If an elevator with mass of 4850kg is designed to have a maximum acceleration of .068g (g is gravity acceleration). What are the maximum and minimum forces the motor should exert?
max=mass(g+a)
min=mass(g-a)
To find the maximum and minimum forces the motor should exert, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
Given:
Mass of the elevator (m) = 4850 kg
Maximum acceleration (a) = 0.068g
Let's calculate the maximum and minimum forces:
1. Maximum force:
To find the maximum force, we need to use the maximum acceleration. We can convert the acceleration due to gravity (g) to m/s^2 by multiplying it with 9.8 (approximate value):
Maximum acceleration = 0.068g * 9.8 m/s^2
Maximum acceleration = 0.6684 m/s^2
Now we can calculate the maximum force:
Maximum force = mass * maximum acceleration
Maximum force = 4850 kg * 0.6684 m/s^2
Maximum force = 3247.628 N (Newton)
Therefore, the maximum force the motor should exert is approximately 3247.628 N.
2. Minimum force:
The minimum force occurs when the elevator is moving downward and decelerating. In this case, the motor should exert a force equal to the weight of the elevator minus the force due to deceleration.
The weight of the elevator can be calculated using the formula:
Weight = mass * gravity
Weight = 4850 kg * 9.8 m/s^2
Weight = 47530 N
Now, let's calculate the force due to deceleration:
Force due to deceleration = mass * acceleration
Force due to deceleration = 4850 kg * 0.068g
Force due to deceleration = 316.18 N
Therefore, the minimum force the motor should exert is approximately 47530 N - 316.18 N = 47213.82 N.
In conclusion, the maximum force the motor should exert is approximately 3247.628 N, and the minimum force is approximately 47213.82 N.
To find the maximum and minimum forces the motor should exert, we need to consider the maximum acceleration and the mass of the elevator.
1. Calculate the maximum force:
The maximum force occurs when the elevator is accelerating upwards at its maximum acceleration. We can calculate this force using Newton's second law: F = m * a.
Given:
Mass of the elevator, m = 4850 kg
Maximum acceleration, a = 0.068g
First, we need to convert the acceleration from g to m/s^2:
g ≈ 9.8 m/s^2 (acceleration due to gravity)
Maximum acceleration, a = 0.068 * 9.8 = 0.6664 m/s^2 (approximately)
Now we can calculate the maximum force:
F_max = m * a
F_max = 4850 kg * 0.6664 m/s^2
F_max ≈ 3233.36 N (approximately)
Therefore, the maximum force the motor should exert is approximately 3233.36 N.
2. Calculate the minimum force:
The minimum force occurs when the elevator is in its downward motion and decelerating with maximum acceleration. In this case, the net force exerted by the motor should oppose the force due to gravity acting on the elevator.
To calculate the minimum force, we need to consider the opposing force due to gravity:
Weight = m * g
Weight of the elevator:
Weight = 4850 kg * 9.8 m/s^2
Weight ≈ 47530 N (approximately)
The minimum force required to decelerate the elevator (oppose the force due to gravity) is equal to the weight of the elevator:
F_min = Weight ≈ 47530 N (approximately)
Therefore, the minimum force the motor should exert is approximately 47530 N.