A thin rectangular plate of uniform areal density ? = 2.89 kg/m 2 has length of
ID: 2242084 • Letter: A
Question
A thin rectangular plate of uniform areal density ? = 2.89 kg/m2 has length of 38.0 cm and width of 27.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis.
(a) There is a circular hole of radius 8.00 cm with center at (x,y) = (13.00,11.50) cm in the plate. Calculate the mass of plate.
(b) Calculate the x-coordinate of CM of the plate.
(c) Calculate the distance of the plate's CM from the origin.
Explanation / Answer
a)
the total mass, M = density*area
M = 2.89*0.38*0.27
M = 0.297 kg
let m bethe mass of the circular plate, m = density*area
= 2.89*pi*0.08^2
= 0.058 kg
m' is the mass of remaining part
m' = M- m = 0.297 - 0.058 = 0.239 kg
b)
x1,y1 represents center of mass of the circular plate
x1 = 13 cm
y1 = 11.5 cm
x2 , y2 is the x coordinate of center of mass of remaining plate.
Xcm is x coordinate of center of mass of system
.Xcm = 19.......Ycm = 13.5 cm
Xcm = m*x1+m'*x2/(m+m')
19 = ((0.058*13)+(0.239*x2))/0.297
x2 = 20.456 cm
Ycm = m*y1+m'*y2/(m+m')
13.5 = ((0.058*11.5)+(0.239*y2))/0.297
y2 = 13.985 cm
c) r2 = sqrt(x2^2+y2^2) = sqrt(20.456^2+13.985^2)
r2 = 24.78 cm
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.