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 2.6 Ag; the Young's moduli of the cylinders are related by EA= 1.9 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 dg for cylinder B. (c) What is the ratio dalds? com of brick (a) Number (b) Number (c) Number Unit Unit Units

Explanation / Answer

Area of A, AA =2.6 AB
young modulus of A , EA=1.9 EB
The fraction of the brick mas sis supported by A
A)
Since (Strain )A = (Strain) B
(?l/L)A = (?l/L)B
f A/A E A =f B/AB E B
so F A/F B =(A A/AB)(E A/E B)

Putting,

AA= 2.6 AB

EA= 1.9 EB

FA/F B= (2.6A B/AB ) *(1.9E B/EB ) = 2.6*1.9 = 4.94

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b)Now ,

FA= 4.94* FB

Equilibrium of vertical Forces considering"w" be the weight of the brick
FA +FB =w  
4.94 FB+ FB=w
5.94 FB =w
FB=w/5.94 (ans part (b))

FA= 0.831 w (ans part (a))

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c)
For the moment of force
FA* d A =FB*dB
dA/dB = FB/FA= 1/4.94

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