Finding Force and Angle for Mop Head Movement

[intenzxboi]

Homework Statement

In Figure 6-62 a fastidious worker pushes directly along the handle of a mop with a force . The handle is at an angle θ = 40° with the vertical, and μs = 0.61 and μk = 0.48 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 = 0.65 kg is in its head. (a) If the mop head moves along the floor with a constant velocity, then what is F? (b) If θ is less than a certain value θ0, then (still directed along the handle) is unable to move the mop head. Find θ0.

Im having trouble understanding how to solve for part b.

i got to:
Fsin0 - Fs (mg-Fcos0)=0

but i can't solve of the angle.

 

[tiny-tim]

Hi intenzxboi!

(have a theta: θ and a phi: φ )

Hint: put Asinθ + Bcosθ in the form C(sinθcosφ + cosθsinφ), for some angle φ