A 250 g block is dropped onto a relaxed vertical spring that has a spring consta

Question

A 250 g block is dropped onto a relaxed vertical
spring that has a spring constant of 2.5 N/cm (see
the Figure). The block becomes attached to the
spring and compresses the spring 12 cm before
momentarily coming to rest. While the spring is
being compressed, what work is done on the block
by (a) the gravitational force
on it and (b) the spring force?
(c) What is the speed of the
block just before it hits the
spring? (Assume that friction
is negligible.) (d) If the speed
at impact is doubled, what is
the maximum compression of
the spring?

Explanation / Answer

(a) work done by gravitational force Wg= mgx = 0.250x9.81x0.12 = 0.294 (b) work done by spring force is Ws= -1/2 kx2 = -1.8 (c) consider two positions of block (1) just when block is got attached to spring (2) when spring in its max compression, i.e., velocity of block is 0 work done by all forces = change in kinetic energy => 0.294 - 1.8 = 0 - 1/2 mv2 => v2 = 12.04 => v = 3.47m/s. (d) Wg + Ws = -1/2 m(2v)2 mgx - 1/2 kx2 = -6.02 on solving this x = 0.229m = 22.9cm

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