x. THE FIGURE IS NOT DRAWN TO SCALE. The body shown is contructed rrem a right c

Question

x. THE FIGURE IS NOT DRAWN TO SCALE. The body shown is contructed rrem a right circular cylinder of radius r·74 mm and hei ht h-200 mm, and a hemisphere or radius R-166 mm. The density of the cylinder is 2 ko/m and the denaity of the hemisphere is 3 ko/m Oescription Answer Chk History What is the first mass moment of the cylinder about the axis? (include units with answer) what is the first mass moment of the hemsphere about the x axis? finclude units with answer) what is the position, 1G, of the body's mass center? Cinclude units with answer) egts.oo"I # tries: o i sioninn

Explanation / Answer

given

right circular cylinder, r = 74 mm

h = 200 mm

hemisphere, R = 166 mm

denisty of cylidner, rhoc = 2 kg/m^3

density of hemisphere, rhoh = 3 kg/m^3

a. first moment of cylider about axis = Mc

Mc = mass of cylinder * center of mass

Mc = rhoc*pi*r^2*h*(R + h/2)

Mc = 2*pi*74^2*200*(166 + 200/2)*10^-9

Mc = 0.5826464 kg m

b. first mass moment of the hemisphere = Ms

center of mass location of hemisphere = 5R/8

hence

Ms = rhos*2*pi*R^3*5R/3*8 = 2.98189425 kg m

c. position of zo = (Mc + Ms)/(mass of cylidner + mass of hemisphere ) = 100.06432 mm

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