How Does a Climber Use Friction to Stay Stationary?

[WoArt]

Homework Statement

A 75kg climber is supported in a "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are .8 and .6, respectively. what is the minimum normal force he must exert? Assume the walls are verticle and that friction forces are both a maximum.

Homework Equations

F=ma

The Attempt at a Solution

This one confuses me. If the climber is to stay in place, its the lower static friction coefficient that matters, isn't it? That being the case, in order to stay in place acceleration must be zero so Ff + Fmg = 0? Working that out though gives .6Fn + 75*9.8 = 0, which comes out to 735, which seems too high.

I have to assume I am completely missing something, can someone point me in the right direction?

 

[kreil]

in order for the climber to stay in place, the frictional force must at least be equal to the force due to gravity. If you write out all the forces (best way to start EVERY problem), you will see that F_g is aimed down, F_f is aimed upward, So, using F_f=F_g and solving for N gives the minimum normal force needed.

remember that since the climbers shoes and back are touching in different places there is more than one F_f to consider

 

[WoArt]

Yea, that's what I thought I was doing with f_f+f_mg=0. F_f being a function of F_n * .6 (friction coefficient). F_n is equal and opposite the force of the climber's push, right? Doesn't that give you .6Fn + 75kg *9.8 = 0?