Question

Suppose the ceiling in the previous problem is that of an elevator which is going up with an acceleration of 2.0 m/s². Find the elongation.

Answer 1

When the ceiling of the elevator is going up with an acceleration 'a', then a pseudo-force acts on the block in the downward direction.

a = 2 m/s²

From the free-body diagram of the block,
kx = mg + ma
⇒ kx = 2g + 2a
= 2 × 9.8 + 2 × 2
= 19.6 + 4
$\Rightarrow x=\frac{23.6}{100}=0.236\approx 0.24\mathrm{m}$

When 1 kg body is added,
total mass = (2 + 1) kg = 3 kg
Let elongation be x'.
∴ kx' = 3g + 3a = 3 × 9.8 + 6
$$\begin{gathered} \Rightarrow x\text{'}=\frac{35.4}{100} \\ =0.354\approx 0.36\mathrm{m} \end{gathered}$$
So, further elongation = x' − x
= 0.36 − 0.24 = 0.12 m.