Mechanical work is line integral of force
=========================================

Mechanical work is a scalar quantity denoting the energy transferred to or from an object via the
application of force along a displacement.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.dynamics.vector.mechanical_work_is_line_integral_of_force

.. py:data:: work

    Mechanical :attr:`~symplyphysics.symbols.basic.work` done by the :attr:`~force` to displace the body.

Symbol:
    :code:`W`

Latex:
    :math:`W`

Dimension:
    :code:`energy`


.. py:data:: position_vector

    Position vector of the body. See :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_origin`.

Symbol:
    :code:`r`

Latex:
    :math:`{\vec r}`

Dimension:
    :code:`length`


.. py:data:: force

    Vector of the exerted force as a function of :attr:`~position_vector`.

Symbol:
    :code:`F(r)`

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

Dimension:
    :code:`force`


.. py:data:: curve

    Curve given by the body's trajectory during its displacement.


.. py:data:: initial_parameter

    Initial value of the curve parameter.

Symbol:
    :code:`t_0`

Latex:
    :math:`t_{0}`

Dimension:
    :code:`any_dimension`


.. py:data:: final_parameter

    Final value of the curve parameter.

Symbol:
    :code:`t_0`

Latex:
    :math:`t_{0}`

Dimension:
    :code:`any_dimension`


.. py:data:: law

    :code:`W = LineIntegral(dot(F(r), dr), C)`


    Latex:
        .. math::
            W = \int_{C} \left( {\vec F} \left( {\vec r} \right), d \vec r \right)