Question

A $24 \, kg$ block resting on a floor has a rope tied to its top. The maximum tension, the rope can withstand without breaking is $310 \, N$ . The minimum time in which the block can be lifted a vertical distance of $4.6 \, m$ by pulling on the rope is

• A. $1.2s$
• B. $1.3 \, s$
• C. $1.7 \, s$
• D. $2.3 \, s$

Answer 1

Answer: (C)

Effective upward force = 310 $-mg$
$=310-24\times 9.8=74.8$ N
Upward acceleration
$\therefore a = \text{74.8/24} = \text{3.12 m s}^{- 2}$
As $s=ut+\frac{1}{2}at^{2}$
4.6 $=0+\frac{1}{2}\times 3.12\times t^{2}$
or $t^{2}=\frac{4.6}{1.56}=2.95$
or $t=\sqrt{2.95}=1.7 \, $ s