The Russell Traction System To immobilize a fractured

QUESTION:

The Russell Traction System To immobilize a fractured femur (the thigh bone), doctors often utilize the Russell traction system illustrated in Figure 6-29. Notice that one force is applied directly to the knee, \(\vec{F}_{1}\) , while two other forces, \(\vec{F}_{2}\) and \(\vec{F}_{3}\) , are applied to the foot. The latter two forces combine to give a force \(\vec{\mathbf{F}}_{2}+\vec{\mathbf{F}}_{3}\) that is transmitted through the lower leg to the knee. The result is that the knee experiences the total force \(\vec{\mathbf{F}}_{\text {total }}=\vec{\mathbf{F}}_{1}+\vec{\mathbf{F}}_{2}+\vec{\mathbf{F}}_{3}\) . The goal of this traction system is to have \(\vec{\mathbf{F}}_{\text {total }}\) directly in line with the fractured femur, at an angle of \(20.0^{\circ}\) above the horizontal. Find (a) the angle \(\theta\) required to produce this alignment of \(\vec{\mathbf{F}}_{\text {total }}\) and (b) the magnitude of the force, \(\vec{\mathbf{F}}_{\text {total }}\) that is applied to the femur in this case. (Assume the pulleys are ideal.)