An escalator moves 2 passengers every minute from the first floor of UTS to the second floor. The second floor is located 6.8 meters above the first floor. The average passenger's mass is 53.4kg. Determine the power in Watts needed to move this number of passengers in a minute. g = 9.81m/s2. Only put in the numerical value. Answer to 1 decimal place and do not write the unit in your answer.

This is a short-answer question. Show all working on paper, including the relevant equations and units.

Question

An escalator moves 2 passengers every minute from the first floor of UTS to the second floor. The second floor is located 6.8 meters above the first floor. The average passenger's mass is 53.4kg. Determine the power in Watts needed to move this number of passengers in a minute. g = 9.81m/s2. Only put in the numerical value. Answer to 1 decimal place and do not write the unit in your answer.

This is a short-answer question. Show all working on paper, including the relevant equations and units.

BlackTom AI · Accepted Answer

To begin, restate the scenario: two passengers per minute are moved up a height of 6.8 m, each with mass 53.4 kg. The acceleration due to gravity is g = 9.81 m/s^2.

First, compute the total mass being moved per minute: m_total = 2 passengers × 53.4 kg/passenger = 106.8 kg.

Next, determine the work done in lifting that mass through the height difference. Work against gravity is W = m g h, so W = 106.8 kg × 9.81 m/s^2 × 6.8 m.

Calculate the product step by step: 106.8 × 9.81 = 1047.708, then 1047.708 × 6.8 = 7124.4144 J. This is the energy transferred (work done) per minute.

Power is work per unit time. Since this energy is expended over 60 seconds (one minute), P = W / t = 7124.4144 J / 60 s ≈ 118.74024 W.

For reporting, the units should be Watts, and the value should be rounded to one decimal place. Note that 118.74024 W rounds to approximately 118.7 W when expressed to one decimal place. Consider verifying the intermediate steps or recalculating if a different rounding convention is specified, as small changes in intermediate rounding can affect the final one-decimal result.

If a quick consistency check is desired, you can think of it as energy per minute being about 7.12 kJ, and dividing by 60 s yields roughly 119 J/s, which aligns with the computed value within rounding tolerance.

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