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:

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