Final answer:
To find the maximum force the motor should exert, calculate the maximum acceleration in m/s², then apply Newton's second law F = ma with the elevator's mass. The total force will include the weight of the elevator and the force due to the acceleration.
Step-by-step explanation:
To determine the maximum force the motor should exert on the supporting cable, we need to consider the maximum permissible acceleration and the mass of the elevator. The question mentions an acceleration of 6.20×10⁻²g, which is a multiple of the acceleration due to gravity (g = 9.8 m/s²). The maximum force, Fmax, can be calculated using Newton's second law, F = ma. The mass of the elevator is given as 4550 kg.
First, we calculate the maximum acceleration (amax) in meters per second squared (m/s²) by multiplying the given ratio by gravity's acceleration:
amax = 6.20×10⁻² × 9.8 m/s²
Next, we apply Newton's second law to find the force:
Fmax = mamax = (4550 kg) × amax
Here, Fmax includes both the force to overcome gravity (the weight of the elevator) and the force to provide the additional upward acceleration. This force will be larger than just the weight of the elevator itself, because of the acceleration factor.
The weight of the elevator, W, is its mass times the acceleration due to gravity:
W = mg = (4550 kg) × (9.8 m/s²)
To get the total force exerted by the motor, we add the force needed to accelerate to the weight:
Ftotal = W + Fmax
By computing these values, we can find the maximum force the motor should exert on the supporting cable for the elevator design specified in the question.