Mopping baby

Classical Mechanics Level 2

In the above figure, a baby pushes directly along the handle of a mop with a force of $F.$ The handle is at an angle of $\theta$ with the vertical, and $\mu_s = \frac{1}{\sqrt{3}}$ and $\mu_k = \frac{1}{3}$ are the coefficients of static and kinetic frictions, respectively, between the head of the mop and the floor. If the mop has no mass and $\theta$ is less than some angle $\theta_0,$ then the baby is unable to move the head of the mop. What is $\theta_0$ in degrees?

45 30 60 10

3 solutions

Rwit Panda
Jun 10, 2015

We know that coefficient of static friction is 1/sqrt(3). we just need to overcome static friction and then kinetic friction will automatically start functioning and we don't need to worry about it. coming to the question, the minimum angle of inclination for mop to move is suppose 'x'. Static friction is therefore, Fcosx/sqrt(3). this acts backwards. Fsinx acts forward. As this is the minimum x, so Fcosx/sqrt(3)=Fsinx, cosx=sqrt(3)sinx, sinx=30 degrees

Adrian Peasey
Jun 29, 2015

We want the limiting case when $F=R\mu_s$ , where $F$ is the parallel force and $R$ is the perpendicular reaction force.

Taking the appropriate components gives: $F\sin\theta_0=F\cos\theta_0 \mu_s\Rightarrow \tan\theta_0=\mu_s=\frac{1}{\sqrt{3}}\Rightarrow \theta_0=\boxed{30}$ .

Leonblum Iznotded
Jul 24, 2018

(This is no solution, this is about vocabulary.)

I had to read the text 4 or 5 times, and search on the net, about "head of the mop", to understand the problem was not the slippery of kid's hands on the handle but the mop's cleaning end on the floor.

Mopping baby

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