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11) A metal wire of diameter 0.68 mm and natural length 1.5 m is fixed firmly to the ceiling at one end. When a 6.8 kg mass is hung from the free end, the wire extends by 2.8 mm.

Calculate:

a) the stress in the wire

B) the Young modulus of the material of the wire.

 Dec 2, 2017
 #1
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FIRST find the VOLUME of the wire:

pi x r^2 x l = 5.45 x10^-7 m^3

 

THEN find its diameter given the NEW length of 1.5028 M

 

pi x r^2 x l = 5.45 x 10^-7    results in r =3.3968 x10^-4 m

then, as before   Stress = F/A      F= ma  = 6.8(9.8) = 66.64 newtons

A= area = pi x r^2    where r is the 'new ' stretched r   

     Let me know what you come up with for an answer and we will continue.....   ~EP

 Dec 2, 2017
 #2
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If you have the correct answer for stress (I got 1.83838 x 10^8 P )

 

 then, (I had to look this one up !)

Young's Modulus =  Stress / (\( \Delta \)L/ Lo)         \(\Delta \)L = change in length = .0028 m     Lo=1.5 m   (given)

 Dec 2, 2017
 #3
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Hi ElectricPavlov,

It is great to see you on the forum again  laugh

 Dec 3, 2017
 #4
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Thanx, Melody !    

ElectricPavlov  Dec 3, 2017

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