Q.374. Center of mass

Question 374.
The assembly is made from a steel hemisphere, ρ_st= 7.80 Mg/m³, and an aluminum cylinder, ρ_al= 2.70 Mg/m³. Determine the height h of the cylinder so that the mass center of the assembly is located at z(bar)= 160 mm.

Answer 374.

Mass of steel hemisphere, m1

= (2/3) π r1^3 * ρ_st
= (2/3) π (16)^3 * (7.8) g
= 66913 g

Mass of aluminium cylinder, m2
= π r2^2 h * ρ_al
= π (8^2) h * 2.7 g
= 543h g

 => 16 = [m1 * (5/8) * 16 + m2 * (16 + h/2)] / (m1 + m2)
=> 16m1 + 16m2 = 10m1 + 16m2 + (m2/2) h
=> (m2/2) h = 6m1
=> (543/2) h^2 = 6 * 66913
=> h^2 = (12 * 66913) / 543
=> h = 38.45 cm = 384.5 mm.

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