SOLUTION: The stiffness of a beam varies jointly as its width and thickness and inversely as the square of its length. Find the change in stiffness if each of the three dimensions is increas
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Question 1047396: The stiffness of a beam varies jointly as its width and thickness and inversely as the square of its length. Find the change in stiffness if each of the three dimensions is increased by 10%.
Answer by mathslover(157) (Show Source): You can put this solution on YOUR website!
Let the stiffness be denoted by S, the width be denoted by w, the thickness by t and the length by l
Given S = k (w*t)/l^2 where k is a constant.
if all the dimensions are increased by 10% the new dimensions are 1.1w, 1.1t and 1.1l . So the new stiffness (S1) is
S1= k(1.1w*1.1t)/(1.1l)^2
S1=k(1.21wt)/1.21l^2
=kwt/l^2
S1-S = kwt/l^2 -kwt/l^2
=0
Hence, there is no change
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