Part b: Solving for Force & Friction to Find θ0 Angle

[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?

 

[tiny-tim]

Hi demonelite123!

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

just use the same method as for a) …

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

 

[demonelite123]

Hi demonelite123!


just use the same method as for a) …

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

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

 

[tiny-tim]

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

(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 - μ_scosθ) is 0, then the force would have to be infinite, in other words no force will be able to move the mop.

 

[demonelite123]

(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 - μ_scosθ) is 0, then the force would have to be infinite, in other words no force will be able to move the mop.

ok now i understand, thanks!