# Formula Mechanical Work Force Distance Angle

## Work

`$$ \Delta W $$`Unit

`$$ \mathrm{J} $$`

This is the energy that a body (e.g. a trolley) gains or loses when a force \(F\) is applied TO the body or BY the body.

## Force

`$$ F $$`Unit

`$$ \mathrm{N} $$`

This is the force exerted by the body (work is done BY the body) or exerted on the body (work is done ON the body).

## Distance

`$$ \class{red}{s} $$`Unit

`$$ \mathrm{m} $$`

Distance along which, the body exerts the force \(F\) or along which, on the body the force \(F\) is exerted. For example, if the force is applied to the body along a distance \(s\), then the body gains kinetic energy.

## Angle

`$$ \class{green}{\alpha} $$`Unit

`$$ - $$`

This is the angle enclosed by the force vector \(\boldsymbol{F}\) and the displacement vector \(\class{red}{\boldsymbol{s}}\).

If the force vector is *orthogonal* to the displacement vector, i.e. at a 90 degree angle, then the cosine is zero and so is the work done \(\Delta W = 0\). If, on the other hand, the force vector points *parallel* to the displacement vector, the work done \(\Delta W\) is maximum because then the cosine is one (maximum).