<p>If the rope wasn’t massless, then the tension in the rope isn’t constant, making majorineverything’s solution invalid.</p>
<p>@Andrelguodala The rope has a mass, but the tension in the rope is nonetheless still constant - the problem stipulates that the helicopter is moving at constant velocity, and asks for the shape/orientation of the rope.
This suggests it must be in equilibrium - the problem simply doesn’t make sense if the orientation is not constant. There are three forces on the rope - gravity, tension, and resistance. Refer back to my longer post for more detailed explanation.
Gravity must balance with the vertical component of tension, and resistance must balance with the horizontal component. The string is only in horizontal equilibrium for ONE value of θ, implying that the curve must be a line (equal inclination).
Keep in mind that in order to do this analysis, you must look at a small segment of rope - a differential mass/length, to be more specific. By tension, I mean the net tension force on a piece of rope - at any place there is a tension pulling up (supporting that piece and the ones below it) and a tension pulling down (supporting the ones below it). These cancel to some extent, leaving only the net tension force on the segment you’re focusing on, isolating it from the rest of the system.</p>
<p>If the tension is constant, then the tensions at the top and bottom of the rope should be the same. This doesnt make sense, because at the top of the rope the tension has to balance the weight of the whole rope, while at the bottom it doesn’t.</p>
<p>@Andre, sorry about this. What major means is that the net force of tension acting on each differential mass segment is constant. You are correct to say the tension is higher at the top. However, on each segment there acts a tension force from the top and one from the bottom. The top and bottom add together at each rope segment to form the same constant value for tension.</p>
<p>@Andrelguodala Yes, I’m sorry if I wasn’t clear, but I did specify that I mean the net tension, or the part of the tension that supports only a specified segment of the rope, is constant for any segment of equal size. This means the tension at any point increases linearly along the rope.</p>
<p>Quoted from my last post:
“Keep in mind that in order to do this analysis, you must look at a small segment of rope - a differential mass/length, to be more specific. By tension, I mean the net tension force on a piece of rope - at any place there is a tension pulling up (supporting that piece and the ones below it) and a tension pulling down (supporting the ones below it). These cancel to some extent, leaving only the net tension force on the segment you’re focusing on, isolating it from the rest of the system.”</p>
<p>You can also think of it like this. Each element of the string must experience zero torque total. The only two things applying torque are gravity and the force of air resistance. This is how the angle is determined. Since the force of gravity does not change from rope element to rope element (it’s a uniform rope), and the force of air resistance does not change (for that same reason) the angle must be the same at each point. So it must be straight.</p>
<p>Does anyone know what time the results are coming out?</p>
<p>this argument was a pleasure to read</p>
<p>it’s like an argument on whether candidate A or candidate B will win an election a day before the election actually happens: there’s no clear answer that everyone agrees on, and the answer will be released in a day anyway, which makes it even more pointless</p>
<p>speaking of which, how much longer is the wait?</p>
<p>Of all the arguments I have seen on CC, the aforementioned standoff has to be one of the greatest, ever. </p>
<p>Any of you guys on the west coast? </p>
<p>It’s not a standoff - everyone with a real, logic-supported answer is agreeing. </p>
<p>I just want the results :P</p>
<p>west coast here.</p>
<p>@gatsby, except there is no “correct candidate” that must win.</p>
<p>and there is no given time that results come out</p>
<p>results are out for me :D</p>
<p>How do you get results?</p>
<p>web assign</p>
<p>.</p>