To immobilize a fractured femur (the thigh bone), doctors often utilize the Russ

Question

To immobilize a fractured femur (the thigh bone), doctors often utilize the Russell Traction System illustrated in Figure 3. Notice that one force is applied directly to the knee, F1, while the other two forces, F2 and F3, are applied to the foot. The latter two forces combine to give a force F2 +F3 that is transmitted through the lower leg to the knee. The result is that the knee experiences a total force Ftotal = F1 + F2 + F3. The goal of this traction system is to have Ftotal directly in line with the fractured femur, at an angle of 20 degrees above the horizontal.
Find (a) the angle required to produce this alignment of Ftotal and (b) the magnitude of the force, Ftotal that is applied to the femur in this case. (Assume that the pulleys are ideal).

http://www.cramster.com/answers-oct-10/physics/russell-traction-system-russell-traction-system-immobilize-fractured-femur_1008547.aspx?rec=0 for the picture

Explanation / Answer

We note that since the rope is in equilibrium: | F1 | = | F2 | = | F3 | = m g = (4.25) (9.8) = 41.65 N We define a coordinate system that has the x-axis along the femur, with the positive direction being toward the body. For F1: Fx = - 41.65 cos (? - 20) Fy = 41.65 sin (? - 20) For F2: Fx = - 41.65 N Fy = 0 For F3: Fx = - 41.65 cos (40) = - 31.906 N Fy = - 41.65 sin (40) = - 26.772 N Therefore: a) Since the knee is not moving: S Fy = 0 Since, sin (? - 20) = sin (40) then, ? = 60° b) Since: Fy = 0 Ftotal= S Fx = -41.65 cos (40) - 41.65 - 31.906 = 105.46 N

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