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![[Post New]](/templates/default/images/icon_minipost_new.gif) 22 Mar 2008 20:51:15 IST
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A simple one
Thermo challenge
A copper and a tungsten plate having a thickness of 2 mm each are riveted together at 00C 2 form a bimetallic strip
Find the average radius of curvature of this plate at 2000C
The coefficients of linear expansion for copper and tungsten are
1.7*10-5 and.4*10-5 K-1 respectively
edited:10-5K-1 not 10-1K-1
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edit
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22 Mar 2008 20:59:03 IST
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have u missed out the initial length??
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22 Mar 2008 21:13:33 IST
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nope
not required (though im not supposed 2 mention it)
This shud give u a clue
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22 Mar 2008 21:18:21 IST
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edit
sorry i did complete crap...:
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22 Mar 2008 21:32:08 IST
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edited:
din c u chng value
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22 Mar 2008 21:35:15 IST
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Isn't it 19 units
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22 Mar 2008 21:35:39 IST
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r@=l(1+a2 T)
(r+4)@=l(1+a1 T)
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22 Mar 2008 21:43:09 IST
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870mm
P.S:872.5217402
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22 Mar 2008 22:18:28 IST
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Hint:
For the formula, u gotta use mean radius
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22 Mar 2008 22:31:15 IST
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0.86m
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22 Mar 2008 22:42:22 IST
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Here's my attempt:
When they expand together, they form something like a part of a circle, though not exactly a circle. Let the angle subtended at the center of this so called circle be @ radians.
Now, for copper, we have l1 = l(1+at)
For tungsten, we have l2 = l(1+bt) where the terms on LHS are the lengths after expansion. Hence, we get, from simple trigonometry,
l1 = (R+d)@
l2 = (R-d)@
Hence, subtracting, we get :
2d@ = l(a-b)t
But @ = l/R (This is where my mind is full of doubts... I've taken l almost equal to l1 or l2... :( Probably this might screw my solution)
Hence, using this, we get:
2d/R = (a-b)t
where 2d = 2mm
Hence, on putting values, we get R to be about 74 cms.
edit - I did the calculations using a calculator now, and the exact ans is 76.8797cm
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Will nip in at times to solve problems :)
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22 Mar 2008 22:43:41 IST
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okay... ans is right :)
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Will nip in at times to solve problems :)
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22 Mar 2008 22:51:39 IST
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question is find radius
n 4 u tht turns out to be 434mm
but ans is in 700s
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22 Mar 2008 23:35:27 IST
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karthik expain:
acc 2 u :
2d/R=2.3*(10^-5)*200
=>1/R=2.3*10^-3
so R=1000/2.3
how is tht 770mm??
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