84_Problem CHAPTER 10

84_Problem CHAPTER 10 - PROBLEM 10.74 In Problem 10.40...

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PROBLEM 10.74 In Problem 10.40, determine whether each of the positions of equilibrium is stable, unstable, of neutral. (See the hint for Problem 10.73.) SOLUTION Potential Energy 2 1 sin 2 VKP l θ =− cos dV KP l d 2 2 sin dV l d =+ Equilibrium 0: cos dV K dP l == For 1260 lb, 10 in., and 150 lb ft/rad Pl K = () 150 lb ft/rad cos 10 1260 lb ft 12 =    or cos 7 = Solving numerically, 1.37333 rad, 5.652 rad, and 6.616 rad = or 78.7 , 323.8 , 379.1 ° ° Stability At 78.7 : ( ) 2 2 10 150lb ft/rad 1260lb ft sin78.7 12 d =⋅+ ° 1179.6 ft lb
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