The leg and cast in the figure below weigh 312 N (w1). Determine the weight w2 a

Question

The leg and cast in the figure below weigh 312 N (w1). Determine the weight w2 and the angle needed so that no force is exerted on the hip joint by the leg plus cast.

see image here: http://www.webassign.net/sercp/p4-18alt.gif

The answers I put were: 201.1 for w2 and 66.2 degrees fo alpha. But these are apparantly wrong by 10%!! Help!!

I saw numerous examples of this problem, but when it comes to the trigonometry I STILL don't get how people put the equations together and solve for it!! Please help!!!!!!!!!!

Explanation / Answer

Require that the leg be in equilibrium with just the forces given, so no additional forces need be exerted by the hip joint. The weights W1 and W2 are transferred by the pully(s) to the leg. This means W1 acts as a tension force along the direction of the leg and W2 supports the leg at the CM, at angle alpha. Take force components in horizontal and vertcal directions and require they be zero, for equilibrium. Vertical: W2 Sin(alpha) + W1Sin(40) - W = 0 Horizontal: W2Cos(alpha) - W1Cos(40) = 0 Rewrite these as: W2Sin(alpha) = W - W1Sin(40) W2Cos(alpha) = W1Cos(40) Divide eqs: Tan(alpha) = [W-W1Sin(40)]/W1Cos(40) alpha = 66.2 deg Sub. this back into one of the force eqs to find W2 W2 = W1Cos(40)/Cos(66.2) = 201.1 N

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