Energy possessed by a body by virtue of its height above surface of earth is known as gravitational potential energy. It is equal to the work done by the body situated at some height in returning back slowly to the surface of earth.Consider a body of mass m situated at height h above the surface of earth.
Force applied by the body in vertically downward direction is Energy possessed by the spring by virtue of compression or expansion against elastic force in the spring is known as elastic potential energy.Spring It is a coiled structure made up of elastic material & is capable of applying restoring force & restoring torque when disturbed from its original state. When force (F) is applied at one end of the string, parallel to its length, peeping the other end fixed, then the spring expands (or contracts) & develops a restoring force (FRR) which balances the applied force in equilibrium. On increasing applied force spring further expands in order to increase restoring force for balancing the applied force.Thus restoring force developed within the spring is directed proportional to the extension produced in the spring.
FRR or, FRR = xx (k is known as spring constant or force constant) Hence force constant of string may be defined as the restoring force developed within spring when its length is changed by unity. But in equilibrium, restoring force lances applied force. F = FRR = k x If x = 1, F = 1 Hence force constant of string may also be defined as the force required to change its length by unity in equilibrium.Mathematical Expression for Elastic Potential Energy L -DXL ox Consider a spring of natural length ‘L’ & spring constant ‘k its length is increased by ox. Elastic potential energy of stretched spring will be equal to total work done by the spring in regaining its original length.
If in the process of regaining its natural length, at any instant extension in the spring was x then force applied by spring is F = xx If bring normalizes its length by elementary distance DXL opposite to x under this force then work done by spring is Do = F. (-DXL) .