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Work and Energy
Work Done by a Constant Force
Definition of Work:
The work done by a constant force acting on an
object is equal to the the displacement times the
component of the force parallel to that displacement.
Units of work: newton•meter (N•m).
1 N•m is called 1 Joule.
Work Done by a Constant Force
In (a), there is a force but no displacement: no work is
done. In (b), the force is parallel to the displacement, and
in (c) the force is at an angle to the displacement.
Work Done by a Constant Force
If there is more than one force acting on an
object, it is useful to define the net work:
The total, or net, work is defined as the work done
by all the forces acting on the object, or the scalar
sum of all those quantities of work.
Work Done by a Variable Force
The force
exerted by a
spring varies
linearly with
the
displacement:
Work Done by a Variable Force
A plot of force versus displacement allows us to
calculate the work done:
1 2
W= kx
2
Work is Energy : Kinetic Energy
We know that the net force acting on an object causes the
object to accelerate, changing its velocity:

We can use this relation to calculate the work done:
Work is Energy : Kinetic Energy
Kinetic Energy Defined:
The net work on an object changes its kinetic
energy.
Work is Energy : Kinetic Energy
This relationship is called the work-energy theorem:
Energy
In physics, energy is an indirectly measured quantity.
Energy is a scalar, so many calculations are made very
easy when considering energy (no components).
Energy can take many forms. Besides converting work
into kinetic energy, we can do work on an object and
change its potential energy, usually called U.
W = ΔU = U-U0
Drawing back on a bow
does work on the system,
this work results in
potential energy
Energy
Energy and mass are related. Like mass, energy cannot
be destroyed. A closed system conserves energy, and
energy conservation is one of the few fundamental laws
of physics.

Potential energy in the bow is converted to kinetic
energy in the arrow. Energy can be converted from
one form to another, but it is never “lost”
Potential Energy
Potential energy may be thought of as stored work, such
as in a compressed spring or an object at some height
above the ground.
We saw earlier the work done when we compress a
spring, now we see it goes into potential energy:
Potential Energy of
a spring:
Potential Energy
Gravitational
Potential Energy
Moving a can up by a
distance “y” involves work,
the work done is W = F d
W = mgy
U = mgy
Potential Energy
Where is potential 0? Only changes in potential energy
are physically significant; therefore the point where U = 0
may be chosen for convenience.
Conservation of Energy
We observe that, once all forms of energy are
accounted for, the total energy of an isolated system
does not change.
The total energy of an isolated system is always
conserved.
We define a conservative force:
A force is conservative if the work done by it in moving an
object is independent of the object’s path.
A force is said to be non-conservative if the work done by
it in moving an object does depend on the object’s path.
Conservation of Energy
So, what types of forces are conservative?
Conservative Forces:
Gravity is one example; the work done by gravity only
depends on the difference between the initial and final
height, and not on the path between them.
Non-Conservative Forces:
One example of a non-conservative force is friction.
Why?
Conservation of Energy
Another way of describing a conservative
force:
A force is conservative if the work done by it in
moving an object through a round trip is zero.
A force is conservative if the path chosen for moving
an object has no effect on the final energy
A
Conservation of Energy
We define the total mechanical energy:
For a conservative force:
Conservation of Energy
Example of how energy considerations can make problems easy:
Assume a man throws three balls at 3 angles (+45°, 0°, -45°) from
a mountain, with the same speed. What are differences in speeds of
the balls just s they hit the ground?
All three of these balls
have the same kinetic and
potential energy when they
start.
Energy is conserved
So, for all three balls, their
speeds just when they hit
the bottom are exactly the
same
Example problem:
Man falls from roof, 5 meters high. How fast is he going when
he makes contact with ground?
E1=E2
Choose coordinates so potential
energy is U on the ground, then
1 2
mgh + 0 = 0 + mv
2
m
v = 2gh = 2 × 5× 9.8 = 9.9
s
Same answer as before
Conservation of Energy
In a conservative system, the total mechanical energy
does not change, but the split between kinetic and
potential energy does.
A look at the Pendulum:
Non-Conservation of Energy
If a non-conservative force is present, the work done by
the non-conservative force is equal to the change in the
total mechanical energy.
Where does the energy go? Depends. For friction, heat
into the environment (rub hands to see the effect)
Consequence of Non-Conservative
Forces: Efficiency
Mechanical Efficiency:
The efficiency of any real system is always less than
100%, because there always some non-conservative
forces to be dealt with.
Example: car engine: energy goes into heat from friction,
sound waves into the air,…
Consequence of Non-Conservative
Forces: Efficiency
Power
Power is defined as energy/time
The average power is the total amount of work done divided by
the time taken to do the work.
“High Power” means large energy or short amount of time, or
both.
The energy in a lithium battery (laptop) is about the same as
the energy in a hand grenade. The difference is their power,
the time over which this energy is released.
Δt=10-5s
Δt=104s