Final answer:
The maximum power needed for an average lift to elevate a person weighing 70kg for a vertical distance of 190m can be estimated using the work-energy principle, considering the work done against gravity and assuming a short burst power output akin to the human capacity of 500W for brief periods.
Step-by-step explanation:
To estimate the maximum total power needed for an average lift to carry people about 190m higher, we use the formula for power, which is the rate at which work is done. Simplified, power (P) can be calculated as P = (Force × Distance) / Time. Assuming the average mass of a person is 70kg, we can calculate the force (weight) exerted by a person as F = m × g, where g is the acceleration due to gravity (approximately 9.8m/s²).
Force exerted by an average person: F = 70kg × 9.8m/s² = 686N. To find the work done to lift this person 190m, we use W = F × distance. Therefore, the work done is W = 686N × 190m = 130,340J. Since we need the maximum power, we consider the minimum time, which we will assume to be a short burst similar to our reference instance (500W for a short burst).
If a person is capable of an output of 500W for a short burst, to calculate the time (t) it takes for this output, we rearrange the power formula: t = W / P. Substituting the values we get t = 130,340J / 500W = 260.68s. This would be the time for one person. The power needed for the lift can be calculated by using the total work divided by this time. The total maximum power considering multiple persons would be significantly greater and would require additional considerations such as the capacity of the lift and efficiency of the motor.