Question

A 1000kg elevator is descending vertically with an acceleration of 1.0ms⁻². If the acceleration due to gravity is 10.0ms⁻², what is the tension in the suspending cable?

Answer 1

To calculate the tension in a descending elevator's cable, apply Newton's second law to account for the elevator's weight and the net force due to its acceleration. For a 1000kg elevator accelerating downwards at 1.0ms⁻², the tension in the cable is 9000N.

Step-by-step explanation:

To calculate the tension in the suspending cable of a descending elevator, we need to consider the forces acting on the elevator. There are two main forces: the gravitational force, which is the weight of the elevator (mass times the acceleration due to gravity), and the tension force from the cable that is working against gravity to slow down the elevator's fall. The formula for tension (T) in the cable can be derived from Newton's second law (F = ma).

Applying Newton's second law:

• Weight (W) = mass (m) × acceleration due to gravity (g)
• Net force (Fnet) = mass (m) × acceleration of the elevator (a)

In this case, since the elevator is moving downwards with an acceleration of 1.0ms⁻², the net force acting upwards is the tension minus the weight of the elevator. Thus, T = W + Fnet.

So the tension in the cable is:

T = m × g - m × a = 1000kg × 10.0ms⁻² - 1000kg × 1.0ms⁻² = 9000N

Therefore, the tension in the cable is 9000 Newtons (N).