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 k = 2.5 N/cm is shown in figure below. The block becomes attached to the spring and compresses the spring 12 cm before momentarily stopping. 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

gravitational force =mgh

Acc to law conservation of energy

work done by gravitational foce = 1/2 *K *x ^2
                                 =1/2 * 2.5 * 0.12 ^2=0.018 J
b)spring force= -kx =-2.5* 0.12 =-0.3 N
c)1/2 * m * V^2 = 0.018
v=0.38 m/s
d)
v^2 proprtional to the compression

v1^2/v2^2=x1/x2

x2=4*x1
X2= 48 cm =0.48

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