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?
Solution
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.
2. (8pts) A system of balls connected by massless rods is initially a.pdf
1. 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?
Solution
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
![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?
Solution
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](https://image.slidesharecdn.com/2-230323121127-a223e277/85/2-8pts-A-system-of-balls-connected-by-massless-rods-is-initially-a-pdf-1-320.jpg)
