A floor wiper makes an angle (90 - θ θ ) with horizontal I floor. μ μ s and μ μ k are coefficients of static and kinetic frictions between the wiper and the floor. The wiper cannot be used to wipe the floor for θ θ < θ θ 0 even if a large force directed along the handle aiming towards the centre is applied. Angle θ θ 0 is given by
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mg + F cos θ θ = R
Where m is mass of wiper. F is applied force towards centre and R is normal reaction of ground upward.
If motion is allowed on the floor.
i.e., F sin θ θ - μ μ (mg + F cos θ θ ) ≥ ≥ 0
i.e., sin θ θ - μ μ cos ≥ ≥ 
or tan θ θ = μ μ
and in limiting case tan θ θ 0 = μ μ s
or θ θ 0 = tan -1 μ μ s
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