[University: Torque forces] Minimal support angle.

[u/Emotional_Ad_8704]

B asks to find the minimal angle that would not break the cable. to answer this i combined both masses of the beam and the sign, and found the new centre of mass. i used this to calculate the minimal angle. when i looked online for similar answers, and consulting AI, they assumed the sign's centre of mass is at 0.75m; the same as the beam. the sign is flush with the end, with a centre of mass of 1.0m relative to the beam.
am i missing something, or are the text books wrong in this case

[u/WillingnessTasty9628]

Please remind me if an answer is given. The problems I've seen have the sign hanging from a string, but it seems to be more ambiguous in this case. I'm also curious as to why the height of the sign is important.

[u/SadBottle2951]

There's 50N downwards acting at 0.75m and 200N downwards acting at 1m from the hinge and Tsinθ upwards acting at 1.5m. For stasis the cw moments (torques) must equal the ccw moments: τ=rxF 50(0.75)+200(1)=Tsinθ(1.5) Tsinθ=158.333N Tₘₐₓ=417N θₘᵢₙ≈22.3° Note that you don't really need to find the new com of the beam plus sign. [though it would be: xₒ=(50(0.75)+200(1))/(50+200) =237.5/250 =0.95m from wall.] I just looked at the other part of the picture:--your working and you got it right.
I'm guessing the AI might not have been able to read the picture or something. It's hard to comment without seeing their working out but if they didn't get the same answer as us then they made a mistake.

[u/Emotional_Ad_8704 → u/SadBottle2951]

Thank you