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I have been browsing for a few hours now and I can't seem to find a reason for why this assumption is made for calculations and such in engineering problems like statics. It's a little embarrassing to be where I am now and not fully understand this, but I know it comes down to a lack of understanding in physics/mechanics. So here I am with the question:

Why do we consider the tension in a taut cable to be zero Newtons or Pound Force? For example, if I pull on a cable, with a force P, that is attached to a fixed joint/point on a wall and I say the cable is taut, the tension in the cable can be assumed to be zero. Typically I see this sort of assumption in "finding the range of values" type of problems.

I assumed that if the cable is taut it must be under tension due to the applied force, so therefore the tension must be greater than zero, but I was wrong. Wouldn't a tension of zero be due to slack in the cable?

I understand that this isn't a do-my-homework forum and this isn't meant to be that kind of question, but if it appears to be, please let me know and I'll work my magic to change it up. Also, if this has been answered before, I'd greatly appreciate the link. Thank you in advance to those who are willing to help me out with my lack of physics knowledge and I'm excited to hear what you all have to say!

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  • $\begingroup$ A cable cannot be taut if it has zero tension (unless you are in space). $\endgroup$ – Yashas Apr 25 '17 at 3:23
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    $\begingroup$ Net force on a cable is zero if the cable is not accelerating. This does not imply anything about the tension in the cable. $\endgroup$ – Whit3rd Apr 25 '17 at 4:48
  • $\begingroup$ @Yashas Whether it's in space doesn't seem to be relevant. A cable can be positioned to be perfectly straight on Earth or in space. But a taut cable is always under tension, by definition (etymonline.com/index.php?term=taut). $\endgroup$ – Chemomechanics Apr 25 '17 at 5:40
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If a cable is taut, then it is under tension. What you may be remembering is that, in a static situation, the total force on the cable must be zero because it is not moving. In the simplest situation of a cable being pulled at both ends, the tension forces at opposite ends are equal in magnitude and opposite in direction. This means that the total force on the cable is zero, not the tension.

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  • $\begingroup$ Excellent. So with this in mind I read over someone who posted the following: "The tension being zero is right at the moment of transition between the string being taut and the string being slack; usually in "particle on a string" problems you have to find the minimum or maximum of some value, and usually the trick is to take the tension equal to zero as this is where the string is "barely" taut." I'm just not really grasping why this is. Thank you so much for the help. $\endgroup$ – mr_trytobeanengineer Apr 25 '17 at 23:30
  • $\begingroup$ For a concrete example, consider a ball on a string being swung in a vertical loop. If you want to know the minimum speed of the ball such that the string remains taut, you find the point of minimum tension, set that to zero, and then solve for the velocity. In this case, that would be at the top of the circle where gravity and the string tension both point in the same direction to keep the ball in a circular motion, thus requiring less tension. If the ball moved slower, then gravity provides too much centripetal force, and the balls falls inside the circle, leaving the string slack. $\endgroup$ – Mark H Apr 26 '17 at 5:45

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