Explain how an object must be displaced for a force on it to do work.
Explain how relative directions of force and displacement of an object determine whether the work done on the object is positive, negative, or zero.
The information presented in this section supports the following AP® learning objectives and science practices:
5.B.5.1 The student is able to design an experiment and analyze data to examine how a force exerted on an object or system does work on the object or system as it moves through a distance.
(S.P. 4.2, 5.1)
5.B.5.2 The student is able to design an experiment and analyze graphical data in which interpretations of the area under a force-distance curve are needed to determine the work done on or by the object or system.
(S.P. 4.5, 5.1)
5.B.5.3 The student is able to predict and calculate from graphical data the energy transfer to or work done on an object or system from information about a force exerted on the object or system through a distance.
(S.P. 1.5, 2.2, 6.4)
What it means to do work
The scientific definition of work differs in some ways from its everyday meaning. Certain things we think of as hard work, such as writing an exam or carrying a heavy load on level ground, are not work as defined by a scientist. The scientific definition of work reveals its relationship to energy—whenever work is done, energy is transferred.
For work, in the scientific sense, to be done on an object, a force must be exerted on that object and there must be displacement of that object in the direction of the force.
Formally, the
work done on a system by a constant force is defined to be
the product of the component of the force in the direction of motion and the distance through which the force acts . For a constant force, this is expressed in equation form as
where
is work,
is the displacement of the system, and
is the angle between the force vector
and the displacement vector
, as in
[link] . We can also write this as
To find the work done on a system that undergoes motion that is not one-way or that is in two or three dimensions, we divide the motion into one-way one-dimensional segments and add up the work done over each segment.
What is work?
The work done on a system by a constant force is
the product of the component of the force in the direction of motion times the distance through which the force acts . For one-way motion in one dimension, this is expressed in equation form as
where
is work,
is the magnitude of the force on the system,
is the magnitude of the displacement of the system, and
is the angle between the force vector
and the displacement vector
.
Examples of work. (a) The work done by the force
on this lawn mower is
. Note that
is the component of the force in the direction of motion. (b) A person holding a briefcase does no work on it, because there is no displacement. No energy is transferred to or from the briefcase. (c) The person moving the briefcase horizontally at a constant speed does no work on it, and transfers no energy to it. (d) Work
is done on the briefcase by carrying it up stairs at constant speed, because there is necessarily a component of force
in the direction of the motion. Energy is transferred to the briefcase and could in turn be used to do work. (e) When the briefcase is lowered, energy is transferred out of the briefcase and into an electric generator. Here the work done on the briefcase by the generator is negative, removing energy from the briefcase, because
and
are in opposite directions.
