Posted by K on Monday, October 26, 2009 at 9:55am.
The 49 kg climber is supported in the "chimney" by the friction forces exerted on his shoes and back. The climber has reduced push to verge of slip. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 1.2 and 0.8, respectively. What is the magnitude of the push he must exert? What fraction of the climbers weight is supported by the frictional force on his shoes?

physics  bobpursley, Monday, October 26, 2009 at 10:23am
Well, if he is at the point of slip, then force friction shoes=X*mg
where x is some fraction of weight.
This means force normal=K, and mu*K= Xmg
Now if K is the normal force, then K must be acting on the back, so friction on the back is .8*mg*(1x)
we know the two frictions have to equal weight,
.8(mg)(1x)+1.2*X*mg=mg
.8.8x+ 1.2x=1
.4x=.2
x= .5
so half his weight is supported by his shoes. 
physics  Web, Wednesday, February 10, 2010 at 8:52pm
force of push = (mg)/(u1+u2), so
(49*9.8)/(1.2+.8)=240.1N
fraction of weight= (u1)/(u1+u2),so
(1.2)/(1.2+.8)=.6