1.) Is conservation of mechanical energy likely
  to hold in these situations?
• (a) A hockey puck sliding on a frictionless
  surface of ice
• (b) A toy car rolling on a carpeted floor
• (c) A baseball being thrown into the air
• 2.) A child and sled with a combined mass of 50
  kg slide down a frictionless hill that is 7.34
  meters high. If the sled starts from rest, what
  is its speed at the bottom of the hill?

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Power

• Power is the rate at which work is done.
• P Work W
• time interval ?t
• P Fd
• ?t
• P Fv (Force x speed)
• Power is measured in Watts (W). Horsepower (hp)
  is another unit of power that is sometimes used
  1 hp 746 watts