During peak shopping season at Northbrook Court, an escalator elevates 1233 passengers a vertical distance of 7.43 meters over the course of 30.3 minutes. If the average mass of the passengers is 55.3 kg, determine the power delivered by the escalator to the people.

Power = (1233 passengers x 55.3 kg x 7.43 m) / (30.3 minutes x 60 seconds)

Power = 8,845.7 Watts

To determine the power delivered by the escalator to the people, we can use the formula:

Power (P) = Work/Time

To find the work done by the escalator, we can use the formula:

Work (W) = Force × Distance

First, we need to find the force exerted on each passenger.

Force (F) = mass × acceleration

Since the escalator elevates the passengers vertically, the acceleration due to gravity (g) should be used.

Acceleration (a) = g ≈ 9.8 m/s²

Thus, the force exerted on each passenger can be calculated as:

Force (F) = mass × acceleration
= 55.3 kg × 9.8 m/s²

Next, we can calculate the work done by the escalator.

Work (W) = Force × Distance
= F × d

The distance (d) traveled by the passengers can be calculated by multiplying the number of passengers (N) by the vertical distance (h) traveled by each passenger.

Distance (d) = N × h
= 1233 passengers × 7.43 m

Finally, we can calculate the power delivered by the escalator by dividing the work done by the time taken.

Power (P) = Work/Time
= W / (30.3 minutes × 60 seconds/minute)

Now, let's input the values into the formulas to calculate the power.

Force (F) = 55.3 kg × 9.8 m/s²
Distance (d) = 1233 passengers × 7.43 m
Power (P) = (F × d) / (30.3 minutes × 60 seconds/minute)

To determine the power delivered by the escalator to the people, we need to use the formula for power:

Power (P) = Work (W) / Time (t)

First, let's calculate the work done by the escalator. Work is calculated as the product of force and displacement:

Work (W) = Force (F) * Displacement (d)

The force exerted on each passenger is equal to their weight. The weight is calculated as the product of mass (m) and acceleration due to gravity (g):

Force (F) = mass (m) * acceleration due to gravity (g)

Acceleration due to gravity is approximately 9.8 m/s².

Displacement (d) is given as 7.43 meters.

To determine the total mass of the passengers, we can multiply the average mass (55.3 kg) by the number of passengers (1233).

Now, let's calculate the power using the provided values:

force (F) = mass (m) * acceleration due to gravity (g)
force (F) = 1233 * 55.3 * 9.8

work (W) = force (F) * displacement (d)
work (W) = 1233 * 55.3 * 9.8 * 7.43

Finally, we can calculate the power:

power (P) = work (W) / time (t)
power (P) = (1233 * 55.3 * 9.8 * 7.43) / (30.3 * 60)

Now, you can plug in the values and calculate the power delivered by the escalator to the people.