(20 points total) A current problem in the U.S. Army is the neck/shoulder fatigue experienced by helicopter pilots. To be able to fly missions at night, the pilots wear night vision goggles, which are attached to the front of the helmet. Unfortunately, these are fairly heavy, causing a large downward torque of the head. This torque must be counteracted by the neck muscles, which then fatigue. To alleviate this problem, many pilots have started attaching random lead weights to the back of the helmet. Find the appropriate weight that would best balance the head and minimize neck fatigue. Assumptions: (a) cg of goggles is 10 cm in front of neck pivot point; (b) goggles weigh 1kg; (C) maximum volitional neck torque is 86 cm.kg; (d) cg of lead weight is 13 cm behind neck pivot point; (e) bare helmet weighs 2.5 kg; and (f) cg of helmet is 1 cm in in front of neck pivot