Question

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

Answer 1

Please see below as the answer is self-explanatory.

Step-by-step 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:

`T - m*g = m*a (1)`

• 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.

Answer 2

F = W + ma a> 0

Step-by-step explanation:

For this exercise let's use Newton's second law

we assume the upward direction as positive

F - W = m a

F = W + ma

F = m (g + a)

In this case they indicate that the speed is less and less as it goes down, therefore the acceleration must be opposite to the speed, that is, the acceleration is upwards, consequently it is positive

We can see that since a> 0 the force F must have greater than the weight of the elevator