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/s²) must be at least :

Solution

Physics sir · 3 steps

Constant speed means the motor balances weight plus friction. Multiply that force by v.

1. Total mass. Ten persons have a mass of 10 × 68 = 680 kg. With the elevator itself, the total mass is 680 + 920 = 1600 kg.
2. Force from motor. The speed is constant, so the net force is zero. The weight mg = 1600 × 10 = 16000 N and the friction 6000 N both act downward, against the upward motion. So the motor must pull up with 16000 + 6000 = 22000 N.

   P = Fv = 22000 N × 3 m s⁻¹ = 66000 W

3. So. The motor must deliver at least 66000 W, which is option (d).

The idea to keep. For anything moving at constant velocity, the driving force equals the sum of all opposing forces, and power is that force times the speed: P = Fv.

Answer from the NTA final answer key. Solution by PrepWiser.