Class 11 Physics Work Energy Power | Potential energy of spring |

Potential energy of spring

- The spring force is an example of a variable force, which is conservative.
- In an ideal spring, F
_{s}= − kx , this force law for the spring is called Hooke’s law. - The constant k is called the spring constant. Its unit is N m
^{-1}. - The spring is said to be stiff if k is large and soft if k is small.

- Spring force is position dependent as first stated by Hooke, (F
_{s}= − kx) - Work done by spring force only depends on the initial and final positions. Thus, the spring force is a conservative force.
- We define the potential energy V(x) of the spring to be zero when block and spring system is in the equilibrium position.
- For an extension (or compression) x, V(x) = kx
^{2}/2

If the block of mass m is extended to x_{m} and released from rest, then its total mechanical energy at any arbitrary point x (where x lies between – x_{m} and + x_{m}) will be given by:

**Example**: A car of mass M travelling with speed v, collides with a spring, having spring constant k. The car comes to rest (momentarily) when spring is compressed to a distance of x_{m }. Find x_{m }

_{}

.