Question

Consider the objects on the coordinate grid: a rod with m 5.50 kg, a right triangle with m2 36.0 kg, and a square with m3 3.15 kg. Calculate the center of gravity for the system. Assume the objects are uniform. (Give the coordinates of the center of gravity in m.) y (m) in 1 (9, 7) (2,7) (8, 5) ig mg x-coordinate y-coordinate

Answer 1

for a sod, centre of mass 1 dema , yen="/ rem= 8 + 7 = 11 sa, 9,=7 Carp90) =(4,7) for a Right Angled Triangle, centre of mass, xcm= 3a Yam-1 So 22 = 4+314) = 2013 42=1+ (4) = 7/3 a) (,) (401) for a square, centre of mass rom=al, Yem = 6/2 A3 = -5+2=-712 Y₂=2+2/2 = -2 (23143) - (311)

Given masses . M,=5-50kg M2= 3600kg mg=3. 15 kg xam = minit M2 M27 M 323 mitm₂ + M3 = (5.50) 6 + (36)(30)+(2-15)(-73) kom (5.50+ 36+3-15) 17 xam = 859-225. = = 5.806 am 44.65 Yom = mig, tm24+ m3Y, - mit mat M3 = (5.50)(7)+ (36) (73) +(2-15)(7/2) (5.50f 36 +3.15) u = 133.525 Rom g.99 m .44.65 Yyy jam=2.99 (alcm , Sooms) = (50806 m, 2.99m) ham = 5.806 m, am= 2.99m