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 $3m/s$. 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. $62360W$
• B. $56300W$
• C. $48000W$
• D. $66000W$

Answer 1

The correct option is D $66000W$

Step1: Draw a free body diagram of the given problem.

Step2: Find the tension in the cable of the elevator.

The elevator moving with constant speed hence

$T=10mg+Mg+f$

$T=6800+9200+6000$

$T=22000N$

Step3: Find the power supplied by the motor.

Formula used: $P=F.v$

The power delivered by the motor to the elevator
Power $=T.v$

$=22000\times 3$

$=66000W$

Final Answer: (c)