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Progetto “Physics in English”
Work and energy
WORK
WO R K I S DO N E O N A N O B J EC T
WHEN A F O R C E C A USES A
DI S P L A C EM EN T O F THE
O B J EC T
Prof.ssa A. Martorana
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Positive work is done on a textbook when it is
raised vertically at a constant velocity. A force
resulted in a displacement. Work was done.
Displacement means change in position,
from origin to finish.
EXAMPLE
Imagine that your car has run out of
gas and you have to push it down the
road to the petrol station.
Example
If you push the car with a costant horizontal force, the
work you do on the car is equal to the magnitude of
the Force F times the magnitude of the displacement
of the car
W = Fd
Work is not done on an object unless the object is
moved with the action of a force
WORK
Read the following statements and
determine whether or not they
represent examples of work.
Statement
 A teacher applies a force to a wall and becomes
exhausted.
Answer
 No.
 This is not an example of work. The wall is
not displaced. A force must cause a
displacement in order for work to be done.
Statement
A book falls off a table and free falls to the ground.
Answer
 Yes.
 This is an example of work. There is a force
(gravity) which acts on the book which
causes it to be displaced in a downward
direction (i.e., "fall").
Statement
A rocket accelerates through space.
Answer
Yes.
This is an example of work. There is a force
(the expelled gases push on the rocket)
which causes the rocket to be displaced
through space.
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However, the application of a force alone does
not constitute work
Work is done only when components of a
force are parallel to a displacement
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When the force on an object and the object’s
displacement are in different directions,
only the component of the force that is
parallel to the object’s displacement does
work.
Components of the force perpendicular to a
displacement do not work
Example
A waiter carries a tray full of meals above his head by
one arm straight across the room at constant
speed. Is this an example of work being done on
an object?
Answer
 No.
 This is not an example of work. There is a force (the
waiter pushes up on the tray) and there is a
displacement (the tray is moved horizontally across
the room). Yet the force does not cause the
displacement. To cause a displacement, there must
be a component of force in the direction of the
displacement.
Explanation
 The waiter does not do work upon the tray as he
carries it across the room. The force supplied by the
waiter on the tray is an upward force and the
displacement of the tray is a horizontal
displacement. As such, the angle between the force
and the displacement is 90 degrees. If the work done
by the waiter on the tray were to be calculated, then
the results would be 0.
Important!
A vertical force can never cause a horizontal
displacement; thus, a vertical force does not
do work on a horizontally displaced object!!
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Mathematically, work can be expressed by the
following equation.
Wnet = Fnet ×d ×cosq
net work=net force×displacement×cosine of the angle between them
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Wnet= Fnetd cos Ѳ
F is the net force, d is the displacement, and the angle
(theta) is defined as the angle between the net force
and the displacement vector.
The angle is a very specific angle; the angle measure is
defined as the angle between the force and the
displacement.
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 Sample problem:
 How much work is done on a vacuum
cleaner pulled 3.0 m by a force of 50.0 N at
an angle of 30.0° above the horizontal?
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The sign of work is important
Work is a scalar quantity and can be
positive or negative.
 It is positive when the component of force is
in the same direction as the displacement.
 Work is negative when the force is in the
direction opposite the displacement.
THE MEANING OF NEGATIVE WORK
On occasion, a force acts upon a moving object to
hinder a displacement. (hinder - to interfere with
action or progress).
An example might include a car skidding to a stop
on a roadway surface. In such an instance, the
force acts in the direction opposite the object’s
motion in order to slow it down.
The force doesn't cause the displacement but rather
hinders it.
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Work is negative when the force is in the
direction opposite to the displacement.
For example, the force of kinetic friction between
a sliding box and the floor is opposite to the
displacement of the box, so the work done by
the force of friction on the box is negative.
cos Ѳ is negative for angles greater than 90° but
less than 270°
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 Units of Work
 Whenever a new quantity is introduced in
Physics, the standard metric units associated
with that quantity are discussed.
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 In the case of work (and also energy), the
standard metric unit is the Joule
(abbreviated J). One Joule is equivalent to
one Newton of force causing a displacement
of one meter. In other words,
 The Joule is the unit of work.
 1 Joule = 1 Newton × 1 meter
1J=1N×m