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Work and Energy
Outcomes
Upon completion of this unit you will be able to:
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Analyze force problems in terms of energy.
Define the term "work" as it relates to physics.
Calculate work problems using the various equations.
Identify which forces are at work in a given problem situation.
Interpret a force displacement curve in relation to work.
Calculate work as done by a spring.
Define power and efficiency.
Calculate power and efficiency using the appropriate formulas.
Demonstrate an understanding that power is a product of force
and velocity.
Objectives Con’t
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Demonstrate an understanding of kinetic energy as a concept
and as an equation.
Calculate the change in kinetic energy using the work-energy
theorem formula.
Explain potential energy.
Calculate gravitational potential energy.
Define spring force.
Calculate spring force using the formula for Hooke's Law.
Describe conservative forces.
Write the conservative energy statement using the correct
mathematical forms.
Solve energy problems using the appropriate energy equations.
Work
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Work is done if a force is applied for a particular
distance.
In Physics there is one more stipulation: the force and
displacement vectors must point in the same direction.
W = Fxdx
Fx is the applied force in the direction of the object's
displacement and
dx is the object's displacement.
 Why the x-subscript? This shows that in order for work
to be done, the force and displacement must be in the
same direction.
Extreme Work
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This formula for work leads us to three
possible extreme cases
Force and Displacement in the Same
Direction : (results in max. positive work)
 Example?
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Force Perpendicular to Displacement
No work is done in this case
 Example?
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Force and Displacement in Opposite
Directions
this results in max. negative work
 Example?
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Identify the Force at Work
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It is extremely important to identify what
force is doing the work in question. Look
at the case of lifting then lowering a box.
Lifting a box
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As you lift the box, you
exert a force in the same
direction as the
displacement, so you do
positive work. Gravity
(weight) always acts
straight down and here
that means it is in the
opposite direction to the
displacement, so it does
negative work.
Lowering the box
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As the box is
lowered, you still
exert an upward
force to keep the box
from simply falling.
Now your force and
the displacement are
at 180 degrees, so
you do negative
work. Gravity is now
doing positive work.
Units for Work
The unit of work is the joule (J).
 lifting a good sized apple at a constant
velocity straight up for a distance of 1 m
requires about 1 J of work.
 While work can be positive or negative
and its calculation depends on direction,
it is not a vector. Work is a scalar.
Direction is important for calculating
work, but work itself has no direction.
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Try It
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You exert a force of 20 N in order to slide
a textbook across a table a a constant
speed. If the textbook has a mass of 20
kg and you slide it a distance of 50 cm,
How much work do you perform?
Try it Again
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A 1500 kg car is brought to a complete stop over a
distance of 43 m. If the coefficient of friction between
the car and the road is 0.32, how much work is done
by friction in bringing the car to a stop?
Start by drawing a rough FBD of the situation:
Force Displacement Graph
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Another useful fact is that the area under
a force displacement curve is equal to
the work done. Of course, the force that
is plotted will have to be the component
that is in the same direction as the
displacement.
Work done on a Spring
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The work done on a spring when it is compressed or
stretched is given by the formula shown below:
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where k is the spring constant (N/m) and x is the
amount of compression (m).
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You can not use the basic work formula W = Fx for a
spring. The formula W = Fx assumes that the force is
constant. As you well know, the force a spring exerts
(F) changes as the displacement (x) changes. You
must use the special formula above if you need to
calculate the work done by a spring.
Power and Efficiency
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Power is simply the rate at which you do work.
The formula for average power is shown
below.
 ΔW = change in work (J)
 Δt= change in time (s)
 The unit of power is the joule/second or the
watt (W). When you see a light bulb rated at
60 W, it means that it consumes 60 J of
electrical energy every second.
Example
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An elevator motor lifts a mass of 1000 kg
over a distance of 20 m in 15 seconds.
What power must it develop?
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A winch rated at 1.5 kW pulls a heavy
box along a horizontal floor. It takes the
winch 1.00 min to pull the box over a
distance of 250 m. What Force is it
exerting?
Power as a product of F and V
It is possible to show that power is equal
to the force times the velocity. The
formula for this is shown below:
 P = Fv
 F = applied force (N)
v = object's velocity (m/s)
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Efficiency
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Efficiency is the ratio of energy output to
energy input:
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Efficiency = Eo /Ei x 100%
Eo – energy output
Ei – energy input
It can also be written as a ratio of work output
to work input:
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Efficiency = Wo /Wi x 100%
Wo – work output
Wi – work input
Example
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A toaster transforms 1200 J of electrical energy into
560 J of thermal energy to make a piece of toast.
What is the efficiency of the toaster?
We know that:
Ei = 1200 J Eo = 560 J
So our efficiency is: