A hydrogen balloon rises vertically with an upward force of 500 N and is attached to a point A at an elevation of 1m directly above the origin (0,0,0), which is in turn attached to 3 light ropes on...

A hydrogen balloon rises vertically with an upward force of 500 N and is attached to a point A at an elevation of 1m directly above the origin (0,0,0), which is in turn attached to 3 light ropes on the ground level at D (–3,0,0), B (2,0,2) and C (2,0, –2) in meters. Note the chosen x-y-z coordinate frame. (a) Draw a free body diagram FBD of the balloon with the 3 ropes AB, AC, and AD. (b) Draw a free body diagram FBD of the composite body of ropes AB and AC and the connector A (excluding the balloon and rope AD). (c) Write down the relevant equilibrium equations, and solve for tension of each rope, TAB, TAC, and TAD.