Question

While an elevator of mass 2415 kg moves upward, the tension in the cable is 35.2 kN. Assume the elevator is supported by a single cable. Forces exerted by the guide rails and air resistance are negligible.What is the acceleration of the elevator? If the acceleration is in upward direction, enter a positive value and if the acceleration is in downward direction, enter a negative value.

Answer 1

The tension in the cable is equal to the weight of the elevator plus the force required to accelerate it upward. We can use this fact to find the acceleration of the elevator.

Tension in the cable = mg + ma

where m is the mass of the elevator, g is the acceleration due to gravity, and a is the acceleration of the elevator.

Rearranging this equation, we get:

a = (Tension in the cable - mg) / m

Substituting the given values, we get:

a = (35.2 kN - 2415 kg x 9.81 m/s^2) / 2415 kg

a = 0.26 m/s^2

Since the elevator is moving upward, the acceleration is in upward direction, so we enter a positive value. Therefore, the acceleration of the elevator is 0.26 m/s^2.