Static equilibrium -- A picture hanging on a wall

[siapola1]

Homework Statement

https://imgur.com/v13K6sE
a uniform rod of mass m is placed as shown, with one of its end resting on a smooth wall while 1/4 of the rod's length is sticking out of a rough table. Find the net force the table exert on the rod at the corner.

Homework Equations

i drew the free body diagram and labeled all the forces. i get stuck when i tried to set up the torque equation
because i don't know what is the force that is responsible for rotating the rod.
i have the picture here:
https://imgur.com/ybSWfcT

3. The Attempt at a Solution
its in the picture

 

[haruspex]

There are two things wrong with your torque equation.
1. There is a force missing.
2. Your expressions for the torques for the parts of the rod are wrong. For each part, what is its weight and what is its torque arm?
(Though you don’t really need to treat the rod as two parts. Just find the torque arm for the rod as a whole.)

 

[siapola1]

he didnt give us the weight and is the missing force the normal force at the contact point between the table and the rod?
<a href="https://imgur.com/U6SG6En"><img src="https://i.imgur.com/U6SG6En.jpg" title="source: imgur.com" /></a>

 

[haruspex]

he didnt give us the weight

You are told it is a uniform rod of mass m, so you can find the weight(s).

the missing force the normal force at the contact point between the table and the rod?

Yes.
Edit: I mean no... it is a normal force but not that one.

 

[siapola1]

what is tikd?

 

[haruspex]

what is tikd?

It is a result of fat fingers. Please see edited version.

 

[siapola1]

i still can't figure it out

i check the answer and is this:
mg/3 [√(9+ cot²(φ))]

we have never encounter a problem that the answer is cotangent before its way out of my league can someone please just tell me how to do it?

 

[siapola1]

i just checked the answer and it is
mg/3 ( √(9+cot²(φ))

we have never encounter a problem that its answer has cotangent in it. its way out of our league. can someone please just show me how to derive the answer?

 

[haruspex]

can someone please just tell me how to do it?

That's not how this forum works. Don't be put off by the cotangent. Just try to answer these questions in sequence:
You are given the mass of the rod. What is the force of gravity on it?
Where does that force act?
What is the moment arm of that force about the point of contact?
Unfortunately I made a mistake in answering a previous post of yours. I'll correct that then continue...

 

[haruspex]

ok, I have edited post #4. You need to look for another force that has a torque about the point of contact between rod and table. The contact forces that act there cannot have a moment about it.