Final answer:
The tension in the cable supporting an elevator can be calculated by summing the gravitational force acting on the elevator and the force needed to accelerate it, according to Newton's second law of motion.
Step-by-step explanation:
To find the tension in the cable, we must consider the forces acting on the elevator and its acceleration. The tension in the elevator cable can be found using Newton's second law of motion (F = ma), taking into account both the gravitational force (mg) and the net force required to accelerate the mass of the elevator (ma). For an elevator of mass 1700 kg accelerating upwards at 1.20 m/s², we first calculate the gravitational force using mg (where m is the mass and g is the acceleration due to gravity, approximately 9.81 m/s²). The gravitational force is 1700 kg × 9.81 m/s² = 16677 N. The net force needed to accelerate the elevator is ma = 1700 kg × 1.20 m/s² = 2040 N. The total tension T in the cable is the sum of these two forces, T = 16677 N + 2040 N = 18717 N. For part (b), when the elevator moves at a constant velocity, the acceleration is zero, and thus, the tension is equal to the weight of the elevator, which is 16677 N.