1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Friction Force Theta Problem

  1. Oct 25, 2005 #1
    The handle of a floor mop of mass m makes an angle theta with the vertical direction. Let muK be the coefficient of kinetic friction between the mop and the floor and muS be the coefficient of static friction. Neglect the mass of the handle.

    a) Find the magnitude of the force F directed along the handle required to slide the mop with uniform velocity across the floor

    b) Show that if theta is smaller than a certain angle theta0, the mop cannot be made to slide across the flor no matter how great a force is directed along the handle. What is the angle theta0?

    Answers:

    So far, I have been able to get a. It's an odd question, so the answers are there in the back of the book. I got the answer for part a:
    |F| = MuK *mg / (sin(theta) - MuK *cos(theta))

    But I'm still stuck on B. I know that the horizontal component of the force F must be smaller than friction, so |F|sin(theta0) < MuS(mg+|F|cos(theta0).

    Now, the answer in the back of the book is simply Tan-1(MuS). But the extra MuS*mg is getting in the way. The only solution I see is the claim that because |F|sin(theta0) is so much larger than MuS*m*g, that the mg part of the normal force can be ignored. This allows you to simplify the problem to the answer, but is this right? It seems odd to simply get rid of one of the components.
     
  2. jcsd
  3. Oct 26, 2005 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Think of it this way: As long as the angle of the mop handle is less than [tex]\theta_0[/tex], where [tex]\tan \theta_0 = \mu[/tex], the mop won't slide regardless of its mass. Thus that angle works for any mop with the same [itex]\mu[/itex]. (Of course, as you realize, if you know the mass you can increase that angle a bit.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Friction Force Theta Problem
  1. Friction force problem (Replies: 9)

Loading...