Ch 6 Work and
Energy
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Work in 1 dimension
• Work is when a force is applied and an object is
displaced
• If no displacement occurs or no force is applied then
no work is done.
• The definition of work when the force is parallel to
the displacement
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In the SI system, the units of work are joules:
As long as this person does not lift
or lower the bag of groceries, he is
doing no work on it. The force he
exerts has no component in the
direction of motion.
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Work in 2 dimensions
• If the force is at an angle to the displacement you
must determine the component of the force that is
directed parallel to the displacement.
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Work done by forces that oppose the direction of
motion, such as friction, will be negative.
-Ffr
Fpx
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The work done may be positive, zero, or
negative, depending on the angle between
the force and the displacement
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If there is more than one force acting on an
object, we can find the work done by each force,
and also the work done by the net force
Wtotal=W1 + W2 + W3 … = Σ W
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6-3 & 6-4 KE, PE and Work Energy Principle
• Kinetic energy (KE) is energy of motion
• Gravitational potential energy (PE; often just
called potential energy) is energy of position
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Work and Energy
Mechanical Energy is the sum of the kinetic and
potential energy of an object
ME= KE + PE
Energy was traditionally defined as the ability to
do work.
Not all forces can do work, but ME can
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Kinetic Energy KE
• For objects moving
at speeds much
slower than the
speed of light
Kinetic energy is
calculated by
2
KE=1/2mv
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Potential Energy PE
• An object can have
potential energy by
virtue of its position or
height
– A wound-up spring
– A stretched elastic
band
– An object at some
height above the
ground
PE=mgy
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Work-Energy Principle or Theorem
• The net force done on an object is equal to
the change in the object’s kinetic energy
Wnet=ΔKE
• Work and kinetic energy can be equated and
have the same units; joules.
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Potential energy can also be stored in
certain materials when they are
compressed; the figure below shows
potential energy yielding kinetic energy.
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Hooke’s Law
The force required to
compress or stretch a
spring is:
where k is the spring
constant, and needs to be
measured for each spring.
Negative because it is a
restoring force, acting in
the opposite direction of
displacement
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Elastic potential energy
• The force increases as the
spring is stretched or
compressed
• Potential energy of the
compressed or stretched
spring measured from its
equilibrium position
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6-5 Conservative and Nonconservative Forces
Conservative forces are ones that do not depend
on, or are independent, of the path taken. An
example is gravity
If the object were to return to the starting point
no net work would be done
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http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html
• Nonconservative forces are ones that do
depend on the path taken.
• Also called dissipative forces because the
energy is not stored as mechanical energy but
changed into a different type such as heat
energy
• An example is friction
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Potential energy
can only be
defined for
conservative
forces.
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6-6 Mechanical Energy and Its Conservation
•If there are no nonconservative forces, the sum of the
changes in the kinetic energy and in the potential
energy is zero
• If only conservative forces are acting the total ME of
the system stays constant or is conserved
•This is the principle of conservation of
mechanical energy
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Total mechanical energy ME= KE + PE therefore
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Energy conservation
• The total energy is neither increased nor decreased,
only transformed from one form to another and
transferred from one object to another. The total
amount remains the same.
This is the Law of Conservation
of Energy
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6-10 Power
Power is the rate at which work is done
In the SI system, the units of power are
watts:
The difference between walking and running
up these stairs is power – the change in
gravitational potential energy is the same.
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Efficiency
• The ratio of power output to input
Efficiency=Poutput
Pinput
• Always less than 1 because engines always lose
some input power to friction
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References
• Giancoli, Douglas. Physics: Principles
with Applications 6th Edition. 2009.
• Walker, James. AP Physics: 4th
Edition. 2010
• www.hyperphysics.com
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