A spring of spring constant 200 N m - 1 has a block of mass 1 kg hanging at its one end and from another end, spring is attached to a ceiling of an elevator. The elevator rising upwards with an accele

Question

A spring of spring constant 200 N m - 1 has a block of mass 1 kg hanging at its one end and from another end, spring is attached to a ceiling of an elevator. The elevator rising upwards with an acceleration of g 3 . When acceleration suddenly ceases, then angular velocity and elongation during the time when the elevator is accelerating

TestHub · Accepted Answer

The angular frequency under all circumstances is

$ω = \sqrt{(\frac{k}{m})}$

$= \sqrt{(\frac{200}{1})} = 14.14 rad / s$

When elevator is moving up, using NLM

$T - mg = \frac{mg}{3} \Rightarrow T = \frac{4 mg}{3}$

This tension elongates the spring by x

$T = kx \Rightarrow x = \frac{4 mg}{3 k} = 0.07 m$

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