Question

An elevator in a building can carry a maximum of $10$ persons, with the average mass of each person being $68\text{kg}$. The mass of the elevator itself is $920\text{kg}$ and it moves with a constant speed of $3{\text{ms}}^{-1}$. The frictional force opposing the motion is $6000\text{N}$. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $(g=10{\text{ms}}^{-2})$ must be at least

• A. $56300\text{W}$
• B. $62360\text{W}$
• C. $48000\text{W}$
• D. $66000\text{W}$

Answer 1

The correct option is D $66000\text{W}$

As the lift is moving with a constant speed,

$F=(10m+M)g+f$

where,
$F=$ Force exerted by motor,
$m=$ mass of the person,
$M=$ mass of the elevator,
$f=$ frictional force

$F=\left[\right((10\times 68)+920)\times 10]+6000$
$\Rightarrow F=22000\text{N}$
$\Rightarrow \text{Power,}P=Fv=22000\times 3$
$\therefore P=66000\text{W}$

Hence, option $\left(D\right)$ is correct.