# Work notes

```Three things necessary to do Work in
Physics:
• There must be an applied force F.
• There must be a change in
displacement x (velocity).
• The force must have a component
along the displacement (or velocity).
F
q
F
x
q
If a force does not affect
displacement, it does no work.
The force F exerted on the
pot by the man does work.
F
W
The earth exerts a force W on
pot, but does no work even
though there is displacement.
Definition of Work
Work is a scalar quantity equal to the
product of the displacement x and the
component of the force Fx in the
direction of the displacement.
Work = Force component X displacement
Work = Fx x
Positive Work
F
x
Force F contributes to displacement x.
Example: If F = 40 N and x = 4 m, then
Work = (40 N)(4 m) = 160 Nm
Work = 160 J
1 Nm = 1 Joule (J)
Negative Work
x
f
The friction force f opposes the displacement.
Example: If f = -10 N and x = 4 m, then
Work = (-10 N)(4 m) = - 40 J
Work = - 40 J
Resultant Work or Net Work
Resultant work is the algebraic sum of
the individual works of each force.
x
f
F
Example: F = 40 N, f = -10 N and x = 4 m
Work = (40 N)(4 m) + (-10 N)(4 m)
Work = 120 J
Work of a Force at an Angle
Work = Fx x
F = 70 N
x = 12 m
60o
Work = (F cos q) x
Work = (70 N) Cos 600 (12 m) = 420 J
Work = 420 J
Only the x-component of
the force does work!
Work Done by a Varying Force
For a force that varies, work done is the area under the
force vs. distance curve.
Work and Kinetic Energy
A resultant force changes the velocity of an
object and does work on that object.
vo
m
vf
x
F
F
m
a
Work  Fx  (ma) x;
Work  mv  mv
1
2
2
f
1
2
v v
2
0
2
f
2
0
2x
The Work-Energy Theorem
Work is equal
to the change
in &frac12;mv2
Work  mv  mv
1
2
2
f
1
2
2
0
If we define kinetic energy as &frac12;mv2 then we
can state a very important physical principle:
The Work-Energy Theorem: The work
done by a resultant force is equal to the
change in kinetic energy that it produces.
Problem Solving Using Conservation of
Mechanical Energy
If there is no friction, the speed of a roller coaster will
depend only on its height compared to its starting height.
It does not matter on path taken. Because gravity is the
only force doing work. Why not normal force?
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Conservative and Nonconservative Forces
If friction is present, the work done depends not only on
the starting and ending points, but also on the path taken.
Friction is called a nonconservative force.
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6-5 Conservative and Nonconservative Forces
Potential energy can
only be defined for
conservative forces.
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Conservative and Nonconservative Forces
Therefore, we distinguish between the work done by
conservative forces and the work done by
nonconservative forces.
We find that the work done by nonconservative forces is
equal to the total change in kinetic and potential
energies:
Work Done by a Constant Force
The work done by a non conservative force is also equal
to the following. In this case energy is being added to the
system.
&copy; 2014 Pearson Education, Inc.
6-9 Energy Conservation with Dissipative
Processes; Solving Problems
If there is a nonconservative force such as friction,
where do the kinetic and potential energies go?
They become heat; the actual temperature rise of the
materials involved can be calculated.
&copy; 2014 Pearson Education, Inc.
Power
Power is the rate at which work is done—
(6-17)
In the SI system, the units of
power are watts:
1W = 1 J/s
The difference between walking
and running up these stairs is
power— the change in gravitational
potential energy is the same.
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Power
Power is also needed for acceleration and for moving
against the force of gravity.
The average power can be written in terms of the force
and the average velocity:
(6-18)
```