Question

9) A beam of mass 16 kg and length 1.2 m is supported in two ways: at the wall with a hinge, and by a rope tied to its other end at an angle θ = 34◦ , as Figure 3 shows. At the hinge the wall exerts on the beam a force F of unknown direction and magnitude (shown as a dashed arrow). a) Write three equilibrium equations: for rotation around the hinge (balancing torques), and for translation in x and in y (balancing horizontal and vertical forces). b) Find the three unknowns: the rope tension, the magnitude of F, and the angle β it does with the beam. (Do not forget the sine in the torque equation!). (This problem has a pleasingly symmetric answer)​​​​​​​

Answer 1

answer's are in boxes

  

Tsino THY A Fu Tloso YU M nek het zo mg = Tsing + Fun Fax = T Cose * M Free =0 Ez = zero mg. = Tsino. L T- mg scาง & 16 x 9.8 2x sin34 = 140.2 N

гия - TCes 24 = 1+ь 2 4 Сол 34 - 16 33 м Гиу - ма — Tsin0 = 35-х — 140 2 4s hач 78ч м |+0 1 39 М Fam JET = J 11 25-+ 1812 => ре «н ( ) = " ( 12 ) ax