Question

Obtain expression for potential energy of a spring attached to mass m moving on a frictionless horizontal surface by graphical method.​

Answer 1

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To study this ,consider an electric spring of negligibly small mass .One end of the spring is attached to the rigid wall and another end of spring is attached to a block of mass m which can move on smooth frictionless horizontal surface

Consider the figure given below:-

• We now take the block from its un-stretched position to a point P by stretching the spring

• At this point P restoring force is exerted by the spring on the block trying it bring it back to the equilibrium position.

• Similar restoring force developed in the spring when we try to compress it

• For an ideal spring ,this restoring force F is proportional to displacement x and direction of restoring force is opposite to that displacement

• Thus force and displacement are related as

• F α x or F= - kx

• where K is called the spring constant and this equation (16) is known as Hook's law.negative sign indicates that force oppose the motion of the block along x

• To stretch a spring we need to apply the external force which should be equal in magnitude and opposite to the direction of the restoring force mentioned above i.e for stretching the spring

• Fext=Kx Similarly for compressing the spring

• Fext= - Kx or Fext=Kx (both F and x are being negative)

Answer 2

The area under the force in the spring vs. displacement curve is the work done on the spring. a plot of force on the spring vs. displacement, where displacement is 000 when the spring is unstretched. The work done on a spring stores elastic potential energy U