NOVA Physics: Static Equilibrium/Torque Example (confused)

[Czarcasm]

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I'm not entirely sure what's happening here, especially with regard to the angle. For torque problems, I prefer to find the lever arm and keep the force perpendicular to the lever arm -- their technique has me confused though. Can anyone explain what's happening here? I stared at this for a while and am still lost, lol. (Is it even possible to solve this using the lever arm in this scenario?) I feel like I'm neglecting to see something really obvious. Any input or help is appreciated.

 

[Teleologist]

It's static equilibrium bruh, so sum of the torques = 0. The rest follows from this. The work is simply using trig to find lever arms perpendicular to the applied force. Try remembering SOH CAH TOA to understand how the author derives all these trig relationships. I know that the cos/sin stuff can be tricky; it's hard seeing where they come from.

In the below picture, the dotted line represents the lever arm on which the hanging mass acts perpendicularly on. I can use torque = rF where r is the length of the perpendicular lever arm and find r using trig.

Line AB is the lever arm on which the tension in BC acts perpendicularly on. The rest is just trig brotha.

 

[The Brown Knight]

Try this:
look at the pole as perfectly horizontal and everything else is at angles to it. Something like this:
/______\ <-- T (tension)
................/ <-- mg (weight of box)
(ignore the dots)
considering the center of rotation to be at the point where the pole is attached to the wall, just do a torque balance using the vertical components of the tension and weight: mgLsin a = TLsin(90-a)
for part b, do a separate horizontal and vertical net force balance using the method above. tell me if you want me to do it out.

in general, try to be flexible finding torque both ways:
1. using a horizontal pole and the perpendicular component of the applied force.
2. using a horizontal force and the perpendicular component of the pole.
Sorry, I'm not too familiar with the terms like lever arm, so I might sound jumbled; my point is too practice seeing problems from the perspective of the pole as well as the force. I hope this helps at least a little!

 

[Czarcasm]

Perfect explanation, thanks guys.