Calculating Poisson ratio is a way to measure a material's response to stress.

[buxZED]

Homework Statement

question

A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa

Homework Equations

E=stress/strain

The Attempt at a Solution

my attempt

D original = 0.01m
change in D = 0.000007m
F=15000N
E= 100*10^9

V = passonse ratio = (change in D/D original)/(change in L/ L original)

we can replace (change in L/ L original) by (stress/E)

so

V=(change in D/D original)/(stress/E)

(change in D/D original) = (0.000007/0.01)
(stress/E) = (F/Area)/E
A= pi(0.01/2)^2

that gives me an answer of V = 0.21



but the tutorial sheet says the answer is 0.33

can you explain where i have gone wrong

 

[vela]

Your method looks fine to me, though I got ν=0.27.

 

[buxZED]

Your method looks fine to me, though I got ν=0.27.

elongation D = (4*F*V)/(pi*Doriginal*E)

is this a valid eqation??

 

[vela]

elongation D = (4*F*V)/(pi*Doriginal*E)

is this a valid eqation??

That might look more familiar if you divide both sides by D and rearrange it slightly:

$$\frac{\Delta D}{D} = \frac{4 F \nu}{\pi D^2 E} = \frac{F}{\pi(D/2)^2 E}\nu = \frac{F}{AE}\nu$$

where $A = \pi(D/2)^2$ is the cross-sectional area.

 

[buxZED]

That might look more familiar if you divide both sides by D and rearrange it slightly:

$$\frac{\Delta D}{D} = \frac{4 F \nu}{\pi D^2 E} = \frac{F}{\pi(D/2)^2 E}\nu = \frac{F}{AE}\nu$$

where $A = \pi(D/2)^2$ is the cross-sectional area.

why dose using this equation gives me a different answer for passoinse ratio?

 

[vela]

It shouldn't. I suspect you're just making other errors while calculating or rounding off too much on intermediate steps. After all, I did the exact same calculations you did in your original post and got 0.27 while you got 0.21.

 

[buxZED]

It shouldn't. I suspect you're just making other errors while calculating or rounding off too much on intermediate steps. After all, I did the exact same calculations you did in your original post and got 0.27 while you got 0.21.

i don't get it an I am confused
can u do a quick run true and tell me they are same?