A machinist makes the object shown in the figure. The larger-diameter cylinder i

Question

A machinist makes the object shown in the figure. The larger-diameter cylinder is made of brass (density of 8.6 g/cm3); the smaller-diameter cylinder is made of aluminum (density of 2.7 g/cm3). The dimensions are r1 = 2.51 cm, r2 = 5.02 cm, d1 = 20.1 cm, and d2 = 5.02 cm. (Figure is not to scale.)

a) What is the x-component of the center of mass?

b) What is the y-component of the center of mass?

c) If the object is on its side, as shown in the figure, is it in equilibrium? If yes, is this stable equilibrium?

1/ The object is in stable equilibrium.

2/ The object is in equilibrium

3/ The object is not in equilibrium.

A machinist makes the object shown in the figure. The larger-diameter cylinder is made of brass (density of 8.6 g/cm3); the smaller-diameter cylinder is made of aluminum (density of 2.7 g/cm3). The dimensions are r1 = 2.51 cm, r2 = 5.02 cm, d1 = 20.1 cm, and d2 = 5.02 cm. (Figure is not to scale.) a) What is the x-component of the center of mass? b) What is the y-component of the center of mass? c) If the object is on its side, as shown in the figure, is it in equilibrium? If yes, is this stable equilibrium? The object is in stable equilibrium. The object is in equilibrium The object is not in equilibrium.

Explanation / Answer

V1 = pi * 2.51^2 * (20.1 + 5.02) = 497 cm^3
V2 = pi * [(5.02^2 * 5.02) - (2.51^2 * 5.02)] = 298 cm^3
M1 = 497 * 2.7 = 1342 gm
M2 = 298 * 8.6 = 2563
Ycm = 5.02 cm     by symmetry
Xcm = M1 Xcm1 + M2 Xcm2 / (M1 + M2)
Xcm1 = 10.05       Xcm2 = 2.51
Xcm = [1342 * 10.05 + 2563 * 2.51] / (1342 + 2563) = 5.10
The object is unstable since the pivot point would be at X = 5.02 while
the center of mass is at X = 5.10

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