Results 1 to 2 of 2

Thread: Uniform rod / moments

  1. #1
    Sep 2008

    Uniform rod / moments

    The diagram shows a uniform rod AB, of length 2a and weight W, resting in equilibrium with its end A on a rough horizontal floor and the end B connected to a point C on the floor by a light inextensible string. The plane ABC is vertical. The rod makes an angle of 60 degrees with the floor and the string makes an angle of 30 degrees with the floor. The coefficient of friction between the rod and the floor is mew.

    a) Find, in terms of W, the magnitude of the tension in the string

    b) Find the least possible value of mew.

    Ok for part a i'm not sure exactly what to do but i assume you resolve vertically. So by saying the reaction of the rod on the floor is R i get

    R + Tsin30 = W

    but im not sure if this is right or where to go with it :/

    also not sure about part b maybe something to do with when slips
    F< mew*R and taking moments about A ???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Jun 2008
    North Texas
    $\displaystyle \sum \tau = 0$

    $\displaystyle T\sin(30) \cdot 2a = W\sin(30) \cdot a

    $\displaystyle T = \frac{W}{2}$

    $\displaystyle \sum F_y = 0$

    $\displaystyle W + T\sin(30) = N$

    $\displaystyle N = \frac{5W}{4}$

    $\displaystyle \sum F_x = 0$

    $\displaystyle T\cos(30) = f_s$

    $\displaystyle f_s \le \mu \cdot N$

    $\displaystyle T\cos(30) \le \mu \cdot \frac{5W}{4}$

    $\displaystyle \frac{\sqrt{3} W}{4} \le \mu \cdot \frac{5W}{4}$

    $\displaystyle \mu \ge \frac{\sqrt{3}}{5}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Oct 31st 2010, 07:09 PM
  2. Moments
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: Mar 19th 2010, 07:37 PM
  3. uniform differentiable => uniform continuity
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Nov 30th 2009, 03:19 PM
  4. moments
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: May 5th 2009, 08:47 PM
  5. Uniform Continuous and Uniform Convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 28th 2007, 02:51 PM

Search Tags

/mathhelpforum @mathhelpforum