An elevator filled with passengers has a mass of 1843 kg. The elevator accelerates upward from rest at a rate of [tex]1.20 \, \text{m/s}^2[/tex] for 235 s. Calculate the tension in the cable (in N) supporting the elevator.

The tension in the cable supporting the elevator can be calculated by adding the gravitational force and the force required to accelerate the elevator.

Explanation:

To calculate the tension in the cable supporting the elevator, we need to consider two forces: the gravitational force and the force required to accelerate the elevator.

First, let's calculate the gravitational force acting on the elevator. The gravitational force can be calculated using the formula:

Gravitational force = mass of the elevator * acceleration due to gravity

Given that the mass of the elevator is 1843 kg and the acceleration due to gravity is approximately 9.8 m/s2, we can calculate the gravitational force:

Gravitational force = 1843 kg * 9.8 m/s2

Next, let's calculate the force required to accelerate the elevator. The force required to accelerate an object can be calculated using Newton's second law of motion:

Force = mass * acceleration

Given that the acceleration of the elevator is 1.20 m/s2 and the mass of the elevator is 1843 kg, we can calculate the force required to accelerate the elevator:

Force = 1843 kg * 1.20 m/s2

Finally, to find the tension in the cable, we need to add the gravitational force and the force required to accelerate the elevator:

Tension in the cable = Gravitational force + Force required to accelerate the elevator

By substituting the calculated values, we can find the tension in the cable.

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