A block of mass m is dropped onto the top of a coil spring of constant k, which

Question

A block of mass m is dropped onto the top of a coil spring of constant k, which has its cylindrical axis oriented vertically. Consequently, the spring slows and momentarily stops the mass, at which point, the spring has been
compressed by a distance d.

a) While the spring is being compressed, show that the ratio of the work done by the spring to the work done by gravity

Show that the block's speed just before it meets the spring is given by If the block is dropped from a greater height so that its speed is doubled just before it meets the spring, show that the spring will then be compressed by a distance

Explanation / Answer

a. work done =-kd
=in above case mass m travel distance= d+d= 2d
= now

Ws/Wg=-kd/2*mass**g

potential energy of block at top = K.E. energy before hitting spring

= mgh=1/2mv^2
=V^2=2gh h=d

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