The leg and cast in Figure P4.18 weigh 220 N, with the center of mass as indicat

Question

The leg and cast in Figure P4.18 weigh 220 N, with the center of mass as indicated by the blue arrow in the diagram. The counterbalance w1 weighs 150 N. Determine the weight W2 and the angle alpha needed so that no force is exerted on the hip joint by the leg plus cast. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N

Explanation / Answer

T1 =150N                                                     T2 T1y = 150 sin 40 =   96.41N                               T2y= T2 sin T1x = -150 cos 40 = -114.91N                          T2x= T2 cos Fg = -220 N
Fx = -114.91 + T2x =0        T2x =114.91 N Fy = 96.41 + T2y - 220 =0      T2y = 123.59 N T2 = (114.91 2 + 123.592) = 168.76 N = tan-1 (123.59 / 114.91) = 47.08

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