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

Answer 2

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.