Mechanical work is force times distance
=======================================

Work is measured result of force applied. Mechanical work is the only reason for the object energy to be changed.
Work is scalar value equal to force multiplied by distance.

**Notes:**

#. This law works even when the force vector :math:`\vec F` and the displacement vector
   :math:`\vec s` are not collinear or codirectional. In that case one should use the projection
   of :math:`\vec F` onto :math:`\vec s` as the force or the projection of :math:`\vec s` on
   :math:`\vec F` as the distance, due to the projection law. See the second **note** for reference.

.. math::

    W = \left( \vec F, \vec s \right) = \left( \vec F, \frac{\vec s}{\left \Vert \vec s \right \Vert} \right) \left \Vert \vec s \right \Vert = F_s s

    W = \left( \vec F, \vec s \right) = \left( \frac{\vec F}{\left \Vert \vec F \right \Vert}, \vec s \right) \left \Vert \vec F \right \Vert = F s_F

#. Use the :ref:`vector form <Mechanical work from force and displacement>` of this law for
   non-collinear vectors of force and movement.

**Conditions:**

#. The force and displacement vectors are **collinear** and **codirectional**.

**Links:**

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

..
    NOTE: include angle in the formula?

.. py:currentmodule:: symplyphysics.classical_mechanics.dynamics.translational_motion.mechanical_work_from_force_and_distance

.. py:data:: work

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

Symbol:
    :code:`W`

Latex:
    :math:`W`

Dimension:
    :code:`energy`


.. py:data:: force

    The :attr:`~symplyphysics.symbols.classical_mechanics.force` exerted on the body.

Symbol:
    :code:`F`

Latex:
    :math:`F`

Dimension:
    :code:`force`


.. py:data:: distance

    The :attr:`~symplyphysics.symbols.classical_mechanics.distance` the body traveled due to the force exerted on it.

Symbol:
    :code:`s`

Latex:
    :math:`s`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`W = F * s`


    Latex:
        .. math::
            W = F s