Work, Power and Energy

1
Chapter 5

• Work, Power and Energy

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Work

• Provides a link between force and energy
• The work, W, done by a constant force on an
  object is the product of the force times the
  distance through which the force acts.

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Units of Work

• SI
• Newton meter Joule
• N m J
• J kg m2 / s2
• US Customary
• foot pound
• ft lb
• no special name

4
Work, cont.

• In general
• F is the magnitude of the force
• s (or d) is the distance of the object moved
• ? is the angle between force and direction of
  motion

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Work, cont.

• This gives no information about
• the time it took for the motion to occur
• the velocity or acceleration of the object
• Work is a scalar quantity

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More About Work

• The work done by a force is zero when the force
  is perpendicular to the displacement
• F0
• s0
• cos 90 0
• If there are multiple forces acting on an object,
  the total work done is the algebraic sum of the
  amount of work done by each force

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More About Work, cont.

• Work can be positive or negative
• Positive if s is in the same direction as F
• Negative if s is in opposite direction to F
• Zero if s is perpendicular to F

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Work Can Be Positive or Negative

• Work is positive when lifting the box
• Work would be negative if lowering the box
• The force would still be upward, but the
  displacement would be downward

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Example

• 50N force pulls a 20 kg object and moves it 2m,
  friction f15N. Acceleration along the ground?
  Work done? Work done by friction? Total work?
• What about pulling at 30??

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Power

• Power is defined as this rate of work
• SI units are Watts (W)

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Power, cont.

• US Customary units are generally hp
• Need a conversion factor
• Can define units of work or energy in terms of
  units of power
• kilowatt hours (kWh) are often used in electric
  bills 1kWh3.6x106 J
• This is a unit of energy, not power

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Example

• A crane lifts a 5000 kg object 800 m in 10 min.
  How much power must the engine produce?

13
Example

• An 80hp outboard motor, operating at full speed,
  can drive at speed boat at 11 m/s. What is the
  forward thrust(force) of the motor?

14
Conservation Laws

• Mass
• Electric Charge
• Conservation of Energy
• Sum of all forms of energy is conserved

Energy ability to do work
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Forms of Energy

• Mechanical
• Focus for now
• May be kinetic (associated with motion) or
  potential (associated with position)
• Chemical
• Electromagnetic
• Nuclear

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Some Energy Considerations

• Energy can be transformed from one form to
  another
• Essential to the study of physics, chemistry,
  biology, geology, astronomy
• From one body to another Work!
• Can be used in place of Newtons laws to solve
  certain problems more simply

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Potential Energy

• Potential energy is associated with the shape or
  position of the object
• Potential energy is a property of the system, not
  the object
• A system is a collection of objects interacting
  via forces or processes that are internal to the
  system

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Gravitational Potential Energy

• Lift object vertically, work is done against the
  force of gravity of Earth and energy is stored in
  the object in the form of Gravitational Potential
  Energy (Ep)
• PE of water in reservoir is used to generate
  electricity

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Reference Levels for Gravitational Potential
Energy

• A location where the gravitational potential
  energy is zero must be chosen for each problem
• The choice is arbitrary since the change in the
  potential energy is the important quantity
• Choose a convenient location for the zero
  reference height
• often the Earths surface
• may be some other point suggested by the problem
• Once the position is chosen, it must remain fixed
  for the entire problem

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Example

• A 1500kg pile driver lifted 20 m in the air have
  EP

21
Kinetic Energy

• Energy associated with the motion of an object
• Scalar quantity with the same units as work
• Work is related to kinetic energy

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Work and Kinetic Energy

• An objects kinetic energy can also be thought of
  as the amount of work the moving object could do
  in coming to rest
• The moving hammer has kinetic energy and can do
  work on the nail

23
Example

• Consider energy of a falling ball of mass m from
  height of h.

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Energy Conservation

• Energy is never created or destroyed. Energy can
  be transformed from one kind into another, but
  the total amount of energy remains constant.
• Example Pendulum

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Conservation of Mechanical Energy

• Conservation in general
• To say a physical quantity is conserved is to say
  that the numerical value of the quantity remains
  constant throughout any physical process
• In Conservation of Energy, the total mechanical
  energy remains constant

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Conservation of Energy, cont.

• Total mechanical energy is the sum of the kinetic
  and potential energies in the system
• Other types of potential energy functions can be
  added to modify this equation

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Conservation of (mechanical) Energy

• True if only conservative forces are present
• Conservative forces gravity, springs
• Non-conservative forces push, pull, friction,
  air-resistance
• Apply the conservation of energy equation to the
  system
• Immediately substitute zero values, then do the
  algebra before substituting the other values
• Solve for the unknown(s)

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Work and Energy

• If a force (other than gravity) acts on the
  system and does work
• Need Work-Energy relation
• Wnc work done by non-cons. forces

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Example

• Cart on a roller-coaster with no friction. Start
  from rest at h30m. What is the speed at the end
  hA15m.

30
Example

• Two cars each with mass 2000kg and
• speed 80km/h collide and come to rest.

31
Example

• Child on a 3 m high slide (no friction),
• what is the speed at the end?
• If a child of 25kg slides down from rest and
  reaches only 3m/s. What work was done by the
  frictional force acting on the child?
• If the slide is 10 m long, how large was the
  average friction force?

32
Example

• Same child is on a swing with 6m rope and starts
  at 60 with respect to vertical direction.
  Maximum speed?
• If the child starts with speed of 1 m/s with a
  push, what is the max speed?