Circular Motion, Static Friction

[teenholiday]

Homework Statement

An astronaut is training in an earthbound centrifuge that consists of a small chamber whirled around horizontally at the end of a 4.5 m-long shaft. The astronaut places a notebook on the vertical wall of the chamber and it stays in place.

If the coefficient of static friction is 0.70, what is the minimum rate at which the centrifuge must be revolving?
Express your answer using two significant figures.
w = ________ rad/s

Homework Equations

a=v^2/r

F_s= uN

The Attempt at a Solution

u=.7
r=4.5

F_s= uN
f_s=u(mg)

F=ma
F=m(v^2/r)

setting the two forces equal togehter

u(mg)=m(v^2/r)

v= sqrt(ugr)

i got 5.6.

where am i going wrong? thanks

 

[moose]

f_s=u(mg) isn't valid in this problem

The normal force isn't mg because gravity is acting downwards. You need the a=v^2/r.

I think you just had it backwards... You wrote
u(mg)=m(v^2/r)
instead of
u(mv^2/r)=mg

 

[dynamicsolo]

Keep in mind that "normal force" means the force acting perpendicular to the surfaces in contact ("normal" means "perpendicular" in geometry). So, in this situation, the normal force is pointing at the center of the circle.

This means that the centipetal force (which is a resultant force and not a physical force -- which is why we never draw it in a free-body diagram) is provided by the normal force for this sort of problem.