An elevator has a combined mass of 1700kg. Find the tension of the supporting cable when the elevator, originally moving downward at 13 m/s, is brought to rest with constant acceleration in a distance of 44 m.

To find the tension in the supporting cable, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the tension in the cable.

Given information:
- Combined mass of the elevator: 1700 kg
- Initial velocity of the elevator: 13 m/s
- Final velocity (when brought to rest): 0 m/s
- Distance covered during deceleration: 44 m

First, we need to find the acceleration of the elevator. We can use the following kinematic equation:

v^2 = u^2 + 2as

Where:
- v is the final velocity (0 m/s)
- u is the initial velocity (-13 m/s)
- a is the acceleration
- s is the distance covered during deceleration (44 m)

Rearranging the equation, we get:

a = (v^2 - u^2) / (2s)

Substituting the given values:

a = (0^2 - (-13)^2) / (2 * 44)
= (0 - 169) / (88)
= -169 / 88
≈ -1.92 m/s^2

The negative sign indicates that the acceleration is in the opposite direction to the initial motion (downward).

Now, we can calculate the tension in the cable using Newton's second law. The net force acting on the elevator is equal to the tension in the cable:

net force = mass * acceleration

tension = mass * acceleration

Substituting the given values:

tension = 1700 kg * (-1.92 m/s^2)
≈ -3264 N (rounded to three significant figures)

Therefore, the tension in the supporting cable is approximately -3264 N. The negative sign indicates that the tension is in the opposite direction to the motion of the elevator (upward). Note that tension is always positive in magnitude and is sometimes written as 3264 N, neglecting the negative sign.