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How to find acceleration given only angle of slope and coefficient of friction?

  1. Sep 24, 2012 #1
    1. The problem statement, all variables and given/known data
    A crate is placed on an inclined board. The coefficient of friction between the crate and the board is 0.26 , and the angle of the slope is 16 degrees. Calculate the acceleration of the crate down the incline.


    2. Relevant equations
    F=ma
    Ff=umgcos(theta)
    Forge of gravity parallel = mgsin(theta)


    3. The attempt at a solution
    F=ma
    Fg - Ff = ma
    mgsin(theta) - umgcos(theta) = ma
    so this is where it gets tricky for me.. i've tried factoring and removing a mass from each side.. but i'm still left with one mass.
    What do i do? :/
     
  2. jcsd
  3. Sep 24, 2012 #2

    rock.freak667

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    Homework Helper

    From here:

    mgsinθ - umgcosθ = ma

    your mass 'm' cancels out, so the acceleration does not depend on the mass.
     
  4. Sep 24, 2012 #3
    sorry I'm still confused, but which mass comes out? or all the masses cancel out? when i try that, I don't get the answer.
     
  5. Sep 24, 2012 #4

    rock.freak667

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    All of the 'm's in the equation are the same, so they all cancel out.
     
  6. Sep 24, 2012 #5
    Ah true okay thank you sir, help very much appreciated, so then I would just do:

    gsinθ - ugcosθ = a

    Now does the equation above work? because I think I remember trying this cancelling out all of the m's, and I got a wrong answer, but I probably did my math wrong. I'll check once I finish with my chemistry and math homework.
     
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