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 <https://en.wikipedia.org/wiki/Work_(physics)#Path_dependence>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.work_is_integral_of_force_over_distance

.. py:data:: work

    The :attr:`~symplyphysics.symbols.basic.work` done by :attr:`~force`.

Symbol:
    :code:`W`

Latex:
    :math:`W`

Dimension:
    :code:`energy`


.. py:data:: position

    The :attr:`~symplyphysics.symbols.classical_mechanics.position` of the object.

Symbol:
    :code:`x`

Latex:
    :math:`x`

Dimension:
    :code:`length`


.. py:data:: force

    The :attr:`~symplyphysics.symbols.classical_mechanics.force` exerted on the object as a function of :attr:`~position`.

Symbol:
    :code:`F(x)`

Latex:
    :math:`F{\left(x \right)}`

Dimension:
    :code:`force`


.. py:data:: position_before

    The initial :attr:`~symplyphysics.symbols.classical_mechanics.position` of the object.

Symbol:
    :code:`x_0`

Latex:
    :math:`x_{0}`

Dimension:
    :code:`length`


.. py:data:: position_after

    The end :attr:`~symplyphysics.symbols.classical_mechanics.position` of the object.

Symbol:
    :code:`x_1`

Latex:
    :math:`x_{1}`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`W = Integral(F(x), (x, x_0, x_1))`


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