Work is integral of force over distance

Assuming a one-dimensional environment, when the force F on a particle-like object depends on the position of the object, the work done by 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:

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