An elevator (mass 4175 kg) is to be designed so that the maximum acceleration is 0.0700g.
What is the maximum force the motor should exert on the supporting cable?
force=mass*a=mass(1.0700)9.8
To find the maximum force the motor should exert on the supporting cable, we need to calculate the maximum acceleration first.
Given:
Mass of the elevator (m) = 4175 kg
Maximum acceleration (a) = 0.0700g
First, let's convert g, which is the acceleration due to gravity, into m/s^2. The standard value of acceleration due to gravity is approximately 9.8 m/s^2.
g = 9.8 m/s^2
So, the maximum acceleration can be calculated as:
a = 0.0700 * 9.8 m/s^2
Now, we can calculate the maximum acceleration:
a = 0.686 m/s^2
The force (F) exerted on an object can be calculated using Newton's second law of motion:
F = m * a
where:
F = force exerted on the object (in Newtons)
m = mass of the object (in kilograms)
a = acceleration of the object (in meters per second squared)
Now, we can substitute the values and calculate the maximum force:
F = 4175 kg * 0.686 m/s^2
F = 2861.75 N (rounded to the nearest whole number)
Therefore, the maximum force the motor should exert on the supporting cable is approximately 2862 Newtons.