Download Chapter Five Work, Energy, and Power

Chapter Five
Work, Energy, and Power
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Work, Energy, and Power
• Definitions in physics do not always match the usage
of the words.
• We consider mechanical work, energy, and power, for
it is the treatment of these terms from First Principle
that will be applied directly to electrical circuits.
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Work
• Work
down by a constant force F acting on a body
is
where Fs represents the component of force in the
direction
 We define a new unit 1 N-m = 1 joule with symbol J.
• When force and motion are not in the same direction
(see Fig.5-2), we have
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Example 5-1
• A box is pushed 3 m at constant velocity across a
floor by a force F of 5 N parallel to the floor. (a) How
much work was down on the box by the force F,
which clearly opposes friction (see Fig. 5-1). (b) How
much work is down on the box by the force of
friction?
• Sol : (a) W = 5 N 3 m = 15 J
(b) Because a = 0,
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Potential Energy
• Work down against the gravitational force is
independent of the choice of path between any two
fixed endpoints. See Fig. 5-3.
• The potential energy Ep is defined as
where y is the height in a gravitational field.
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• For potential energy a reference level must always be
specified. See Fig. 5-4, 5-5.
• Only the difference in heights needs to be specified to
give the relative difference in potential energy.
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Work Done by a Variable
Force
• See Fig. 5-6.
• When
, we have
• In more general case where F and the general
displacement
are not in the same direction, the
expression for the work becomes
or
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Kinetic Energy
• 1. The force is constant:
The initial position is x = 0, we have
By Newton's second law
Since
where v0 is the velocity at x = 0 and v
is the velocity at x. Thus
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• The work done on a body that changes its velocity
actually changes the quantity
, which is called
the kinetic energy Ek.
• The applied force is not constant:
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• Since
we have
• The work-energy theorem is stated as the work
done by the resultant force acting on a particle
is equal to the change in kinetic energy of the
particle.
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Energy Conservation
• For a mechanically conservative system ( one in
which no energy enters or leaves the system):
– (Ek + Ep)initial = (Ek + Ep)final
– Let us launch an object of mass m from a point y1
above the floor with an initial velocity v1.
Sometime later, the velocity of the object will be v2
and its position y2. See Fig. 5-7. We have
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• Let us assume an idealized pendulum that swings in a
vacuum so that there is no energy lost to air friction
and that is no frictional loss at the pivot (see Fig. 5-8).
We start the pendulum by pulling it to one side and
releasing it with no initial velocity.
• the string does no work on the pendulum because of
where θ is the angle between the string direction and
ds, and θ = 90o.
• For an accountability of energy system we have
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Example 5-2
• Suppose a ball is dropped from a height h = 10 m.
What is its velocity just before it strikes the ground?
• Sol :
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Example 5-3
• A skier is on a 37o slope of length s = 100 m (see Fig.
5-9). The coefficient of friction between his skis and
the snow is 0.2. If he start from rest, what is his
velocity at the bottom of the slope?
• Sol :
• No energy is put in, but
• Let us tilt our coordinate axis so that the slope
becomes the x axis and the normal becomes the y axis.
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Power
• Power is defined as
• The unit of power is joules per second (J/sec).
• New unit: 1 J/sec = 1 watt (W).
• A 100-W light bulb uses 100 J of electrical energy
each second.
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• A kilowatt-hour is the energy dissipated by a
device that uses 103 W for a period of 1 h, that
is,
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Example 5-4
• A tractor can exert a force of 3 104 N while moving
at constant speed of 5 m/sec. What is its horsepower?
• Sol :
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Homework
• 2, 4, 8, 12, 13, 15, 16, 17, 18, 20.
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