A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 700 N is applied to each end of the wire. What minimum diameter is required for the wire?

Video transcript

Welcome back everybody. We are looking at the tendon of a ring finger and we are told that a tangential force is applied to it of 400 newtons. Now this tendon can be modeled as a cylinder with a young's module asse of 1.2 times 10 to the ninth scowls. Now we are tasked with finding what the diameter of our tendon is. Well, diameter is just two times the radius. And we're gonna use this fact in conjunction with this other formula that our youngest modular is equal to this force. This tangential force times the initial length over the area of the cross section of the ring finger, tendon, times the change in length of the ring finger tendon. Now one last thing that we are told here is that this ratio between the change in length over the initial length is equal to the tensile strain Of the Tendon which is given as 6% or 0.06. So let's rearrange this equation to where we can find variables that that we can use here. Well, rearranging this, we get that the area is which area of a cross section of a tendon. If it's modeled as a cylinder is just gonna be a circle. So we have pi R squared is equal to our force divided by our youngest module is times delta L over L. Not, which as you'll see, is our tensile strain. So rearranging this a little bit more to isolate our radius. We have that our radius is equal to the square root of our force divided by pie. Times Are Young's module lists times our tendon. Let's go ahead and plug in our numbers here we have that. This is 400 divided by pi times 1.2 times 10 to the ninth, times 0.6. Which when you plug this into your calculator, you get that. The let's see here, the radius of our tendon Is let's see here, one .33 times 10 to the negative 3rd m or 1. millimeters. Now, this is just our radius. So in order to find our diameter a diameter is equal to two R. So two times are 1.33 mm is going to give us our diameter of 2.66 mm corresponding to our final answer. Choice of D Thank you all so much for watching. Hope this video helped. We will see you all in the next one.