Final answer:
Tension in an elevator cable is higher during upward acceleration because the force required to accelerate adds to the weight, resulting in greater tension. During downward motion, particularly with deceleration, the force opposes the weight, yielding lower tension.
Step-by-step explanation:
Discussing the tension in an elevator cable, we consider two scenarios: when the elevator accelerates upward and when it moves downward. The tension in the elevator cable is higher during upward acceleration due to the addition of the force of acceleration to the weight of the elevator and its load. Conversely, during downward acceleration, the force of acceleration opposes the weight, resulting in lower tension.
To illustrate this, let's use the example of an elevator with a mass of 1700 kg that accelerates upward at 1.20 m/s². Using Newton's second law (F=ma), the upward force needed is F = ma = 1700 kg × 1.20 m/s² = 2040 N. This force is in addition to the weight of the elevator (W=mg), which is 1700 kg × 9.8 m/s² = 16660 N. Therefore, the total tension during upward acceleration is the sum of these two forces: 16660 N + 2040 N = 18700 N.
When the elevator decelerates downward at 0.600 m/s², the force due to deceleration is subtracted from the weight, which results in a lesser tension in the cable. Tension during deceleration would be 16660 N - (1700 kg × 0.600 m/s²) = 16578 N.