“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, a force must be exerted and there must be displacement 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 times the distance through which the force acts. For one-way motion in one dimension, this is expressed in equation form as
=∣∣(cos)∣∣,
W
=
∣
F
∣
cos
θ
∣
d
∣
,
7.1
where
W
is work,
d
is the displacement of the system, and
θ
is the angle between the force vector
F
and the displacement vector
d
, as in Figure 7.2. We can also write this as
=cos.
W
=
Fd
cos
θ
.
7.2
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
=cos,
W
=
Fd
cos
θ
,
7.3
where
W
is work,
F
is the magnitude of the force on the system,
d
is the magnitude of the displacement of the system, and
θ
is the angle between the force vector
F
and the displacement vector
d
.”