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					Work and Energy

     Unit 5

• Issues talked about have the same meaning in
  everyday life as they do in physics
• In everyday life, work means to do something
  that takes physical or mental effort
• In physics work has a different meaning
   Ex: holding a heavy chair at arms length for several
      No work is done on the chair
   Ex: carry a bucket of water along a horizontal path
    while walking at constant velocity
      No work is done on the bucket

• Work is done on an object when a force causes
  a displacement of the object
• Work-the product of the component of a force
  along the direction of displacement and the
  magnitude of the displacement
   W=Fd
   Where W is work, F is force, and d is displacement
   Work is not done on an object unless the object is
    moved with the action of a force
      The object must move otherwise no work is done on the

• Work is done only when components of a force
  are parallel to a displacement
   Components of the force perpendicular to a
    displacement do not do work
   If I push on a crate on a horizontal surface at an
    angle, , below horizontal, only the horizontal
    component of the force causes a displacement and
    contributes to the work
      W=Fd cos()
   If many forces are acting on an object, you can find
    the net work done by finding the net force on the
    object first
      Wnet=Fnetd cos()

• Work has dimensions of force times length
   Units for work
     1 Nm=1J
     1 joule of work is about the amount of work needed
      to raise an apple from your waist to the top of your

• The sign of work is important
   Work is a scalar quantity and can be positive
    or negative
     Work is positive when the component of force is in
      the same direction as the displacement
      • Also for when an object speeds up
     Work is negative when the force is in the direction
      opposite the displacement
      • Ex: kinetic friction, work done by friction is negative
      • Also for when an object slows down

• Ex: How much work is don on a vacuum
  cleaner pulled 3.0 m by a force of 50.0 N
  at an angle of 30.0 degrees above the

• Kinetic energy-the energy of an object that is
  due to the object’s motion
   Kinetic energy depends on speed and mass
   KE=(1/2)mv2
   Mass is measured in kg, velocity in m/s
   Kinetic energy is a scalar quantity and is measured in
    units of joules
   If a bowling ball and a volleyball are traveling at the
    same speed, which do you think has the grater kinetic

• Ex: A 7.00 kg bowling ball moves at 3.00
  m/s. How fast must a 2.45 g table tennis
  ball move in order to have the same
  kinetic energy as the bowling ball? Is this
  speed reasonable for a table-tennis

• The net work done on a body equals its change
  in kinetic energy
   Work-kinetic energy theorem - the net work done by
    all the forces acting on an object is equal to the
    change in the object’s kinetic energy
      Wnet=KE
      Wnet=(1/2)mvf2-(1/2)mvi2
      When using this theorem, you must include all the forces that
       do work on the object in calculating the net work done
      The work-kinetic theorem allows us to think of kinetic energy
       as the work that an object can do while the object changes
       speed or as the amount of energy stored in the motion of an

• Ex: 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?

• Potential Energy-the energy associated
  with an object because of the position,
  shape, or condition of the object
   Potential energy is stored energy
     Associated with an object that has the potential to
      move because of its position relative to some other
     Depends on properties of the object and its
      interaction with its environment

• Gravitational potential energy-the potential
  energy stored in the gravitational fields of
  interacting bodies
   Gravitational potential energy depends on height from
    a zero level
   PEg=mgh
      Only for when free-fall acceleration is constant over the entire
      Zero level can be arbitrarily set
   Ex: marble falls off a table
      Potential energy is converted to kinetic energy

• Elastic potential energy-the energy available for
  use when a deformed elastic object returns to its
  original configuration
   Elastic potential energy depends on distance
    compressed or stretched
   Ex: a spring
      The length of a spring when no external forces are acting on it
       is called the relaxed length of the spring
      When an external force compresses or stretches the spring,
       elastic potential energy is stored in the spring
   PEelastic=(1/2)kx2
      Where k is called the spring constant and x is the distance the
       spring is compressed or stretched

• Ex: 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, and disregard the weight of the
  bungee cord. Assuming the spring constant of
  the bungee cord is 71.8 N/m, what is the total
  potential energy relative to the water when the
  man stops falling?
     Conservation of Energy

• The description of the motion of many
  objects often involve a combination of
  kinetic and potential energy as well as
  different forms of potential energy
   Ex: pendulum clock
     At the highest point of its swing, there is only
      gravitational potential energy associated with its
     At other points in the swing, the pendulum has
      motion so it has kinetic energy as well
     Conservation of Energy

• We can ignore other forms of energy (I.e.
  chemical, heat, etc.) if their influence is
  negligible or if they are not relevant to the
  situation being analyzed
• Mechanical Energy-the sum of kinetic energy
  and all forms of potential energy
   ME=KE+PE
   Nonmechanical energy types: nuclear, chemical
    internal, and electrical
    Conservation of Energy

• Mechanical energy is conserved
  (assuming no friction)
   Conserved means is converted between
    different forms, but not lost
   The total potential energy and kinetic energy
    of an object will be the same anywhere along
    its path
   MEi=MEf (in the absence of friction)
     Depends on the forms of potential energy
   (1/2)mvi2+mghi=(1/2)mvf2+mghf
    Conservation of Energy

• Energy conservation occurs even when
  acceleration varies
   We can apply a new method of solving
    problems because of this instead of worrying
    about constant acceleration
   We set up the initial mechanical energy equal
    to the final mechanical energy and ignore the
    information in between
    Conservation of Energy

• Mechanical energy is not conserved in the
  presence of friction
   Total energy is always conserved
   However, when friction is involved, the
    mechanical energy is converted into forms of
    energy that are much more difficult to account
     Therefore that energy is considered to be “lost”
     Conservation of Energy

• Ex: Starting from rest, a child zooms
  down a frictionless slide from an initial
  height of 3.00 m. What is her speed at the
  bottom of the slide? Assume she has a
  mass of 25.0 kg.

• Power-a quantity that measures the rate at
  which work is done or energy is
   P=W/t
   An alternate form is substituting W=Fd into
    the equation
     P=Fd/t
     d/t is another way of writing the speed of an
     P=Fv

• SI unit is the watt, W
   One joule per second
   Horsepower is another unit of power
      1 hp=746 watts

• Ex: A 193 kg curtain needs to be raised
  7.5 m, at constant speed, in as close to
  5.0 s as possible. The power rating for
  three motors are listed as 1.0 kW, 3.5 kW,
  and 5.5 kW. Which motor is best for the