A standard man holds the upper arm vertical and the lower arm horizontal with an object of mass M = 5 kg resting on the hand, as illustrated in the figure above. The mass of the lower arm and hand is one-half the mass of the entire arm. As shown in the figure below, there are four forces acting on the lower arm: the external force F_ext^→, exerted by the bones and ligaments of the upper arm at the elbow (fulcrum); the tension T^→, exerted by the biceps; a force w^→ due to the weight of the holding object; and the weight w_F^→ of the lower arm. The points along the lower arm at which the forces act are I₁ = 3 cm, I₂ = 14 cm, and I₃ = 44 cm, as shown in the figure below. (Assume the mass of the lower arm is 2.3 kg.)

Arrangement of the biceps muscle (1) and the triceps muscle (2) in the upper arm. The biceps is connected to the scapula (6) and the radius (3), which runs parallel to the ulna (4) in the lower arm. The muscle actions of the biceps and triceps rotate the lower arm, relative to the humerus (5), at the elbow.

(a) Calculate the vertical component of the force F_ext^→.

(b) Calculate the vertical component of the tension T^→.