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Dynamics- Friction

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data

    A box is halfway up a ramp. The ramp makes an angle, θ with the ground. What is the maximum value of θ before the mass will slip? μ[itex]_{s}[/itex]=0.25

    2. Relevant equations

    F[itex]_{x}[/itex]=ma[itex]_{x}[/itex]

    3. The attempt at a solution
    I drew a free body diagram to show the forces affecting the box

    η-mgcos=0
    η=mgcosθ (eq'n 1)


    F[itex]_{x}[/itex]=ma[itex]_{x}[/itex]
    μ[itex]_{s}[/itex]η-mgsinθ=ma[itex]_{x}[/itex] (sub eq'n 1 in)
    μ[itex]_{s}[/itex](mgcosθ)-mgsinθ=ma[itex]_{x}[/itex]
    mg(μ[itex]_{s}[/itex]cosθ-sinθ)=ma[itex]_{x}[/itex]


    I'm not sure where to go from here, or even if this is the correct path for me to take
     
  2. jcsd
  3. Oct 7, 2013 #2

    PhanthomJay

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    You have correctly identified the forces acting, but just as the box is on the verge of slipping, is it accelerating?
     
  4. Oct 7, 2013 #3
    the box wouldn't be accelerating, so would it be

    mg(μ[itex]_{s}[/itex]cosθ-sinθ)=0
    mgμ[itex]_{s}[/itex]cosθ=mgsinθ
    μ[itex]_{s}[/itex]cosθ=sinθ
    μ[itex]_{s}[/itex]=tanθ
    θ=14.036
     
  5. Oct 7, 2013 #4

    PhanthomJay

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    Yes, good, in degrees (don't forget units), but you should round your answer to 14 degrees ( 2 significant figures).
     
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