Work is integral of force over distance

Assuming a one-dimensional environment, when the force \(\vec F\) on a particle-like object depends on the position of the object, the work done by \(\vec F\) on the object while the object moves from one position to another is to be found by integrating the force along the path of the object.

Links:

1. Wikipedia.

work

The work done by force.

Symbol:

W

Latex:

\(W\)

Dimension:

energy

position

The position of the object.

Symbol:

x

Latex:

\(x\)

Dimension:

length

force

The force exerted on the object as a function of position.

Symbol:

F(x)

Latex:

\(F{\left(x \right)}\)

Dimension:

force

position_before

The initial position of the object.

Symbol:

x_0

Latex:

\(x_{0}\)

Dimension:

length

position_after

The end position of the object.

Symbol:

x_1

Latex:

\(x_{1}\)

Dimension:

length

law

W = Integral(F(x), (x, x_0, x_1))

Latex:

\[W = \int\limits_{x_{0}}^{x_{1}} F{\left(x \right)}\, dx\]