2. (8pts) A system of balls connected by massless rods is initially at rest on a

Question

2. (8pts) A system of balls connected by massless rods is initially at rest on a small table as shown in the figure below. All balls have a mass of m = 2.0 kg except for the ball at (0.2m, 0) which has a mass of M = 7.0 kg. a. Find the x-, y-coordinates of the center of mass (center of gravity) of the system. Give your answers to two significant figures. b. Is the system in a stable or unstable equilibrium? Why? c. Is the system in static equilibrium about an axis through the ball at (0.2m, 0)? Why?

Explanation / Answer

a)

Xcm=[(m1*x1)+(m2*x2)+(m3*x3)+(m4*x4)+(m5*x5)+(m6*x6)+(m7*x7)]/(m1+m2+m3+m5+m6+m7)

Xcm=[(2*0.1)+(2*0.1)+(2*0.15)+(2*0.25)+(2*0.3)+(2*0.35)+(7*0.2)]/(2+2+2+2+2+2+7)

=(0.2+0.2+0.3+0.5+0.6+0.7+1.4)/(12+7)

=0.21

Yc.m=[(m1*y1)+(m2*y2)+(m3*y3)+(m4*y4)+(m5*y5)+(m6*y6)+(m7*y7)]/(m1+m2+m3+m5+m6+m7)

=(2*0)+(2*0.1)+(2*0.2)+(2*0.1)+(2*0)+(2*0.2)+(7*0)]/(2+2+2+2+2+2+7)

=(0+0.2+0.4+0.2+0+0.4+0)/(12+7)

=1.2/19

=0.06

center of mass (Xcm, Ycm)=(0.21, 0.06)

b)

stable equilibrium, because initially masses are at rest

c)

the system is not in a

because for static equilibrium

Fnet=0

Tnet=0

but here net torque may not be zero

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