Question

A lift is designed to lift a load of $1000\text{kg}$, through $6$ floors of a building with an averge height of $3.5\text{m}$ per floor in $6\text{s}$. The power of the elevator, neglecting energy losses, will be: $\left[1\text{mark}\right]$

A. $3.5\times {10}^4\text{W}$
B. $4.3\times {10}^4\text{W}$
C. $2.2\times {10}^4\text{W}$
D. $5.6\times {10}^4\text{W}$

Answer 1

Correct answer$:$ option A $-$ $3.5\times {10}^4\text{W}$

Solution:
Since the elevator is gaining height, we can calculate hte power of the elevator by considering the potential energy gained by the elevator in $6\text{s}$.

The height gained by the elevator = $3.5\times 6=21\text{m}$

The mass of the lift, $m=1000\text{kg}$

Therefore, the change in the potential energy = $mgh=1000\times 10\times 21=2.1\times {10}^5\text{J}$

Hence, the power of the elevator = $\frac{2.1\times {10}^5}{6}=3.5\times {10}^4\text{W}$