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81_Problem CHAPTER 10

# 81_Problem CHAPTER 10 - PROBLEM 10.71 Two uniform rods each...

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PROBLEM 10.71 Two uniform rods, each of mass m , are attached to gears of equal radii as shown. Determine the positions of equilibrium of the system and state in each case whether the equilibrium is stable, unstable, or neutral. SOLUTION Potential Energy sin cos 2 2 l l V W W W mg θ θ = + = ( ) cos sin 2 l W θ θ = ( ) sin cos 2 dV Wl d θ θ θ = ( ) 2 2 sin cos 2 d V Wl d θ θ θ = For Equilibrium: 0: sin cos dV d θ θ θ = = − or tan 1 θ = − Thus 45.0 and
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