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

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Work, Power & Energy

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of

3 m / s

. the frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (

g = 10 m / s^{2}

) must be at least:

(A)56300 W
(B)66000 W✓ Correct
(C)62360 W
(D)48000 W

Answer: (B)

Solution

Carrying ten people the lift's total mass is

920 + 10 \times 68 = 1600

kg, so its weight is

1600 \times 10 = 16000

N. Rising at a steady speed, the motor must overcome both this weight and the

6000

N of friction, a pulling force of

16000 + 6000 = 22000

N. At the constant speed of

3

m/s the power it must deliver is

P = F v = 22000 \times 3 = 66000

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option

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JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Work, Power & Energy

Solution

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