In the figure a lead brick rests horizontally on cylinders A

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= 2.9 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 dB for cylinder B. (c) What is the ratio dA/dB?

Solution

we know

F/A = YdL/L

Since the brick is now horizontal and the cylinders were initially the same length L,

then both have been compressedan equal amount dL by young moduli

FA/FB = AA*EA/(AB*EB)

=> FA/FB = 1.6AB*2.9EB)/(AB*EB) = 1.6*2.9 = 4.64

W = FA + FB = 4.64 + 1 = 5.64

A)

by cylinder A = 4.64 /5.64 = 0.8226

B)

by cylinder B = 1 /5.64 = 0.1773

C)

Ta = FdA*sin(thetha)

Ta = Tb

FdA*sin(90) = FdB*sin(90)

=> dA/dB = FB/FA = 0.1773/0.8226 = 0.21553