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Kinetics, force and acceleration

  1. Mar 22, 2010 #1
    1. The problem statement, all variables and given/known data

    The crate has a mass of 80 kg and is being towed by a chain which is always directed at 20º from the horizontal has shown. Determine the crate's acceleration in t = 2 s if the coefficient of static friction is μs = 0.4, the coefficient of kinetic friction is μk = 0.3, and the towing force is P = (90t2) N, where t is in seconds.


    2. Relevant equations

    ΣF = ma

    3. The attempt at a solution

    ΣFx = max
    Pcos(20º) - μkmg = ma
    84.57t2 - 235.44 = (80 kg)a

    solving for a when t = 2
    a = 1.29 m/s2

    The answer at the back of my book is a = 1.75 m/s2. I think I'm supposed to consider that static friction force is greater than kinetic friction force, but I can't figure out how to do that.
  2. jcsd
  3. Mar 22, 2010 #2

    Doc Al

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    Staff: Mentor

    The force of friction is μN, but N does not simply equal mg. Solve for N, taking into consideration that the applied force is at an angle.
  4. Mar 22, 2010 #3
    Then N = mg*cos(20°)?
    But that gives a = 1.46 m/s2, not a = 1.75 m/s2.
  5. Mar 22, 2010 #4

    Doc Al

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    Staff: Mentor

    How did you come to that conclusion?

    To solve for N, add up the vertical components of all forces acting on the body. (N is one of those forces.) The sum must be zero, since the body is not accelerating vertically.
  6. Mar 22, 2010 #5
    Thank you, Doc Al.
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