How Do You Calculate Normal Force with Angles and No Friction?

[hsphysics2]

Homework Statement

Find the normal force in terms of g, m, θ and α. There is no friction. a=0, θ≠α

See first attachment for diagram

Homework Equations

F_x=ma_x

The Attempt at a Solution

I drew a free body diagram including the forces; normal, mg, and |F_A| (See second attachment) I'm not sure if this is complete as I don't know where α would be part of it.

However I did start with this,

η-mgcosθ=0
η=mgcosθ
mg=η/cosθ (eq'n 1)


F_x=ma_x
|F_A|-mgsinθ=ma_x (sub eq'n 1 in)
|F_A|-(η/cosθ)sinθ=ma_x
|F_A|-(ηsinθ/cosθ)=ma_x

 

[NihalSh]

Homework Statement

Find the normal force in terms of g, m, θ and α. There is no friction. a=0, θ≠α

See first attachment for diagram

Homework Equations

F_x=ma_x

The Attempt at a Solution

I drew a free body diagram including the forces; normal, mg, and |F_A| (See second attachment) I'm not sure if this is complete as I don't know where α would be part of it.

However I did start with this,

η-mgcosθ=0
η=mgcosθ
mg=η/cosθ (eq'n 1)


F_x=ma_x
|F_A|-mgsinθ=ma_x (sub eq'n 1 in)
|F_A|-(η/cosθ)sinθ=ma_x
|F_A|-(ηsinθ/cosθ)=ma_x

look at the given information carefully. It tells you that acceleration, a=0, that is the body is in equilibrium so all the force balance out.
So essentially F_net=0

Balance out forces in both directions. And remember that F_A acts at an angle α (alpha), so appropriately use F_A*cos(α) or F_A*sin(α) and balance out the forces.

I hope it helps