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

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= 1.6 AB; the Young's moduli of the cylinders are related by EA= 3.0 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 dBfor cylinder B. (c) What is the ratio dA/dB?

Explanation / Answer

(a)    in the given problem as the brick is nowhorizontal and the cylinders were initially the dsame lengthl then both have been    compressed an equal lengthdell    so we get that    dell / l = F A /AA EA    dell / l =FB / AB EB    FA / FB= AA EA / AB EB                 =...........    if we combine this ratios with the equationthat    FA + FB = W    FA / W = ......... (b)    FA / W = ......... (c)    taking the torques about the centre of masswe get that    dA / dB =FB / FA                 =...........    if we combine this ratios with the equationthat    FA + FB = W    FA / W = ......... (b)    FA / W = ......... (c)    taking the torques about the centre of masswe get that    dA / dB =FB / FA

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