this is incomplete argh

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this is incomplete argh

Mathematics
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|dw:1443611451350:dw|
|dw:1443611647543:dw|
Find the minimum value of \(v\) given all that.

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In the vertical direction,\[\frac{a}{\sqrt{2}} + b\frac{\sqrt{3}}{2} = 5g\]
In the horizontal direction,\[\frac{a}{\sqrt{2}} + \frac{b}2 = \frac{5v^2}{1.6}\]
\[v = \sqrt{0.32 \left(\frac{a}{\sqrt 2} + \frac{b}{2}\right)}\]http://www.wolframalpha.com/input/?i=minimise+sqrt%280.32*%28a%2F2+%2B+b%2Fsqrt%282%29%29%29+constrained+to+sqrt%283%29%2F2*a+%2B+b%2Fsqrt%282%29+%3D+50
Can someone please help me??????
http://www.wolframalpha.com/input/?i=solve+%5Cfrac%7Ba%7D%7B%5Csqrt%7B2%7D%7D+%2B+b%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D+%3D+5*9.8%2C+%5Cfrac%7Ba%7D%7B%5Csqrt%7B2%7D%7D+%2B+%5Cfrac%7Bb%7D2+%3D+%5Cfrac%7B5v%5E2%7D%7B1.6%7D%2Cb%3D0
seriously people?!?!?!
we want to find the minimum value of \(v\), not the exact value of \(v\) so the problem is fine i think
yes, and it's turning out to be zero.
the greater the linear velocity, the greater will be the tension in wires in which wire do you think the tension will be more ?
the minimum value will occur when the tension in the lower string/rod = 0
for a given linear velocity, which wire experiences more tension, AC or BC ?
https://www.desmos.com/calculator
ooo, I forgot to add the fact that a>0, b>0
http://www.wolframalpha.com/input/?i=minimise+sqrt%280.32*%28a%2F2+%2B+b%2Fsqrt%282%29%29%29+constrained+to+sqrt%283%29%2F2*a+%2B+b%2Fsqrt%282%29+%3D+5*9.8%2C+a%3E0%2C+b%3E0 about 3 m/s
if you start it spinning from zero, all the tension will be in the longer string so in the plot follow that red circle out to where it meets the blue circle. that is the cross over
@IrishBoy123 Agree! By intuition, I believe that any one time, only one wire will be in tension. There is (perhaps) exactly one value of v that will give T1>0 and T2>0 on both wires because of the physical arrangement. (assuming the wires don't take compression).
yeah, @mathmate if these are rods ....
Yes, the minimum occurs when the tension in the lower string is zero.
In other words, you mean that if we want to decrease velocity, we increase the radius.
Thanks guys.
this is what i meant to share in that link...when i was talking about red and blue circles |dw:1443613483068:dw|
wait, I'm confused again.
what are those red and blue circles?
|dw:1443613751302:dw|
circles show the radii of the taut strings
oh.
assuming these are strings, if you started at v = 0 and slowly increased the rotat speed, it would be supported by the red string [the higher one] until you reach crossover
so analyse it as a 1 string prpblem where you know that the one string has to reach an angle of 30 degrees \(T = \dfrac{mv^2}{r \sin 30} = \dfrac{mg}{ \cos 30}\)
this is great! thanks!
@irishboy Exactly. I have done just that, and there is no point where both wires are taut. Analyzing separately, the long wire will attain 30 degrees at about 3 m/s. The short wire will attain 45 degrees at almost 4 m/s. So there is no point (velocity-wise) where both wires will be taut.
cool!
Can someone please help me??
Help Me ...Easy Medal ^^^
Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = -3x4 - 2x - 5 Neither Even Odd

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