# Work

Whenever a system interacts with its
surroundings, it can exchange
energy in two
ways- work and heat.

In mechanics, work is defined as the
product of the force and the displacement
in the direction of the force.

**Work done when a spring is
compressed or extended: **According to Hooke's law

Spring force = - k (x – x_{0})

Where k is the spring constant, x_{0} is the
equilibrium position, and x is the final position. The negative sign shows that
the direction of the spring force is opposite the direction of the displacement
from x_{0}. The external force is equal in magnitude but opposite in
sign to the spring force, so

External force (force of your hands) = k (x –x_{0}).

Now, we want to calculate the work done when we stretch
the spring from position 1 to position
2.

W = F dx = k (x – x

_{0}) d(x-x

_{0}) = 1/2 k [(x

_{2}-x

_{0})

^{2}- (x

_{1}-x

_{0})

^{2}]

ConversionConversion EmoticonEmoticon