An elevator in a building can carry a maximum of 10 persons,

Question:

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being $68 \mathrm{~kg}$. The mass of the elevator itself is $920 \mathrm{~kg}$ and it moves with a constant speed of $3 \mathrm{~m} / \mathrm{s}$. The frictional force opposing the motion is $6000 \mathrm{~N}$. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator

$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ must be at least:

  1. (1) $56300 \mathrm{~W}$

  2. (2) $62360 \mathrm{~W}$

  3. (3) $48000 \mathrm{~W}$

  4. (4) $66000 \mathrm{~W}$


Correct Option: , 4

Solution:

(4) Net force on the elevator $=$ force on elevator

+ frictional force

$\Rightarrow \quad F=(10 m+M) g+f$

where, $m=$ mass of person, $M=$ mass of elevator,

$f=$ frictional force

$\Rightarrow \quad F=(10 \times 68+920) \times 9.8+600$

$\Rightarrow F=22000 \mathrm{~N}$

$\Rightarrow P=F V=22000 \times 3=66000 W$

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