Question

The world’s fastest elevator, in Taiwan’s Taipei 101 skyscraper, ascends at the rate of 1010 m/min. Counterweights balance the weight of the elevator’s car, so the motor doesn’t have to lift the car’s weight. If the motor produces 330 kW of power, what’s the maximum number of 67-kg people the elevator can accommodate?

Answer 1

To determine the maximum number of 67-kg people the elevator can accommodate, we use the motor's power and the elevator's velocity to calculate the force, convert it to the maximum weight the motor can lift, and then divide it by the weight of one person.

Step-by-step explanation:

The question involves calculating the maximum number of 67-kg people that an elevator can accommodate based on the motor's power output and the elevator's ascent rate. Given the motor's power of 330 kW and the elevator's speed at 1010 m/min, we can determine the maximum load the motor can lift using the formula for power: Power (P) = Force (F) × Velocity (v). The force the motor can exert is found by rearranging the formula to F = P/v. Since the elevator's velocity is given in meters per minute, we must convert it to meters per second by dividing by 60. Thus, F = 330,000 Watts ÷ (1010 m/min ÷ 60). After calculating the force, the weight of the maximum load can be found, and then it is divided by the weight of one person (67 kg) to get the number of people.