Question

Chapter 09, Problem 005 What are (a) the x coordinate and (b) the y coordinate of the center of mass for the uniform plate shown in the figure if L 16 cm? 2L AL 31 4L 2L (a) Number Units (b) Number Units
please help me answer these two questions i have only one more question to ask

Answer 1

the x coordinate of center of mass is

x cm = sum Area . xi/ total area

= ( 2L- 7L ) ( -L) + ( 4L .L) . 2L + ( 2L. 2L). L/( 2L. 7L) +( 4L. L) + ( 2L. 2L)

= - 2L^3/ 22 L^2

= - L/11

=-16/11 = -1.45 cm

the y coordinate of center of mass is

y cm = sum of area . yi/ total area

= ( 2 L . 7 L) ( -0.5 L) + ( 4L . L) ( 2.5 L) + ( 2L. 2L) ( - 3L)/ ( 2 L. 7L) + ( 4 L L) + ( 2L. 2L)

= - 9L/ 22

= - 9 ( 16)/ 22

=-6.54 cm

(2)

x cm = 37 (0) + 68 ( 7.7)/68 + 37 = 4.98 m