Question

A floor wiper makes an angle (90 - θ) with horizontal I floor. μ_sand μ_k are coefficients of static and kinetic frictions between the wiper and the floor. The wiper can not be used to wipe the floor for θ<θ₀even if a large force directed along the handle aiming towards the centre is applied. Angleθ₀is given by

• A. cos^-1μ_k
• B. tan^-1μ_k
• C. tan-1 μ_k
• D. cot^-1μ_s.

Answer 1

Answer: (B)

tan^-1μ_k

Answer 2

mg + F cos 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 - μ(mg + F cos θ) ≥ 0

i.e., sin θ - μ cos ≥ $\frac { \mu \mathrm { mg } } { \mathrm { F } }$

or tan θ = μ

and in limiting case tan θ₀ = μ_s

or θ₀ = tan^-1 μ_s