Question
Derive an expression for potential energy stored in spring.
Solution
Consider, a massless spring attached with mass m at one end and the other end of spring be connected with a rigid wall.
When we pull the mass towards C, the restoring force directed towards A is set up in spring. Work has to be done against this restoring force in order to displace the mass and hence this work is stored in the form of P.E in the spring.
Let at any instant, mass m be at a distance x from A.
Restoring force at this instance is,
Therefore, to keep the mas in equilibrium, we have to apply the force Fa equal and opposite to -Fr.
If the mass is further displaced by
, the amount of work done dW for this dispalcement by applied force is,
Total amount of work done in order to displace the mass from mean position of A to C is using applied force Fa is,
Work done by applied force against this restoring force is stored in the form of potential energy is,
When we pull the mass towards C, the restoring force directed towards A is set up in spring. Work has to be done against this restoring force in order to displace the mass and hence this work is stored in the form of P.E in the spring.
Let at any instant, mass m be at a distance x from A.
Restoring force at this instance is,
Therefore, to keep the mas in equilibrium, we have to apply the force Fa equal and opposite to -Fr.
If the mass is further displaced by
, the amount of work done dW for this dispalcement by applied force is,Total amount of work done in order to displace the mass from mean position of A to C is using applied force Fa is,
Work done by applied force against this restoring force is stored in the form of potential energy is,
