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Finding an unknown applied force with friction, Fnet and more.

  1. May 14, 2012 #1
    1. The problem statement, all variables and given/known data
    a 20kg Toaster is on a level surface (Cooefficient of friction is 0.1). A rope applies an unknown force to the toaster at 30° from the horizontal upwards to the right. This force causes the toaster to accelerate at 0.277 m/s^2. What is the magnitude of the applied force.



    2. Relevant equations
    Fnet = m * a
    Fn = Fg - Fay
    Fax - Ff = Fnet
    Ff = μFn (Not sure if thats the symbol for mew)


    3. The attempt at a solution
    Found Fnet
    Fnet = 0.277 * 20
    Fnet = 5.54 N


    Friction Along the Floor

    Fn = Fg - Fay
    Fay = FaSin30°
    Fn = (9.8 * 20) - (FaSin30°)
    Fn = 196 - FaSin30°

    Finding Fa
    Fax - Ff = Fnet
    Ff = μFn
    Fax = FaCos30°


    Fax - (0.1*(196 - FaSin30°)) = 5.54 N
    Fax - 19.6 - (0.1 * - FaSin30°) = 5.54 N
    FaCos30° - 19.6 + (0.1 * FaSin30°) = 5.54 N
    FaCos30° + (0.1 * FaSin30°) = 25.11 N
    Cos30° + (0.1 * Sin30°) = 25.11 N / Fa
    0.866 + (0.1 * 0.5) = 25.11 N / Fa
    0.916 = 25.11 / Fa
    0.916Fa = 25.11
    Fa = 27.4 N

    ---------------------------------------------------------

    EDIT: Fax = FaCos30°, making a common variable.
    EDIT2: Factored, checking if its right ATM.
    EDIT3: YAY :D, Working backwards it works :). Excentric, if anyone can double check my work, would be so awesome.
     
    Last edited: May 14, 2012
  2. jcsd
  3. May 14, 2012 #2

    ehild

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    Gold Member

    It is correct at the end :smile:

    ehild
     
  4. May 14, 2012 #3
    Sweet, thank you :)
     
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