Why Does the Cord Break at 200 N Tension in the Elevator Problem?

[Gauss177]

Homework Statement

A 15.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 200 N and breaks as the elevator accelerates. What was the elevator's minimum acceleration (magnitude and direction)?

Homework Equations

The Attempt at a Solution

I labeled the force of rope as Fr, so:

Fr - mg = ma
(200 N) - (15.0 kg)(9.8 m/s^2) = (15.0 kg)a
a = 3.53 m/s^2

This is the answer I came to. My question is why is 200 N plugged into the equation above? I don't see any other way to do it, but the problem states that the cord can withstand a tension of 200 N, so if I plug in 200 N the cord still wouldn't break? But then again I don't see how else to do it.

 

[Hootenanny]

Another way of looking at this question is find the maximum acceleration of the elevator if the maximum tension the cord can withstand is 200N. If the elevator accelerated at a greater rate the cord would break. However, we know that the cord did break, therefore we can say that for the chord to break the inequality a>3.53 must be true. You however, are quite correct, if the elevator accelerated at exactly 3.53m/s², then the cord would not break. If the acceleration was only slightly greater than this value then it would break. Therefore, this value of acceleration is said to be the minimum value at which the cord will break.

I hope that makes sense.

 

[m2003]

The 200 N value is used because it is the maximum tension that the cord can withstand before breaking. This value is important because it determines the maximum force that can be applied to the cord without breaking it. In this problem, the tension in the cord is equal to the weight of the monkey, which is 15.0 kg times the acceleration due to gravity (9.8 m/s^2). So, if the elevator accelerates with an acceleration greater than 3.53 m/s^2, the tension in the cord will exceed 200 N and the cord will break. Therefore, the minimum acceleration of the elevator must be equal to or less than 3.53 m/s^2 in order to prevent the cord from breaking.