Question

The femur of a human leg (mass 10 kg, length 0.9 m ) is in traction, as shown in the figure. The center of gravity of the leg is one-third of the distance from the pelvis to the bottom of the foot. Two objects, with masses m1 and m2, are hung at the ends of the leg using pulleys to provide upward support. A third object of 8 kg is hung to provide tension along the leg. The body provides tension as well. Write a mathematical relationship relating m1 to m2 in terms of m2 and numerical coefficients.

Answer 1

The student is asked to calculate a mathematical relationship between two masses, m1 and m2, attached to a human leg in traction. Using the principles of static equilibrium and torque, the relationship is m1 = 0.5 * m2.

Step-by-step explanation:

The question pertains to the physical concept of static equilibrium where the forces acting on the femur of a human leg in traction are balanced. To find a mathematical relationship between m1 and m2, we use the principle of torques, where the torque produced by one weight must equal the torque produced by the other to maintain equilibrium. Since the center of gravity is one third from the pelvis, we can assume that the leg acts as a lever with the fulcrum at the pelvis. Applying the equilibrium condition for torques, we get m1 * (2/3 * L) = m2 * (1/3 * L) where L is the length of the leg. After simplifying, the relationship becomes m1 = 0.5 * m2.