In the figure, a lead brick rests horizontally on cylinders A and B. The areas o

Question

In the figure, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by AA= 1.5 AB; the Young's moduli of the cylinders are related by EA= 2.4 EB. The cylinders had identical lengths before the brick was placed on them. What fraction of the brick's mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are dAfor cylinder A and dg for cylinder B. (c) What is the ratio dA/dB? com of brick

Explanation / Answer

stress = E strain

F/ A = E (deltaL/ L)

deltaL = F L / A E

FA L / (1.4 AB) (2.4 EB) = FB L / EA AB

FA = 3.36 FB

fraction of FA = FA/(FA + FB) = 3.36 Fb / 4.36Fb

= 0.77

(B) fraction of FB = 1 - 0.77 = 0.23   

(C) FA dA = FB dB

dA / dB = Fb / FA = 1/3.36 Or 0.30

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