Work and Energy

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Work and Energy
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Conception of Work
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For the simplest case, where the force is
constant and the motion takes place in a straight
line in the direction of the force we define the
work done on an object by applied force as a
product of the force and the distance through
which the object is moved. In shorter form Work
force x distance
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More generally, work is a product of only the
component of force that acts in the direction of
motion and the distance moved. For example, when
a force acts at right angles to the direction of
motion, with no force component in the direction
of motion, no work is done!
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Conceptual Question
Does Earth do work on Moon?
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Important Definition of work involves both a
force and a distance.
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Units of Work
1 J 1 N m
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Power
Power work done/time interval
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Units of Power
1 W 1J/s
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Mechanical Energy
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We can define energy as the ability to do work.
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The energy of an object at motion is called
kinetic energy.
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Conservation of Kinetic Energy
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Question
Are the collisions of billiard balls perfectly
elastic?
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Conservation of Kinetic EnergyExample.
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The net work done on an object is equal to the
change in its kinetic energy.
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Conceptual ExampleWork to Stop a car
An automobile traveling 60 km/h brake to a stop
within a distance of 20 m. If the car is going
twice as fast, 120 km/h, what is its stopping
distance? The maximum braking force is
approximately independent of speed.
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Questions
Can an object have energy? Can an object have
work?
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Potential Energy
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Potential energy is the energy associated with
forces that depend on the position or
configuration of a body (or bodies) and the
surroundings.
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PE of Gravity
We will define the potential energy of a body as
the product of gravitational force mg acting on a
body and its height h above some reference level.
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Important The change in potential energy between
any two points does not depend on the choice of
reference level. Important The changes in
gravitational potential energy depend only on the
change in vertical height and not on the path
taken.
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PE of Elastic Spring
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Equation Fs - kx is known as spring equation
and also as Hookes law.
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Elastic PE kx2/2
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Important Potential energy belongs to a system,
and not to a single object alone!!!! The
potential energy is a property of a system as a
whole.
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Mechanical Energy and its Conservation
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If no frictional (or other dissipative) forces
are involved, the total mechanical energy of a
system neither increases nor decreases in any
process. It stays constant it is conserved.
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Total energy cannot be created or destroyed it
may be transformed from one form into another,
but the total amount of energy never changes.
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Problem Solving Using Conservation of Mechanical
Energy
If the original height of the stone is y1 h
3.0m, calculate the stones speed when it has
fallen to 1.0m above the ground.
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Conceptual Example Speeds on Two Water Slides

• Two water slides at a pool are shaped
  differently, but have the same length and start
  at the same height h. Two riders, Paul and
  Kathleen, start from rest at the same time on
  different slides.
• Which rider, Paul or Kathleen, is traveling
  faster at the bottom?
• Which rider makes it to the bottom first?

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Questions

1. You have been asked to analyze a collision at a
   traffic intersection. Will you be better off to
   begin your analysis using conservation of
   momentum or conservation of kinetic energy? Why?
2. If a system has zero kinetic energy, does it
   necessarily have zero momentum? Give an example
   to illustrate your answer.
3. An object has a velocity toward the south. If a
   force is directed toward the north, will the
   kinetic energy of the object initially increase,
   decrease, or stay the same? Explain.

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1. In tryouts of the national bobsled team, each
   competing team pushes a sled along a level,
   smooth surface for 5 meters. One team brings a
   sled that is much lighter than the others.
   Assuming that this team pushes with the same
   force as the others, compare the kinetic energy
   of the light sled to that of the others after 5
   meters . Compare the momentum of the light sled
   to that of the others after 5 meters.
2. Suppose the rules were changed in previous
   question so that the teams pushed for a fixed
   time of 5 seconds rather that a fixed distance of
   5 meters. Compare the momentum of the light sled
   to that of the others after 5 seconds. Compare
   the kinetic energy of the sled to that of the
   others after 5 seconds.