calculate the mass M needed in order to suspend the leg shown in the figure belo

Question

calculate the mass M needed in order to suspend the leg shown in the figure below. (assume the leg (with cast) has a mass of 15.0 kg and its center of gravity (CG) is 35 cm from the hip joint. The sling is 80.5 cm from the hip joint. Assume the mass M is in line with the leg's CG and the hip joint.

Draw free body diagram showing all forces causing moments about the hip joint. Label the forces and associated moment arms

Write equation for the net moment on the hip joint

What is the force of the sling on the leg? what is the mass m? (based on static equilibrium)

 

here's the diagram

Explanation / Answer

The mass of leg M = 15 kg the distance between the CM of leg & hip joint is D = 0.35 m let mass of load = m the distance between the hip joint and the sling L = 0.805 m choosing the clockwise torques as positive and takingmoments about A , we get      MgD = FTL the force of the sling on the leg is       FT = MgD/L            = (15 k g)(9.8 m/s 2)(0.35 m) / (0.805 m)            = 63.91 N here , mass m is in equlibrium. so , there is no acceleration of the hanging mass. thus, here , mass m is in equlibrium. so , there is no acceleration of the hanging mass. thus,       FT = mg mass of the load is        m = FT/g           = (63.91 N / 9.8 m/s2)           = 6.52 kg

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