Question

A block of 2 kg is suspended from the ceiling through a massless spring of spring constant k = 100 N/m. What is the elongation of the spring ? If another 1 kg is added to the block, what would be the further elongation ?

Answer 1

Given, m = 2k , k = 100 N/m

From the free body diagram...

kl - 2g = 0

$\Rightarrow kl=2g$

$\Rightarrow l=\frac{2g}{k}=\frac{2\times 9.8}{100}$

= $\frac{19.6}{100}=0.196\approx 0.2m$

Suppose further elongation happens when 1 kg block us added be x.

Then k (l + x ) = 3g

$\Rightarrow kx=3g-2g=g=9.8N$

$\Rightarrow \frac{2g}{k}=\frac{2\times 9.8}{100}$

=$\frac{19.6}{100}=0.098=0.1m$