What are the physics behind a TV wall mount?

Question

As I was installing this wall mount, I began to wonder how exactly physics is at work with it. In other words, how does the design of the mount play a role in ensuring that the mount itself supports the television/device and distributes the forces at play? I have seen different types of wall mounts (like this). Does the shape or structure of the mount make one much stronger (more efficient at distributing the forces) than another? Outside of allowing rotation does the swivel extension make the mount any better withstanding the forces?

I initially asked this question here on the Physics Stack Exchange but I think it is more suited for this platform. I came across this answer and this question as well. Thank you.

Answer 1

Addressing the most basic but severe conditions we leave alone all the secondary connections, forces, and moments! Let's assume:

• P= the weight of the TV
• L= the length of each one of the two brackets
• H= the height of the brackets
• D= the distance between the two screws fastening the bracket to the wall's 2x4s or load-worthy material.

The highest pullout stress on the fasteners is when the bracket is stretched at 90 degrees to the wall acting as a cantilever beam.

$$T=C=\frac{2L*P}{D}$$ Half this stress is applied at the hinge between the two sub brackets.

The maximum torque is when the bracket is fully extended but almost touching the wall (to pan the TV! say.). there will be a sheer force on the screws trying to rotate them off the wall.

$$\tau= \frac{2LP}{D}$$

Intermediary torque is when the bracket is deployed in an L shape, the sub bracket coming out of the wall the second sub bracket turned 90 degrees.

$$\tau=\frac{PL}{D}$$ And the forces on the hinges are a combination of compression $ \ C=T=PL$ and tension and also shear due to torque $ \ \tau= \frac{PL}{H}$.

In between angles will have the $sin(\theta)PL$ and $cos(\theta)PL$ components.