How Far Should a 100kg Mass Be Placed from Point A to Keep a Rod Horizontal?

[shalikadm]

A light rod is hung by two wires having same length of 2m and the same young's modulus of 8$\times$10¹¹Pa,but having different cross sectional areas of 1mm² and 2mm².
The wire having the cross sectional area of 1mm²,gets an increment of 2mm in length because of a temperature increment.But the other wire remains same..
A mass of 100kg is meant to be put on the rod to keep the rod horizontal..How much distance has it to be on the rod from point A...?

PLEASE SOLVE THIS CITING REASONS...thanks !

 

[tiny-tim]

welcome to pf!

hi shalikadm! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[shalikadm]

Several things

i want to know what the necessity that is to be fulfilled in order to keep it horizontally.
whether it is to have same extension(e) for the two wires
or to have the same total length(l+e) for both of the wires...
or to fulfill e_1mm²+2mm=e_2mm²
want to know whether to get the original length(l) of the 1mm² wire as 2m or 2m+2mm

Y=$\frac{Fl}{Ae}$

please help me...

 

[tiny-tim]

after the temperature increment, one wire is longer

apply the young's modulus equation to those lengths

(of course, you need to extend both wires, to make them the same length)

 

[shalikadm]

is it like this ?

$\downarrow$
for the 1mm²wire,
Y=$\frac{T1*2.002}{1*10^-6*e1}$$\Rightarrow$1

for the 2mm²wire,
Y=$\frac{T2*2}{2*10^-6*e2}$$\Rightarrow$2

hence 1=2 ,
$\frac{T1*2.002}{1*10^-6*e1}$=$\frac{T2*2}{2*10^-6*e2}$$\Rightarrow$A

also,
T₁+T₂=1000$\Rightarrow$B

and also ,
taking moment around the center of 100kg's gravity$\Rightarrow$C

and then solving the A,B,C equations ?
is that right ?

 

[tiny-tim]

yes, but you'll also need an equation relating e₁ and e₂

(btw, please don't make the latex equations larger …

it's not necessary …

each reader can permanently adjust equation size by right-clicking on any equation and choosing "Scale All Math" )​

 

[shalikadm]

how can i get a equation relating e₁ and e₂ ?
sorry for larger Latex...

 

[tiny-tim]

how can i get a equation relating e₁ and e₂ ?

it'll be the equation saying the two wires are the same length

 

[shalikadm]

Is it this ?(i have no idea)
e_1mm²+2mm=e_2mm²

 

[tiny-tim]

Is it this ?(i have no idea)
e_1mm²+2mm=e_2mm²

yes, so it's the same total length for both wires

 

[shalikadm]

hope this help me...thanks a lot...!