82_Problem CHAPTER 10 - PROBLEM 10.72 Two uniform rods AB...

PROBLEM 10.72
Two uniform rods, AB and CD , are attached to gears of equal radii as
shown. Knowing that 3.5 kg
AB
m = and 1.75 kg,
CD
m = determine the
positions of equilibrium of the system and state in each case whether the
equilibrium is stable, unstable, or neutral.
SOLUTION
Potential Energy
( ) ( )
2 2
3.5 kg 9.81m/s sin 1.75 kg 9.81m/s cos
2 2
l l
V θ θ
   
= × − + ×
   
   
( ) ( )
8.5838 N 2sin cos l θ θ = − +
( ) ( )
8.5838 N 2cos sin
dV
l
d
θ θ
θ
= − −
( ) ( )
2
2
8.5838 N 2sin cos
d V
l
d
θ θ
θ
= −
Equilibrium: 0: 2cos sin 0
dV
d
θ θ
θ
= − − =
or tan