An elevator is being lowered at steadily decreasing speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. Why does the upward force exerted on the elevator by the cable have a larger magnitude as the downward force of gravity on the elevator

Please see below as the answer is self-explanatory.

Explanation:

At any time, there are two forces acting on the elevator: the tension in the cable T (upward) and the force of gravity (downward).Taking the upward direction as positive, if we apply Newton's 2nd law, we will have the following equation:

       

Now, we know that the elevator is being lowered at a decreasing speed, which means that the acceleration must have an opposite direction to the displacement.Since the displacement is downward, that means that the acceleration must be positive.If a ≥ 0, this means that T- mg ≥ 0, so the tension T must have a larger magnitude as the downward force of gravity on the elevator.