Question

The mass of an elevator is $4000$kg. Starting from rest how much distance with it rise in $3$s. If the tension in the cable is $48$kN?

• A. $3m$
• B. $4m$
• C. $10m$
• D. $16m$

Answer 1

The correct option is C $10m$

Given ,Mass of elevator = $4000kg$

Weight of elevator = Mass × gravity

Weight, mg $=4000\times 9.8$

$=39200N$

Upward Force applied =$48000N$

So, F(net) = $48000-mg$

F(net) = $48000-39200$

F(net) =$8800N$

Also, F(net) = mass (m) × acceleration (a)

$a=\frac{F\left(net\right)}{m}$

$a=\frac{8800}{4000}$

$a=2.2m/s^2$

Now,

Initial velocity ,$u=0m/s$

Time,$t=3sec$

s = ?

Using Newton's equation of motion,

$s=ut+\frac{1}{2}a{t}^2$

$s=\left(0\right)t+\frac{1}{2}\times 2.2\times (3{)}^2$

$s=9.9m$

Hence, the elevator is raised by 9.9 m.