work
where v is the velocity of the point of application of F. The second integral is an alternative form, where r denotes displacement, so that dr/dt = v and r1 and r2 are the initial and final displacements.
From the equation of motion ma = F for a particle of mass m moving with acceleration a, it follows that ma. v = F. v, and this then gives
By integration, it follows that the change in kinetic energy is equal to the work done by the force.
Suppose that a particle has displacement x(t)i is acted on by a constant force Fi in the same direction. Then the work done during the time interval from t = t1 to t = t2 equals
This is usually interpreted as ‘work=force × distance'.
The work done against a force F should be interpreted as the work done by an applied force equal and opposite to F. When the force is conservative, this is equal to the change in potential energy. When a person lifts an object of mass m from ground level to a height z above the ground, work is done against the uniform gravitational force and the work done equals the increase mgz in potential energy.
Work has the dimensions ML2 T−2, the same as energy, and the SI unit of work is the joule.
- approximation theory
- a priori
- a priori
- apse
- Apéry's constant
- Arabic numeral
- arbitrarily large/small
- arbitrary
- arc
- arc
- arc-connected
- arccos
- arccosh
- Archimedean property
- Archimedean solid
- Archimedean spiral
- Archimedes
- Archimedes' constant
- Archimedes' method
- arc length
- are
- area
- area of a surface of revolution
- area under a curve
- arg