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91_Problem CHAPTER 10

# 91_Problem CHAPTER 10 - PROBLEM 10.80 A slender rod AB of...

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PROBLEM 10.80 A slender rod AB , of mass m , is attached to two blocks A and B that can move freely in the guides shown. Knowing that the spring is unstretched when AB is horizontal, determine three values of θ corresponding to equilibrium when 125 kg, m = 320 mm, l = and 15 kN/mm. k = State in each case whether the equilibrium is stable, unstable, or neutral. SOLUTION Using the results of Problem 10.79, particularly the condition of equilibrium () ( ) cos sin cos 1 1 tan 0 2 mg kl θθ  + −− =   Now, with 2 125 kg 9.81 m/s 1226.25 N, 320 mm, Wm g l == = = and 15 kN/m, k = Now ( ) 1226.25 N 1.2773 2 2 15000 N/m 0.32 m W kl so that ( )( ) cos sin cos 1 1 tan 1.2773 0 + = By inspection, one solution is cos 0 or 90.0 = Solving numerically: 0.38338 rad 9.6883 and 0.59053 rad 33.8351 ° ° Stability ( ) ( ) 2 2 2 1 cos sin cos sin sin cos 1 sin cos sin
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