Question

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

• A. $66000W$
• B. $63360W$
• C. $48000W$
• D. $56300W$

Answer 1

The correct option is A

$66000W$

Step 1. Given data:

Mass of elevator, $m_e=920Kg$

Total mass of persons, $m_o=\left(68\times 10\right)Kg$

$<span\; style="font-family:"Cambria\; Math",serif;mso-bidi-font-family:"Cambria\; Math";">\therefore </span>m_o=680Kg$

Speed of elevator, $u=3\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Frictional force, $f=6000N$

Force applied by the motor, $T=?$

Step 2. Calculating net force on the motor, $F_m$

Net force on motor will be,

Now, $\sum _{}^{}F=ma$

$T-f-\left(m_e+m_o\right)g=0$ $\left[a=0,Asspeed=cons\tan t\right]$

$$\begin{gathered} T-6000-(680+920)\times 10=0 \\ \therefore T=22000N \end{gathered}$$

Step 3. Calculating the power delivered by motor to the elevator,

$\begin{array}{rcl}Power& =& Force\times Speed\\ & \Rightarrow & Power=22000\times 3\\ \therefore Power& =& 66000W\end{array}$

So, the required power of the motor $=66000W$

Hence, correct option is (A),