Force of block pushed against wall

[uph0]

Homework Statement

A block of mass 20 kg is pushed against a vertical surface (see picture). The coefficient of friction, μ, between the surface and the block is 0.2. If θ = 30°, what is the minimum magnitude of P to hold the block still?

Homework Equations

f = force of friction = μN

The Attempt at a Solution

I drew a force body diagram and got equations for x and y.
x: N - Psinθ = 0
Y: -pcosθ + mg + f = ma_y

N = psinθ
so f = μ psinθ
I put f = μ psinθ into the y equation

so i get
-pcosθ + mg + μpsinθ = ma_y

I'm stuck here. I want to find P but I don't know the acceleration.

 

[256bits]

The problem states that the block is still, which would mean that ay = ?

 

[Simon Bridge]

I'm stuck here. I want to find P but I don't know the acceleration.

The question asks:

what is the minimum magnitude of P to hold the block still?

Therefore the magnitude of the velocity is...?
The change in velocity is ...?
The acceleration is ...?

Why "minimum"? What kind of friction is this?