30anybody?
Q. A slightly conical wire of length L and end radii r1 and r2 is stretched by two forces F, F applied parallel to length in opposite directions and normal to end faces. If Y denotes the Young's modulus, then extension produced is ?
Since, the cross-sectional area changes at different points of the wire, we have to take a small element in the wire. But, I'm blank out here. Please help on how to proceed.
-
UP 0 DOWN 0 0 3
3 Answers
1total extension= sum of all little extensions
a little extension to which an element at x from the bottom is subjected to is
∂(change in length)= L(x)∂x / E* A(x) by hooks law
so
all we need to do is sum up all the ∂(change in length)
find L(x) = load at x distance from the lower part, by considering a free body diagram
= ∫ A(x) *(density)*dx from 0 to x
find A(x) which is Area as a function of x
= r(x) ^2 * pi, find r(x) using the linear variation relation
and integrate L(x)∂x / E* A(x)
tell me if you still have problems.