Potential Energy Of A Spring

Potential energy of a spring

Let an elastic spring of negligible small mass with its one end attached to a rigid support. Its other end is attached to a block of mass m which can slide over a smooth horizontal surface. The position x=0 is the equilibrium position. When the spring is stretched or compressed by pulling or pushing the block, the spring force Fs begins to act in the spring towards the equilibrium position.

Potential Energy Of A Spring
Potential Energy Of A Spring

According to Hooke’s law the spring force Fs is proportional to the displacement of the block from the equilibrium position

Potential Energy Of A Spring
Potential Energy Of A Spring

Its SI unit is the N/m. The negative sign shows Fs acts in the opposite direction of x. The work done by the spring Force for a small extension dx is

dWs = Fs.dx = -kx.dx [Fs = -kx]

Potential Energy Of A Spring
Potential Energy Of A Spring
Conclusion

1. The spring force is position dependent.

2. The work done by the spring force depends on initial and final position.

3. The work done by the spring force in a cyclic process is zero.

Thus, spring force is a conservative force.

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