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Question
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 ms−1. 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 ms−2) must be at least
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 ms−1. 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 ms−2) must be at least
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Solution
The correct option is D 66000 W
As the lift is moving with a constant speed,
F=(10m+M)g+f
where,
F= Force exerted by motor,
m= mass of the person,
M= mass of the elevator,
f= frictional force
F=[((10×68)+920)×10]+6000
⇒F=22000 N
⇒Power, P=Fv=22000×3
∴P=66000 W
Hence, option (D) is correct.
As the lift is moving with a constant speed,
F=(10m+M)g+f
where,
F= Force exerted by motor,
m= mass of the person,
M= mass of the elevator,
f= frictional force
F=[((10×68)+920)×10]+6000
⇒F=22000 N
⇒Power, P=Fv=22000×3
∴P=66000 W
Hence, option (D) is correct.
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