A thin rectangular plate of uniform area density s1 = 1.15 kg/m2 has a length a

Question

A thin rectangular plate of uniform area density s1 = 1.15 kg/m2 has a length a = 0.760 m and a width b = 0.320 m. The lower left corner is placed at the origin, (x, y) = (0, 0). A circular hole of radius r = 0.061 m with center at (x, y) = (0.086 m, 0.086 m) is cut in the plate. The hole is plugged with a disk of the same radius that is composed of another material of uniform area density s2 = 5.25 kg/m2. What is the distance from the origin of the resulting plate's center of mass?

A thin rectangular plate of uniform area density s1 = 1.15 kg/m2 has a length a = 0.760 m and a width b = 0.320 m. The lower left corner is placed at the origin, (x, y) = (0, 0). A circular hole of radius r = 0.061 m with center at (x, y) = (0.086 m, 0.086 m) is cut in the plate. The hole is plugged with a disk of the same radius that is composed of another material of uniform area density s2 = 5.25 kg/m2. What is the distance from the origin of the resulting plate's center of mass?

Explanation / Answer

center of mass=COM of rectengular sheet - change in COM due to circuler hole + change in COM due to filling the circuler hole

=COM of rectengular sheet +  change in COM due to filling the circuler hole by the sheet of density of =(2-1)=4.1 kg/m2

1 = 1.15 kg/m2

2 = 5.25 kg/m2

a = 0.760 m

b = 0.320 m

a`=0.086

r = 0.061

X=a/2*(1*a*b)+a`*(**r^2)/(1*a*b+**r^2)=0.3367 m

Y=b/2*(1*a*b)+a`*(**r^2)/(1*a*b+**r^2)=0.1491 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.