Statics – Friction problem

1. The problem statement, all variables and given/known data

Determine the minimum horizontal force P required to hold the crate from sliding down the plane. The crate has a mass of 35kg and the coefficient of static friction between the crate and the plane is μs = 0.40

2. The attempt at a solution

Fx = P cos 30 – 343.35 sin 30 + F = 0
Fy = -P sin 30 – 343.35 cos 30 + N = 0

F = (μs)(lNl) = 0.40 (N)

so,

Fx = P cos 30 – 343.35 sin 30 + 0.40(N)

therefore,

Fy = -P sin 30 – 343.35 cos 30 = -N

so, F = 0.40 (P sin 30 + 343.35 cos 30)

Sub into Fx,

P cos 30 – 343.35 sin 30 + 0.40 (P sin 30 + 343.35 cos 30) = 0

Now solving for P I get 51.6 N, which is incorrect.
The answer is given. P = 49.5 N

Can anyone give me an indication of where I have gone wrong please.

Thank You.

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