Strain in elevator cable during constant descent and braking

[Tycho]

I'm having a real problem with this question, could someone please give me a hand?

A 1260kg freight elevator is supported by a steel cable of diameter 34.9mm. It is loaded with a crowd of people collectively having a mass of 2850kg and it is descending.

a) What is the strain on the cable while the elevator is descending at the constant speed of 2.30 m/s?

b) What is the strain in the cable when it is brought to a stop in 0.600s?

I THOUGHT i was okay with this question at first... but then i realized that i had totally ignored the fact that the elevator is moving downwards! I don't know what i need to do to factor that in?? Help!

 

[Doc Al]

first find the tension

The first step, in each case, is to find the tension in the cable. To do that, indentify the forces acting the elevator car (there are only two) and apply Newton's 2nd law.

 

[wais]

Hello there,

I can definitely understand how this question can be confusing, but let's break it down step by step to help you solve it.

First, let's define strain. Strain is the measure of deformation or elongation of a material due to an applied force. In this case, the steel cable is being elongated due to the weight of the elevator and the people inside it.

a) To calculate the strain on the cable while the elevator is descending at a constant speed, we need to use the formula: strain = change in length/original length. In this case, the change in length is the distance the elevator travels in one second (2.30 m/s) and the original length is the length of the cable. We also need to take into account the weight of the elevator and the people inside it, as this is the force causing the elongation. So the formula becomes: strain = (2.30 m/s x 1s)/original length x (1260kg + 2850kg). This will give you the strain in the cable while the elevator is descending at a constant speed.

b) To calculate the strain in the cable when it is brought to a stop in 0.600s, we need to use the formula: strain = change in length/original length. In this case, the change in length is the distance the elevator travels in 0.600s (since it is brought to a stop) and the original length is the length of the cable. We also need to take into account the weight of the elevator and the people inside it, as this is the force causing the elongation. So the formula becomes: strain = (distance traveled in 0.600s)/original length x (1260kg + 2850kg). This will give you the strain in the cable when it is brought to a stop.

Remember to always double check your units to make sure they are consistent and to use the correct formula for each scenario. I hope this helps and good luck with your calculations!