High School

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.

Answer :

Final answer:

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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