1. Limited time only! Sign up for a free 30min personal 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 + centripetal acceleration problem

  1. Oct 19, 2005 #1
    A small cube of mass m is placed on the inside of a funnel rotating about a vertical axis at a constant rate of w revolutions per second. The wall of the funnel makes an angle theta with the horizontal. The coefficient of static friction between cube and funnel is u and the center of the cube is at a distance r from the axis of rotation. Find the (a) largest and (b) smallest values of w for which the cube will not move with respect to the funnel.

    I of course try to draw a free body diagram that looks pretty weird.

    does w_min look like sqrt(g(sin(theta)-ucos(theta))/r(cos(theta)+usin(theta)))? And wmax the same except for the fact that you add ucos)theta_ on the top except for subtracting.

    The problem is also Halliday volume 1 chapter 5 problem 18

    Thanks!
     
  2. jcsd
  3. Oct 19, 2005 #2

    Galileo

    User Avatar
    Science Advisor
    Homework Helper

    Ugh, let's put that in https://www.physicsforums.com/showthread.php?t=8997":
    [tex]\omega_{min}=\sqrt{g(\sin(\theta)-\mu\cos(\theta))/r(\cos(\theta)+\mu \sin(\theta))}[/tex]
    or, dividing top and bottom of the fraction by cos(theta) and using some cosmetics:
    [tex]\omega_{min}=\sqrt{\frac{g}{r}\cdot \frac{\tan \theta-\mu}{1+\mu \tan \theta}}[/tex]

    Much prettier o:)

    By the way, I got the same answer for [itex]\omega_{min}[/itex], for [itex]\omega_{max}[/itex] I get:

    [tex]\omega_{max}=\sqrt{\frac{g}{r}\cdot \frac{\tan \theta+\mu}{1-\mu \tan \theta}}[/tex]
    so there's a change in the denominator too.
     
    Last edited by a moderator: Apr 21, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Friction + centripetal acceleration problem
Loading...