# Homework Help: Force and friction

1. Oct 13, 2009

### demonelite123

A worker pushes on a mop with a force F. The handle is at an angle θ with the vertical and μs and μk are the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop's mass m is in its head.

a) If the mop head moves along the floor with a constant velocity, then what is F?

b) Show that if θ is less than a certain value θ0, then F is unable to move the mop head. Find θ0

i got part a) to be F = μk(mg) / (sinθ - μkcosθ).

but i can't get part b). all i have is Fn(μs) = Fsinθ0 where Fn is the normal force. the book's answer is θ0 = tan-1(μs). how did they get that?

Last edited: Oct 14, 2009
2. Oct 14, 2009

### tiny-tim

Hi demonelite123!
just use the same method as for a) …

you'll have (sinθ - μscosθ) on the bottom, and that has to be … ?

3. Oct 14, 2009

### demonelite123

if (sinθ - μscosθ) is 0, then the force is undefined?

4. Oct 15, 2009

### tiny-tim

(just got up :zzz: …)

hmm … this is physics, not maths! …

in maths, things can be undefined, but in physics either they exist or they don't …

in this case, if (sinθ - μscosθ) is 0, then the force would have to be infinite, in other words no force will be able to move the mop.

5. Oct 15, 2009

### demonelite123

ok now i understand, thanks!