Understanding Hinge Reactions: Debunking Common Misconceptions

[Svelte1]

Homework Statement

https://postimg.cc/JtP2h113

Relevant Equations

f=ma

https://postimg.cc/JtP2h113

I think I may have forgotten some more basic elements of tension and normal reactions. I do not understand why the vertical component of the normal reaction =Tsin60-15g

Because Tsin60-15g is negative when resolving upwards, i would have thought this meant that the normal vertical reaction would have to be upwards so that that we would have 0 acceleration

 

[haruspex]

why the vertical component of the normal reaction =Tsin60-15g

You mean the reaction at the wall, not the normal reaction. (By definition, the normal reaction would be at right angles to the wall.)
Whether it is Tsin60-15g or 15g-Tsin60 depends on which way you are defining as positive. Tsin60-15g is right if down is positive.

 

[Svelte1]

You mean the reaction at the wall, not the normal reaction. (By definition, the normal reaction would be at right angles to the wall.)
Whether it is Tsin60-15g or 15g-Tsin60 depends on which way you are defining as positive. Tsin60-15g is right if down is positive.

In the books workings it says they are resolving vertically upwards and clarifies that it is indeed the reaction at the hinge:
https://postimg.cc/Wtn5VyxJ

 

[haruspex]

that it is indeed the reaction at the hinge:

Yes, reaction at the hinge, not normal reaction.

The book is wrong about the direction. If you take moments about B, both weights have a clockwise torque, so the hinge reaction must be upwards.