Final answer:
The tension in the elevator cable is 13720 N when moving at a constant speed both upward and downward. If the elevator accelerates upward at 3.3 m/s², the tension is 18340 N, and if accelerating downward at 3.3 m/s², the tension is 9100 N.
Step-by-step explanation:
To calculate the tension in the elevator cable for the various cases described, we can apply Newton's second law of motion, which states that the force acting on an object equals its mass times its acceleration (F = ma).
Case a: Constant Upward Speed
For an elevator moving at constant speed, the acceleration is zero. Therefore, the tension in the cable (T) is equal to the weight of the elevator (W), which is the mass times the acceleration due to gravity (g = 9.8 m/s2).
T = m × g = 1400 kg × 9.8 m/s2 = 13720 N
Case b: Constant Downward Speed
The case for downward motion at constant speed is identical to that of upward motion; thus, the tension is the same: T = 13720 N.
Case c: Upward Acceleration
When accelerating upward, the net force is the tension minus the weight. Let 'a' be the upward acceleration.
T = m × (g + a)
Plugging in the values, we get:
T = 1400 kg × (9.8 m/s2 + 3.3 m/s2) = 18340 N
Case d: Downward Acceleration
For downward acceleration, the tension is the weight minus the force due to the elevator's downward acceleration.
T = m × (g - a)
So,
T = 1400 kg × (9.8 m/s2 - 3.3 m/s2) = 9100 N