More logic than math

Geometry Level 1

I have a 30 centimeter-long fishing line that weighs 7 grams, and a 30 centimeter-long string (like yarn) that weighs 10 grams. If I grab both of the ends of both objects and bring my hands closer, then which vertex would be closer to the ground?


Note: By vertex , I mean the lowest point of the "droop" the two objects make as shown below:

Bonus: Why?

The fishing line The string The vertices would be the same

Blan Morrison by Blan Morrison , 18, USA

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5 solutions

Weight doesn't matter (it's just there to bamboozle you). Both the fishing line and string are of the same length so both vertices are the same.

12 Helpful 0 Interesting 0 Brilliant 0 Confused
Blan Morrison
Dec 3, 2017

Regardless of the weight of the string, the vertex will always be the same. What matters is how long the string is, and the distance between its two roots. Since the two strings share both of those factors they will (essentially) have the same vertex. β ⌈ ∣ ⌉ ~\beta_{\lceil \mid \rceil}

9 Helpful 0 Interesting 0 Brilliant 0 Confused

But what about density. Their value is same but masa is diffrent. String is more dense then fishing kine that makes it stronger. Thing about 30cm steel wire. İt wont bent.(sorry for bad english).

Ata Temur - 3 years, 5 months ago

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Weight doesn’t matter only if the strings are inextensible. If the strings are elastic then Young’s modulus, density and diameter will influence the answer

Alpesh Hirani - 3 years, 5 months ago
Harsh Mishra
Feb 17, 2018

Weight doesn't matter here. Both have same length and thus will have same vertices

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Alpesh Hirani
Dec 30, 2017

Weight doesn’t matter only if the strings are inextensible. In which case both strings will take the same shape. If the strings are elastic then Young’s modulus, density and diameter will influence the answer

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Correct Saying the vertex remains the same height above the ground requires the strings to be inelastic

Vincent Wood - 2 years, 8 months ago
MegaMoh .
Sep 14, 2020

simply imagine when his hands get so close that they touch, the string and fishing line, intuitively and logically, would be the same length.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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