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Homework Help: How do I find Theta critical

  1. Oct 8, 2007 #1
    We have Uk and/or Us and angle of inclination (theta)

    Are these eq-ns relevant? sin(theta critical)=Us(tan(theta critical))=Us
    and sin(theta static)/cos(theta static)=Uk(tan(theta static)=Uk

    How do I even interpret these eq-ns? Exam is tomorrow and I need to know how to find the angle of inclination that allows an object to start sliding (theta critical) and the angle of inclination so that the object will slide w/o accelaration. This is for an object on an inclined plane w/ friction.
  2. jcsd
  3. Oct 8, 2007 #2


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    Homework Helper

    I'm confused by the equations you wrote... can you write them exactly as they are?

    The moment when sliding occurs is when the static frictional force becomes [tex]\mu_s*F_n[/tex].

    Take the equation perpendicular to the plane... [tex]F_n - mgcos(\theta) = 0[/tex], so [tex]F_n = mgcos(\theta)[/tex]

    The equation parallel to the plane is: [tex]mgsin(\theta) - f = 0[/tex]

    so this is while the block is not sliding...

    ie: [tex]f = mgsin(\theta)[/tex] (1)

    so this equation is always true while the block is not sliding... you will notice that as theta becomes larger (the incline becomes steeper)... f becomes larger... this is all while the block is still not sliding... but there is a limit to how long this can go on... the limit occurs when f becomes [tex]\mu_s*F_n = \mu_s*mgcos(\theta)[/tex].

    so to find the angle at which this limit occurs substitute [tex]f = \mu_s*mgcos(\theta)[/tex] into (1)

    so you get:

    [tex]\mu_s*mgcos(\theta) = mgsin(\theta)[/tex]

    [tex]\mu_s = tan(\theta)[/tex]
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