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Static Friction Problem

  1. Sep 29, 2004 #1
    Hi, I'm having trouble solving this problem:

    A woman attempts to push a box of books that has mass up a ramp inclined at an angle (alpha) above the horizontal. The coefficients of friction between the ramp and the box are (mu_k) and (mu_s). The force F applied by the woman is horizontal.

    If (mu_s) is greater than some critical value, the woman cannot start the box moving up the ramp no matter how hard she pushes. Calculate this critical value of (mu_s).

    I know that the maximum value of mu_s is f_mu/N. So, using F(y) = ma(y), I got: N - F*Gcos(alpha) - F*Gsin(alpha) = 0. Therefore, making N = F*Gcos(alpha) + F*Gsin(alpha). That's it. I don't know what to do next. Any ideas?
     
  2. jcsd
  3. Sep 30, 2004 #2
    You have to resolve F in two directions: parallel to the incline and perpendicular to it. This will give you two equations, both involving F and one involving the normal reaction N, friction force f and acceleration a. Since the mass (of books) does not move up or down the incline, the acceleration a = 0. So this problem reduces to

    [tex]\sum F_{x} = 0[/tex]

    [tex]\sum F_{y} = 0[/tex]

    where x and y are the directions parallel and perpendicular to the incline.

    You should get the following equations as a result

    [tex]F\cos\alpha - mg\sin\alpha - f_{s} = 0[/tex]
    [tex]N - mg\cos\alpha - F\sin\alpha = 0[/tex]

    Solve them to get the value of [tex]\mu_{s}[/tex] using the fact that [tex]f_{s} = \mu_{s}N[/tex].

    Hope that helps...

    Cheers
    Vivek

    EDIT--The above equations are valid iff F is applied in the horizontal direction (i.e. in a direction parallel to the base of the incline).
     
    Last edited: Sep 30, 2004
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