(Solved):   Three cables are used to tether a balloon as shown. The vertical force \( \mathbf{P} \) ex ...

 

Three cables are used to tether a balloon as shown. The vertical force \( \mathbf{P} \) exerted by balloon at the point \( A \) and knowing that the tension force \( T_{A D} \) in the cable \( A D \) is \( 300 \mathrm{~N} \). The resultant force of all the forces at \( \mathrm{A} \) is \( \mathbf{F}_{\mathrm{R}}=\{0,0,0\} \mathrm{kN} \). 1) Draw the force diagram of the joint \( A \); 2) Determine the unit vectors of \( \mathbf{T}_{\mathrm{AB}}, \mathbf{T}_{\mathrm{AC}} \), and \( \mathbf{T}_{\mathrm{AD}} \); 3) From the given condition, \( \mathbf{F}_{\mathrm{R}}=\{0,0,0\} \mathrm{kN} \) to form the system of algebraic equations for solving the magnitude of tension forces \( T_{A B}, T_{A C} \), and the vertical force \( P \); 4) \( n^{2} \) optional: Solve the tension forces \( T_{A B}, T_{A C} \), and the vertical force \( P \). (3)