Static Equilibrium Climber Problem

[craig22]

Homework Statement

A climber with a weight of 510 N is held by a belay rope connected to her climbing harness and belay device; the force of the rope on her has a line of action through her center of mass.The indicated angles are θ = 41˚ and φ = 26˚. If her feet are on the verge of sliding on the vertical wall, what is the coefficient of static friction between her climbing shoes and the wall?

Homework Equations

Sum of all forces = 0
Sum of all torques = 0

The Attempt at a Solution

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F_N - Normal force from the wall
T - Tension from rope
F_s - Static friction

What am I doing wrong?

 

[Astronuc]

One has

F_N - Normal force from the wall
F_s - Static friction

but F_s = μF_N and must act vertically, opposite the weight of the climber.

T must be resolved into x (horizontal) and y (vertical) components,

and one must consider the torques, which must equal zero.

The climber's moment is the length of rope, but the moment opposing is the distance from from the rope at the wall to the feet.