S3.2 Work
Preamble
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Preamble
In everyday life, the term ‘work’ is applied to any activity requiring the exertion of muscular or mental effort. In physics the term is used in a much more specific sense namely to quantify the amount of energy transferred to an object by a force acting on it.[A] Definition
- When a force acts on a body to produce a displacement, work is
done. Work is a scalar quantity measured in newton-meters
(Nm) or Joules (J).
- If a constant force
acts on a body to produce a straight line displacement
, the amount of work W done on the body by the force is given by the dot product (Key Point 0.3):
- If the force
is not constant, and the resultant displacement is not a straight line, the amount of work that the force does is:
Key Point 3.4
Work:
∙ This is the sum, over the entire path, of all the infinitesimal bits of work done along all the infinitesimal displacements , by the force
which is, in general, different at every point along the path.
- In one dimension, with a varying force F(x)
∙ The work done, W, by the applied force, F(x), between the start and finish points is the area under the curve.
[B] Traps for the unwary!
- Work is defined as the work done by the force on the body.
- It can be positive or negative,
depending on the sign of the force and the displacement.
Examples
- The work done by a force to lift an object is positive. However, the work of the gravitational force on the object being lifted is negative.
- When a gas is compressed, the work done by the compressing force is positive.
- When an object slides on a rough surface, the work done by the frictional force is negative.
- A force acting perpendicular to the direction of motion of a
body does no work, since the scalar product between
and
is zero.
Example: the force of gravity on a satellite orbiting in a circle is always perpendicular to the displacement. Forces that do no work are common in circular motion (S2.10). - ‘Hard work’ is somtimes nothing of the sort
Learning Resources
![]() | HRW Chapter 7. HRW starts with kinetic energy, then moves on to define work. Otherwise the treatments are identical. |
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