The world's fastest elevator, in Taiwan's Taipei 101...

The world's fastest elevator, in Taiwan's Taipei 101 skyscraper (Fig. 6.19 ), ascends at the rate of $1010 \mathrm{~m} / \mathrm{min}$. Counterweights balance the weight of the elevator car, so the motor doesn't have to lift the car's weight. If the motor produces $330 \mathrm{~kW}$ of power, what's the maximum number of 67 -kg people the elevator can accommodate? (Your answer somewhat overestimates the actual rated load of 24 people.)

Key Concepts

Power

Power is the rate at which work is done or energy is transferred. It is a fundamental concept that determines how quickly energy can be converted into work, which is critical in systems like elevators where energy is used to lift loads over time.

Work

Work is the energy transferred when a force is applied over a distance. In the context of mechanical systems, such as lifting an object against gravity, work quantifies the amount of energy required to elevate a mass, which directly relates to the gravitational potential energy gained.

Gravitational Potential Energy

Gravitational potential energy refers to the energy an object possesses due to its position in a gravitational field. It is calculated by the product of mass, gravitational acceleration, and height, and is a key concept when analyzing the energy needed to lift a load in an elevator system.

Energy Conversion and Rate Equations

This concept involves understanding how mechanical energy provided by a motor is converted into potential energy. By equating the power output (energy per unit time) of the motor to the rate at which gravitational potential energy is increased, one can determine the system's capacity to lift a mass, which is essential in designing and analyzing mechanical systems.

Unit Conversion and Dimensional Analysis

Unit conversion and dimensional analysis ensure that all physical quantities are expressed in compatible units during calculations. This is critical for accurately determining results in problems that involve converting power, mass, acceleration due to gravity, and distance into a consistent system of units.

Transcript

00:01 So we have an elevator in taiwan's taipei 101 skyscraper that ascends at a rate.

00:11 So this is going to be a speed of 110 meters per minute.

00:24 Sign, where'd that come from? minute.

00:33 So i'm going to convert that to seconds already.

00:36 There are 60 seconds in a minute.

00:43 And so 110 divided by 60 is going to give me 16 .83 meters in one second.

01:05 That is incredibly fast.

01:08 Okay, so we have counterweights that balance the weight of the elevator car, so the motor doesn't have to lift the car's weight.

01:19 But it does have to lift the weight of the people.

01:24 So the force that it has to lift is the number of people times the average weight of the person, which we're asked to use 67.

01:39 Kilograms.

01:42 Okay, if the motor produces 3 ,000, no, 330 kilowatts of power, so our power is 330 kilowatts, then how many people can the elevator accommodate? well, power is work over time, which is force times distance over time, and distance over time is velocity.

02:17 So that's force times velocity.

02:22 So our power is 330 ,000 watts.

02:32 Our force is n times, which is the number of people, times 67, kilograms and our velocity is 16.

02:53 Why didn't it write? let me pause because i don't know why this thing isn't writing.

03:03 All right.

03:03 I think i'm good now...

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