A block is gently placed at y=0 on a relaxed vertical spring in a coordinate sys

Question

A block is gently placed at y=0 on a relaxed vertical spring in a coordinate system in which the positive y direction is vertically upward. When the block is gently release from this position, it moves down compressing the spring and conies to a rest again momentarily when the spring is compressed by a vertical distance d. Dependence of some of the energies involved on the y-coordinate of the block are plotted in the graph at right. Which of the following statements accurately assign plots shown in the graph to respective energies? Graph 4: Spring potential energy, Graph 1: Kinetic energy Graph 1: Spring potential energy, Graph 3: Kinetic energy Graph 2: Spring potential energy, Graph 3: Gravitational potential energy Graph 2: Kinetic energy, Graph 3: Gravitational potential energy

Explanation / Answer

When a spring is compressed , it's potential energy increases . So as the block moves by compressing the spring , the potential energy of spring will increase from zero to maximum at y = -d . So only graph 2 fits this . So graph 2 is the spring potential energy. gravitational potential of the system will simply be mgy . i.e it is a linear function of y . Thus graph 3 which is linear is the gravitational potential . Kinetic energy of the body is always positive. And in the given situation , the block starts moving at y =0 , it will attain a maximum speed at some point then it will again come to rest at y = -d, so graph 1 is Kinetic energy . So option (C) is correct

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