Question

question 21 (1 point)
taipei 101, one of the worlds tallest buildings, has the worlds fastest ascending elevator that moves at a speed of 1010 m/min. if the elevator and its passengers have a mass of 975 kg, what power output is required to move the elevator at that speed?
98.6 kw
161 kw
292 kw
376 kw

Explanation:

Step1: Convert speed to m/s

First, convert the speed from meters per minute to meters per second:
$$v = \frac{1010\ \text{m}}{1\ \text{min}} = \frac{1010\ \text{m}}{60\ \text{s}} \approx 16.833\ \text{m/s}$$

Step2: Calculate force (weight)

Find the gravitational force (weight) of the elevator and passengers, using $F = mg$ where $g=9.8\ \text{m/s}^2$:
$$F = 975\ \text{kg} \times 9.8\ \text{m/s}^2 = 9555\ \text{N}$$

Step3: Compute power output

Use the power formula $P = Fv$ to find the required power:
$$P = 9555\ \text{N} \times 16.833\ \text{m/s} \approx 160840\ \text{W} = 160.84\ \text{kW} \approx 161\ \text{kW}$$

Answer:

161 kW