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!

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

    learningphysics

    User Avatar
    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]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How do I find Theta critical
  1. I cant find theta (Replies: 7)

Loading...