Finding angle of hinge reaction force on a trapdoor

[ephphatha16]

1.
Find the value of tan φ to 2 sf where φ is angle made by line of action of reaction force at hinge above horizontal.
https://isaacphysics.org/questions/trapdoor_num
Part B Angle of reaction force

Homework Equations

• Mass of uniform trapdoor: m=4.0kgm=4.0kg
• The trapdoor is held open making an angle θ=60∘θ=60∘ to the horizontal.

Information assumed
- Magnitude of the gravitational field strength, g=9.81ms−2

The Attempt at a Solution

[/B]Don't know how to move on with this simultaneous equation

Fcosθ + Nsinθ=mg
Fsinθ = Ncosθ

 

[haruspex]

Fcosθ + Nsinθ=mg
Fsinθ = Ncosθ

Shouldn't some of those angles be φ?
You will also need to consider torque balance.

 

[ephphatha16]

Shouldn't some of those angles be φ?
You will also need to consider torque balance.

Yeah true

Fcos θ + Nsin φ = mg
F sin θ = N cos φ

But I don't know what values to plug in ... is the first equation about vertical component and the second equation about horizontal component?

 

[haruspex]

I don't know what values to plug in

φ will not depend on m or g. You are given a value for θ.

is the first equation about vertical component and the second equation about horizontal component?

Yes, but you have three unknowns, F/mg, N/mg and φ. You need a torque balance equation.