Final answer:
To find the tension in the cable of an elevator with a mass of 2840 kg and an upward acceleration of 1.22 m/s^2, we add the gravitational force (weight) to the net force caused by the acceleration, resulting in a tension of 31317.2 N.
Step-by-step explanation:
To calculate the tension in the cable when an elevator with a mass of 2840 kg is given an upward acceleration of 1.22 m/s2, we need to apply Newton's second law, which relates the net force acting on an object to the acceleration of the object. The net force in this case is the difference between the tension in the cable and the gravitational force acting on the elevator (which is the weight of the elevator).
The gravitational force is calculated as weight = mass × gravitational acceleration (where the gravitational acceleration, g, is approximately 9.81 m/s2). For the elevator, this is 2840 kg × 9.81 m/s2 = 27850.4 N.
To find the total net force providing the upward acceleration, we use net force = mass × acceleration. Therefore, the net force is 2840 kg × 1.22 m/s2 = 3466.8 N.
The tension in the cable is then the sum of the gravitational force and the net force (since they both act upward in the case of the accelerating elevator): tension = weight + net force, which is 27850.4 N + 3466.8 N = 31317.2 N.