Spring reaction is proportional to deformation (vector)
=======================================================

The empirical law known as **Hooke's law** states that that the force needed to extend or compress
a spring by some distance scales linearly with respect to that distance. Also see the :ref:`scalar
counterpart <Spring reaction is proportional to deformation>` of this law.

**Conditions:**

#. The deformations are elastic (reversible).

#. The stiffness coefficient is a scalar.

**Links:**

#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Hooke's_law#Linear_springs>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.springs.vector.spring_reaction_is_proportional_to_deformation

.. py:data:: force

    Vector of the :attr:`~symplyphysics.symbols.classical_mechanics.force` exerted onto the end of the spring.

Symbol:
    :code:`F`

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

Dimension:
    :code:`force`


.. py:data:: stiffness

    :attr:`~symplyphysics.symbols.classical_mechanics.stiffness` coefficient of the spring.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`force/length`


.. py:data:: deformation

    Vector of the deformation of the string, which is the difference between the position vector of
    the end of the spring after and before the deformation. See :attr:`~symplyphysics.symbols.classical_mechanics.distance`.

Symbol:
    :code:`s`

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

Dimension:
    :code:`length`


.. py:data:: law

    :code:`F = -k * s`


    Latex:
        .. math::
            {\vec F} = - k {\vec s}