Question

The assembly is made from a steel hemisphere,ρst = 7.80 Mg/m3, and an aluminum cylinder, ρal = 2.70 Mg/m3. (Figure 1)

Determine the mass center of the assembly if the height of the cylinder is h = 250 mm .

Express your answer to three significant figures and include the appropriate units.

EMCH 211 Statics Homework 14 Problem 9.81 ③ 12 08 13 The assembly is made from a wel hemisphere P.-7.0 Mg/m, and an einer 2 .70 M /m . Figure 1) P Determine the masserter of the assembly the height of the cylinders P ROB? Value Units Submit Figure Feedback

Answer 1

Given data Sex = 7.80 mg/m3 Sal = 2.70 mg/m? 1. h= 250 mm. 250m mass of hemifphene (ne) mia Sixu m1=7,80 x 2 (R)? mi=7180x2 t (0.16)" Volume of hemisphere mi=0.067 mg. V=ZTR? R=160mm mass of Cylinder (me) m2 = Sal XV. M2=2.78 TTR? m₂ = 2.78 TX (0.0888x250x103 m2=0.0185 mg. Determine the most center of assembly. мэ - - + + + 0 | are av м - м + м, 2 . where ma mith

213 Ro- Si a) ERA 21= 5(0.016) 3 21zoolm. 22= Rith = 0.16+ 0.25 2 . 2₂= 0.285 m Substitute all the balues in canation o z = mizituzZz (mitme) z= 0.067 (0.1) +0.03s (0.285) (0.067 +0.0135) z = o.olos 0.0805 z = 0.1304 m. 2= 130.43 mm