An elevator (cabin mass 600 kg) is designed for a maximum load of 2800 kg, and to reach a velocity of 3.6 m/s in 5 s. For this scenario, what is the tension the elevator rope has to withstand?
Acceleration is required to be
a = (3.6 m/s)/5 s = 0.72 m/s^2
Total tension in cable when accelerating upward =
Mtotal*(a + g) = 3400*(0.72 + 9.81)
= 35,800 N
To find the tension the elevator rope has to withstand, we need to consider the acceleration experienced by the elevator.
Step 1: Find the net force acting on the elevator.
The net force acting on the elevator can be found using Newton's second law:
F_net = m * a
where F_net is the net force, m is the total mass (cabin mass + load), and a is the acceleration.
Given:
Cabin mass (m_cabin) = 600 kg
Maximum load (m_load) = 2800 kg
Total mass (m) = m_cabin + m_load
Step 2: Calculate the total mass of the elevator.
m = m_cabin + m_load
= 600 kg + 2800 kg
= 3400 kg
Step 3: Calculate the acceleration.
We are given that the elevator reaches a velocity of 3.6 m/s in 5 s. The acceleration can be calculated using the formula:
a = (v_f - v_i) / t
where v_f is the final velocity, v_i is the initial velocity, and t is the time taken.
Given:
Initial velocity (v_i) = 0 m/s
Final velocity (v_f) = 3.6 m/s
Time (t) = 5 s
Substituting the values:
a = (3.6 m/s - 0 m/s) / 5 s
= 0.72 m/s^2
Step 4: Calculate the net force.
F_net = m * a
= 3400 kg * 0.72 m/s^2
= 2448 N
Step 5: Calculate the tension in the elevator rope.
The tension in the elevator rope is equal to the net force acting on the elevator.
Tension = F_net
= 2448 N
Therefore, the tension the elevator rope has to withstand is 2448 N.
To find the tension the elevator rope has to withstand, we need to calculate the net force acting on the elevator.
Step 1: Calculate the net force
The net force is equal to the mass of the elevator plus the maximum load multiplied by acceleration.
Total mass = cabin mass + maximum load
Total mass = 600 kg + 2800 kg
Total mass = 3400 kg
Acceleration (a) = velocity / time
a = 3.6 m/s / 5 s
a = 0.72 m/s^2
Net force (F) = Total mass * Acceleration
F = 3400 kg * 0.72 m/s^2
F = 2448 N
Step 2: Find the tension
The tension in the elevator rope is equal to the net force acting on the elevator.
Therefore, the tension the elevator rope has to withstand is 2448 Newtons.