Problem

$\bullet$$\bullet$ Block $A$ in Figure 5.64 weig…

04:29

Problem 70 Hard Difficulty

$\bullet$$\bullet$ The stretchy silk of a certain species of spider has a force
constant of 1.10 $\mathrm{mN} / \mathrm{cm}$ . The spider, whose mass is 15 $\mathrm{mg}_{1}$
has attached herself to a branch as shown in Figure 5.63 . Cal-
culate (a) the tension in each of the three strands of silk and (b)
the distance each strand is stretched beyond its normal length.

Answer

a) $14.02 \times 10^{-5} \mathrm{N}$
b) $1.336 \times 10^{-3} \mathrm{m}$

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Physics 101 Mechanics

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Video Transcript

Okay, so you start off with the free body diagram of the situation to have three strings string a three strands, strand a strand, be instruments, See through their intentions and each a different angle from the vertical s o. We first know that T c attention and stand C is equal to the weight of the spider. So that's 15 milligrams milligrams ar 15 times 10 to the negative three grams. Uh, so that's multiplied by 10. And like doing again for kilogram value. So 15 times in a layer of six kilograms, its mass, uh, tons. She pointing yes for second square. That gives us one point for seven times 10 to the negative floor mutants and tell this problem use of exponents will be essential. So that's Ah, that's the attention and string. See, uh, next we, um, we resolve forces. Right? So let's do it, Partner. Uh, Miz all forces in the ex direction. You have no net force. So that means that the ex component of T air will be called to the ex component of TB. Answer acting opposite directions. So, t heir, uh, we want so Okay, so this is 30 degrees. Um And so from the vertical from the horizontal, you have 60 degrees. And similarly, since that is 70 degrees with from the radical for T B from the horizontal angle is 20. All right, so, uh, the horizontal part of T A S t a co signed 16. That's a call to the horizontal compos T b. Okay. Oops. Teo co signed 20. That's O T B. It's just tea. Air Times Co signed 60 over co signed 20. And that comes out to be about point. Um, but 532 can't steer, um, for for the y direction. Now we're going to resolve forces again. And huh? And again, no, no force in the UAE Directions and equilibrium. So we have the vertical components of T and T TV Announcer t assigned 60 plus to be, uh, sign 20. They're acting member, the same directions upwards that will be equal to and she able to both I guess a t c. Which is in court with you. Does he call it T C, which is called G self? We can. What we can do is take tear comin by, replacing TV by this 0.5 to 2 ta about. Okay, so that's what we do here. Signed 61.5 32 time sign. 60 books 20 so that he has us and she is one point for a seven times 10. Warn Eaton's It's a T heir comes out to be 1.4 times 10 to the negative score. No, therefore, to be here's 0.5 to 2 times. That's so that's it's closer to 7.5 times 10. All right. Okay, so that was part and part B. We use hooks law. Ethical. I can't next. So we want to find X for all these. Absolutely Doing a carriage. Uh, okay. Is one point of it's give it. It would see what it's given us. Given us one 0.1. Millie Mutants. One point 1,000,000 Asians for senators for analysis. Converting per centimeters s 0 1,000,000 sterling of three sorts, 1.1 middens centimeters. Yes, that's care. And so, Mel, let's find X for all of them. So if it's just the tension in each strand, so for strength and you have a sub bay over can And so that's one point four times. Tena lady for Newton's over 1.1 times 10 to the negative Newtons for centimeters and get something in terms of centimeters snow. So that comes out to be, um, 0.13 centimeters. Similarly, for Strand B of B over care and F B is just tension and B never care. And you work that out, Tio and so t be a 7.5 ten 10 5 Divide that one times 10,000,000 3 You get point 068 centimeters, which, by the way, is also 0.68 millimeters. And lastly, Miss Francie, you just take tension and strength. See insurgency divide. That bike is constant. It's, uh, it's chancy. Tension is on 0.47 10th inning. The floor's a little more than tension. Hey, and so you worked that out and you get 0.1 teo centimeters and that's it.

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