# Find Value of tan φ of Reaction Force | Isaac Physics

• ephphatha16

#### 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

#### Attachments

Last edited:
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?

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.

• ephphatha16