HW33 - p a _ B ‘9“! fog 7 N / f .r l " (7,";...

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Unformatted text preview: p a _ B ‘9“! fog 7 N / f .r l " (7,"; “‘l/ i f 9 I z ,2 A ’w PROBLEM 10.17 Derive an expression for the magnitude of the couple M required to maintain the equilibrium of the linkage shown. SOLUTION Have x5 : lsinfl 5x3 = 10051960 y“, = [0050 514 = —l sina966 Virtual Work: 5U = 0; M69 — P519; + P5y4 : 0 Mé‘fl — P(lcos€56) + P(7lsin¢966) = 0 M = Pl(sin6 + 9056) 4 PROBLEM 10.20 A couple M of magnitude 75 lb'ft is applied as shown to the crank of the engine system. Knowing that AB = 2.5 in. and BC : 10 in, determine the force P required to maintain the equilibrium of the system when (a) 0 = 60°, (11) 9 = 120°. SOLUTION Bsin(0 + ¢) P From the analysis of Problem 10.19, M 2 A cos¢ Now, with M = 751b-ft = 9001b-in. (a) For 6 : 60° sin¢ = Zlégsin 60°, ¢ = 12504" (900113411) = (2.5 MW c0512.504° (P) or P 2 368.5 lb P = 3691b -> 4 (b) For 6 2 120° sin¢ = %sin120°, ¢ : 12.504° sin(120° + 12.504°) c0512.504° (P) (900 lein.) = (2.5 in.) or P=476.7 1b P : 4771b -+ 4 PROBLEM 10.29 Two rods AC and CE are connected by a pin at C and by a spring AE. The constant of the spring is k, and the spring is unstretched when 0 : 30°. For the loading shown, derive an equation in R63, 1, and k that must be satisfied when the system is in equilibrium. s rwmwmmww-TE P SOLUTION yE = 10059 6yE = —lsin6l§t9 Unstretched length = 21 x = 2(ZIsin6l) = 4lsint9 5x = 4Zcos€50 F = k(x — 21) F = k(4lsin€ — 21) Virtual Work: 6U = 0: Pb‘yE —F6x = 0 P(—lsin¢9§0) — k(4lsint9 — 21)(41c05050) = 0 —Psinl9 — 8k1(2sin0 —1)cos6 = 0 or i=(l—23in9)césg L=—;23ing‘ 8k] sml9 8k] tam9 ...
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This note was uploaded on 05/18/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

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HW33 - p a _ B ‘9“! fog 7 N / f .r l " (7,";...

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