Physics

Problem

A block of mass m is gently placed on a vertical light spring fixed to the floor. The spring constant is k and its natural length is L. The upper surface of the block is then at a height h above a nearby reference mark on the wall. The block is now pushed further down so that the spring is compressed by an additional distance a and released from rest. a. (i) Derive an expression for the maximum additional extension x (beyond the natural length) that the spring will attain in the subsequent motion. b. (ii) Show that, if

h = 0

(that is, the upper surface of the block is level with the reference mark when the spring is uncompressed), the expression in (i) reduces to

x = \frac{2mg}{k}

. c. (iii) For

m = 0.40\,\text{kg}

k = 320\,\text{N m}^{-1}

h = 0.10\,\text{m}

and

a = 0.04\,\text{m}

, calculate the numerical value of x.

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