An elevator (cabin mass 540 kg) is designed for a maximum load of 3500 kg, and to reach a velocity of 4 m/s in 3 s. For this scenario, what is the tension the elevator rope has to withstand?
mass = 4040 kg
a = (4/3) m/s^2
F = m a
To determine the tension the elevator rope has to withstand, we need to consider the net force acting on the elevator. Let's break down the problem into smaller steps:
Step 1: Calculate the total mass of the elevator and its maximum load.
Total mass = Cabin mass + Maximum load
Total mass = 540 kg + 3500 kg
Total mass = 4040 kg
Step 2: Calculate the net force acting on the elevator.
Net force = mass × acceleration (from Newton's second law)
Acceleration = Change in velocity / Time
Acceleration = (4 m/s - 0 m/s) / 3 s
Acceleration = 4/3 m/s^2
Net force = Total mass × Acceleration
Net force = 4040 kg × (4/3 m/s^2)
Net force = 16160/3 N
Net force = 5386.7 N (rounded to the nearest tenth)
Step 3: Calculate the tension in the elevator rope.
In order to move up, the tension in the rope must be greater than the force of gravity acting on the elevator.
Force of gravity = mass × gravitational acceleration
Force of gravity = Total mass × 9.8 m/s^2 (gravitational acceleration)
Force of gravity = 4040 kg × 9.8 m/s^2
Force of gravity = 39632 N
Therefore, the tension in the elevator rope needs to be greater than the force of gravity, which is 39632 N.