I hiave a question that I am having a bit of a problem with, i wonder if anyone could help. I don't know where to go with it after the point i have reached already. The question is:
The coefficient of rigidity n of a wire of length L, and uniform diameter d is given by
Where (alpha) is a constant. If errors of up to + or - 0.1% & + or - 0.5% are possible in measuring L & d respectively, determine the maximum percentage error in the calculated value of n, assuming (alpha) is known exactly.
I have sdone the following so far.
|(delta)L/L x 100| less than or equal to + or - 0.1, |(delta) d/d x 100| less than or equal to + or - 0.5
n = (alpha)L/d^4 => n(sub)l = (alpha)/d^4, n subd = -4 (alpha) L / d^5
(delta)n approx. = n subL + n subd x (delta)d
=> (delta)n approx. = (alpha)/ d^4 (delta)L - 4(alpha)L/d^5 x (delta)d
=> (delta)n/n approx. = d^4/(alpha)L [(alpha)/d^4 x (delta)L - 4(alpha)L/d^5 x (delta)d]