A light spring with a spring constant k = 304 N/m is attached to a vertical wall

Question

A light spring with a spring constant k = 304 N/m is attached to a vertical wall at one end and a block with a mass m = 0.560 kg at the other end. The block rests on a horizontal frictionless surface and is initially at the equilibrium length of the spring. The block is then displaced from the equilibrium position of the spring in such a manner as to stretch the spring by an amount A = 0.190 m and then released. As the block oscillates about the equilibrium position, determine the amount of work done on the block by the spring for the following segments of travel. (a) the block traveling from the equilibrium position (x = 0) to the position x = A (Enter your answer to at least two decimal places.) W0 right arrow = J (b) the block traveling from the position x = A to the equilibrium position (x = 0) (Enter your answer to at least two decimal places.) WA right arrow 0 = 0 J (c) the round trip from the equilibrium position (x = 0) to the position x = A and then back to the equilibrium position W0 right arrow A right arrow 0 = 0 J

Explanation / Answer

work is given by the formula 1/2(kx^2) for this spring problem ( frictionless surface )

1. from 0 to A , the displacement is opposite to the force of spring , so work is negative , work = (-1/2)kx^2 = -5.4872J

2. from A to 0 , the displacement is in the direction of force of spring ,so work done is positve and same in magnitude , i.e . Work = (1/2)Kx^2 = 5.4872J

3. adding up the above 2 solutions , we know that the amount of work done in moving the block from 0 to A and from A to 0 is equal to ZERO.

Alternate way for 3 ,

at the end points the velocity of the block is ZERO , and we know that Work done is equal to the Difference in kinetic energy at 2 points , at both points , velocity is ZERO , so kinetic energy is ZERO and their difference too is ZERO , so the work done is equal to ZERO

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