5-52 A cylinder with a conical cavity and a hemispheri-cal cap is shown in Fig. P5-52.Locate the center of mass of the composite volume ifthe cylinder is made of brass (p = 875ó kg/m) and thecap is made of aluminum (p = 2770 kg/m®).R

Answered: 5-52 A cylinder with a conical cavity…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

5-52 A cylinder with a conical cavity and a hemispheri-
cal cap is shown in Fig. P5-52.
Locate the center of mass of the composite volume if
the cylinder is made of brass (p = 875ó kg/m) and the
cap is made of aluminum (p = 2770 kg/m®).
R

Expert Solution

Step 1

$G i v e n d a t a D e n s i t y o f t h e c y l i n d e r m a d o f b r a s s ρ_{b r a s s} = 8750 (k g / m^{3}) D e n s i t y o f c a p m a d f a l u m i n i u m ρ_{a l u m i i u m} = 2770 (k g / m^{3}) T o d e t e r m i n e t h e c e n t e r o f m a s s o f t h e g i v e n c y l i n d e r a n d c a p s y s t e m a s s h o w n i n f i g u r e$

$R = R a d i u s o f t h e c y l i n d e r a n d h e m i s p h e r e h = H e i g h t o f t h e c y l i n d e r$

Step 2

$C a l c u l a t i o n o f c e n t e r o f m a s s o f t h e g i v e n c y l i n d e r a n d h e m i s p h e r e s y s t e m A s t h e g i v e n c o m p o s i t e i s s y m m e t r i c i n x a n d y d i r e c t i o n s t h e r c e n t e r o f m a s s l i e s a t (0, 0, Z_{G}) x_{Z} = 0 a n d y_{Z} = 0 . G i v e n c y l i n d e r a n d h e m i s p h e r e i s n o t s y m m e t r i c a b o u t z a x i s .$