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A wire can withstand the tension $T_{max} = M_{max}\cdot g$. If we hang on an object with the mass of $m = \frac{M_{max}}{10}$ at the end of the wire, how much $g$ can the wire be accelerated? ($g$ is gravitational force)

I've tried equate them

$T_{max} = M_{max}\cdot g = \frac{M_{max}}{10}$

and found the answer as $9g$. However, I'm not sure.

Regards!

Displayed
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1 Answers1

2

HINT

We have that (neglecting the wire mass)

  • initial tension: $T_0=mg=\frac{M_{max}}{10}g$
  • increment in tension due to an up acceleration $a$: $\Delta T=ma=\frac{M_{max}}{10}a$

then the total tension in the wire is

$$T=T_0+\Delta T=\frac{M_{max}}{10}(g+a)$$

user
  • 154,566
  • Is my answer correct? – Displayed May 04 '18 at 15:57
  • @Displayed You can check directly form the last equating $\frac{M_{max}}{10}(g+a)=M_{max}g$ and finding out $a$. – user May 04 '18 at 15:58
  • That was an olympiad question. I'm so excited to see the correct answer. So, am out of my mind right now. – Displayed May 04 '18 at 16:01
  • Is it correct? :) – Displayed May 04 '18 at 16:10
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    @Displayed If I have intepret the problem correctly by the givens, yes from $\frac{M_{max}}{10}(g+a)=M_{max}g$ we obtain easily $a=9g$. The only doubt is that if it is an olympiad question it seems too easy to solve. To be sure, do you have the original full text or the official solution? – user May 04 '18 at 16:14
  • I don't believe in myself! I really have 20 correct answers of 23! You're awesome now dont know what to write oh wait ! Sorry am so excited right now oh lol! You gave me the biggest prize! and yes I'd like to know the full solution. – Displayed May 04 '18 at 16:15
  • @Displayed You are welcome! I'm happy if my hint has been useful! Bye – user May 04 '18 at 16:19
  • Also in particle physics or anything, does this seem correct $I_0 \frac{1-(v/c)^2}{1+(v/c)^2}$? – Displayed May 04 '18 at 16:22
  • I had a conceptual question if you can reply. – Displayed May 04 '18 at 16:24
  • @Displayed Of course if I can, what is the question? – user May 04 '18 at 16:25
  • In optics, if the refractive index of a medium is $4/3$, what would you say for rays? For example, you're at an aquarium and take a look at the window(with the refractive index of $4/3$ where fishes are located. What is the magnification? – Displayed May 04 '18 at 16:30
  • @Displayed I should revise this topic. In case you can try to ask on Physics.SE! :) – user May 04 '18 at 16:31
  • Or imagine you have a capillary tube in a medium whose refractive index is $n = 2$. You notice that the radius of capillary tube is $1.50mm$ What is the real radius of capillary tube? The best answer seems to be $2.00mm$, right? – Displayed May 04 '18 at 16:33
  • what do you think? – Displayed May 04 '18 at 17:07
  • @Displayed I'm really sorry but at the moment i can't answer on this particular topic, I should revise the subject about optics. As suggested you coul ask for specific physics answer on Physics.SE! Bye – user May 04 '18 at 17:08
  • Just a reminder, gimusi, this user asked this trolling non-sense question yesterday: https://math.stackexchange.com/questions/2765393/is-it-correct-to-say-a-g-sin-frac-alpha2. Remember it? Anyways, I guess no harm done in your answer. Cheers! – amWhy May 04 '18 at 17:34
  • @amWhy Ops, is he the same! I didn't recognize him! at least this question seems to have more sense than the question made Yesterday. Cheers! – user May 04 '18 at 17:39
  • @gimusi The answer $9g$ is correct,right? – Displayed May 04 '18 at 17:58