A box of mass hangs from the ceiling of an elevator by a light spring balance

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A box of mass

4\,\text{kg}

hangs from the ceiling of an elevator by a light spring balance. Starting from rest at

t = 0

, the elevator moves upward such that its displacement from the initial floor level is described by

s = 0.5t^{3}

metres for the first

3\,\text{s}

. (i) Obtain expressions for the velocity

v(t)

and acceleration

a(t)

of the elevator during the interval

0 \le t \le 3\,\text{s}

. (ii) Derive an expression for the reading

R(t)

of the spring balance as a function of time in the stated interval. (iii) Calculate the readings at

t = 0\,\text{s}

t = 1\,\text{s}

and

t = 3\,\text{s}

. Also determine the maximum reading attained during this interval.