Problem 14: A uniform rectangular plate of length B 21 cm and height A 24 cm has
ID: 2030365 • Letter: P
Question
Problem 14: A uniform rectangular plate of length B 21 cm and height A 24 cm has a rectangular corner cut out of it of length D = 8 cm and height C= 8 cm. The plate is made of a material of area mass density . For this problem we set the origin at the lower left corner of the plate with the x-axis horizontal pointing right and the y-axis vertical pointing up ©theexpertta.com Part (a) Calculate the value of the y-coordinate, in centimeters, for the center of mass of the plate. Numeric Anumeric value is expected and not an expression. ycm = Part (b) Calculate the value of the x-coordinate, in centimeters, for the center of mass of the plate. Numeric A numeric value is expected and not an expression cmExplanation / Answer
Consider the lower rectangular plate of dimensions of height 24 - 8 = 16 cm and width 21 cm. The center of mass can be written as
(x1, y1) = (21/2, 16/2) = (10.5, 8)
The upper rectangular plate has the dimensions of height 8 cm and width 21 - 8 = 13 cm. Its center of mass can be written as (x2, y2) = (13/2, 8/2)
= (6.5, 4)
a)
Y-coordinate of the center of mass of the given shape, y = (y1 + y2)/2
= (8 + 4) / 2
= 6 cm
b)
X-coordinate of the center of mass is given by, x = (x1 + x2)/2
= 8.5 cm