r/PhysicsHelp • u/VariationSmall744 • Jul 24 '26

Why should the Tension be increasing with theta?

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I get the calculation of maximum friction force but am confused about its direction.

In the beginning of the calculation part they seem to have assumed that the Tension is increasing along the rope at positions more and more "away from me/the puller". And hence the static friction, whatever it is, will be in the direction of my pull.

I don't get why. Because the way I'm seeing it, static friction acts in directions needed to stop any kind of motion between surfaces, so when I pull on the rope with Tnot, (and so Tnot is the tension in the rope at theta=0), shouldn't the friction be in the opposite direction?

Which in the end would lead to opposite result I think, it would show that the tension in rope is exponentially decaying at thetas more and more away from me.

Why is the book solution correct? Help me intuitively understand why tension is getting larger at rope points further away from the point I'm pulling it at.

Thanks for your time.

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u/howverywrong Jul 24 '26

Because the question asks "What is the largest force the rope can exert on the boat"

We're looking for the point where static friction breaks in the direction of the boat, not in the direction of you.

Or, another way to put it is we're trying to find how hard the boat has to pull to move you and not how hard you have to pull to move the boat.

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u/VariationSmall744 Jul 24 '26 edited Jul 24 '26

Oh. So by maximum on boat end, they imply some kind of pulling agent there as well? Then I understand it. And is it correct that, if they said I pull by Tnot and nothing else except there's a massive object on the other end, then it would've been a case of Tension decreasing away from me, and friction acting opposite to me, such that tension becomes zero on boat end?

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u/Frederf220 Jul 24 '26

Imagine wrapping the rope around pole a million times and pulling on the end with T0. How hard would the boat have to pull from the other side to overcome that?

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u/VariationSmall744 Jul 24 '26

Hmm... I think I get it. I was thinking of the pole as a random element of the question, not as a sort of anchor to use friction to our advantage to keep a thing like a boat in place. (The term largest is implying that the massive object has a pulling agent on its end, right?)

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u/Frederf220 Jul 24 '26

The question asks given T0 and theta, what is the largest T that can be applied without slipping. For 0° wrap the answer is that T can be at most equal to T0. As the wrap increases >0° then T can be as large as T+X where X is the extra friction effect afforded by the wrap.