Dynamics Spring 1998 Exam 2

Dynamics Spring 1998 Exam 2 - ME 242 Exam 2 Solutions,...

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ME 242 Exam 2 Solutions, 10/20/2008: 1) Block A weighs 30 lb and block B weighs 50 lb. They are connected by a rope as shown in the figure below. The kinetic coefficients of friction, μ k , are 0.35 for block A and 0.15 for block B. As the blocks slide down the inclined plane; A) Find the acceleration of block B. (17 pts) B) Find the tension in the rope. (17 pts) 30 O B A SOLUTION Assume that block B wants to move faster than block A since it is heavier and has a smaller coefficient of friction. Therefore, the rope will remain taut and the 2 blocks will have the same acceleration. a A = a B Free-Body diagram of A 30 O W A x F A N A T y 30 O 30 O F y = 0 F x : N A = W A cos30 = 26 lb Friction: F A = μ A N A =(.35)(26) = 9.1 lb = 0 30 O : T + W A sin30 - F A = m A a T + 5.9 = (30/32.2) a T = (0.93) a – 5.9 (eq 1) Free-Body diagram of B W B x F B N B T y 30 O 30 O F y = 0 F x : N B = W B cos30 = 43 lb Friction: F B = μ B N B =(.15)(43) = 6.5 lb : W B sin30 – F B – T = m A a = 0 18.5 – T = (50/32.2) a 18.5 – (0.93) a + 5.9 = (1.6) a a = 9.83 ft/s 2 T = 3.23 lb 2) The 15-kg slender rod shown below is rotating counterclockwise about a smooth pin at A.
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This note was uploaded on 07/13/2009 for the course ME a taught by Professor Dr. during the Spring '09 term at University of Nevada, Las Vegas.

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Dynamics Spring 1998 Exam 2 - ME 242 Exam 2 Solutions,...

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