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ME 211 Homework 2 Solutions - Problem#14.5...

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ME 211 Homework Set #2 Solutions 9‐19‐2008 Problem #1 – 4.5 Determine the magnitude of force at the pin A and in the cable BC needed to support the 500lb load. Neglect the weight of the boom AB. Solution 1.) Draw the Free Body Diagram (FBD) 2.) Write the equilibrium equations. Always write an equation that sums the forces in the x‐direction, a summation of the forces in the y‐direction, and a moment equation around a point where you want to eliminate an unknown. ( F x , F y , and M) M A = 0 = 8 ft * F BC *sin(13) 8 ft *500 lb *cos(35) F x = 0 = 500*sin(35) F BC *cos(13) + A X F y = 0 = 500*cos(35) + F BC *sin(13) + A y 3.) With the equations above, we now have 3 equations and 3 unknowns, so we can solve for all three unknowns (Ax, Ay, and FBC)
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M A = 0 = 8 ft * F BC *sin(13) 8 ft *500 lb *cos(35) F BC = 1820.73 lbs F x = 0 = 500*sin(35) F BC *cos(13) + A X A X = 2060.91 lbs F y = 0 = 500*cos(35) + F BC *sin(13) + A y A y = 0 lbs 4.) With these unknowns, you can solve for the magnitude of the force at A, and the magnitude in BC is already solved for above. Magnitude A = (2060.91 2 + 0 2 = 2060.91 lbs Magnitude BC = 1820.73 lbs Answers
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Problem #2 – 4.9 Determine the tension in the cable and the horizontal and vertical components of reaction of the pin A. The pulley at D is frictionless and the cylinder weighs 80lbs. 1.) Draw the FBD 2.) Write the equilibrium equations. ( F x , F y , and M) M A = 0 = T *5 ft + T *( 2 5 )*10 ft 80 lbs *13 ft F x = 0 = A X T *( 1 5 ) F y = 0 = A y + T + T *( 2 5 ) 80 lbs 3.) With the equations above, we now have 3 equations and 3 unknowns, so we can solve for all three unknowns (Ax, Ay, and T)
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M A = 0 = T *5 ft + T *( 2 5 )*10 ft 80 lbs *13 ft T = 74.6 lbs F x = 0 = A X T *( 1 5 ) A X = 33.4 lbs F y = 0 = A y + T + T *( 2 5 ) 80 lbs A y = 61.324 lbs Answers
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Problem #3 – 4.24 The crane consists of three parts, which have weights of W1 = 3500lbs, W2 = 900lbs, W3 = 1500lbs and centers of gravity at G1, G2, and G3, respectively. Neglecting the
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