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Finding coefficient of kinetic friction

  1. Nov 2, 2007 #1
    A 37 kg box slides down a 35 degree ramp with an acceleration of 1.35 m/s^2. The acceleration of gravity is 9.81 m/s^2.

    Find the coefficient of kinetic friction between the box and the ramp.


    Ff= MkFn


    37 * 1.35 = 49.95 N
    Fgx = 49.95 sin 35 = 28.650143
    Fgy = 49.95 cos 32 = 40.91664461


    Ax = (1/m)(Ff - Fgx)

    Ax= ((1/m)(Ff)) - ((1/m)(Fgx))
    Ax + ((1/m)(Fgx)) = ((1/m)(Ff))
    1.35 + ((1/37)(28.650143)) = ((1/37)(Ff))
    2.124328189 = ((1/37)(Ff))
    2.124328189 * 37 = Ff
    78.600143 = Ff

    Mk = 78.600143 / 40.916
    Mk = 1.921012391

    I think I did something wrong because the coefficient is greater than one

    Please check what I did wrong and how can I fix it?
     
  2. jcsd
  3. Nov 3, 2007 #2

    Astronuc

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    Staff: Mentor

    This approach is not correct.

    The acceleration of 1.35 m/s2 is the consequence of friction, and has no effect on the normal force.

    Start with the weight components normal and parallel with the plane of the incline.

    mg = 37 kg * 9.81 m/s2 = 363 N.

    Fgx = mg sin 35° = 363 sin 35° = 208.2 N
    Fgy = mg cos 35° =363 cos 35° = 297.4 N

    Now the normal force of the box on the incline produces friction according to [itex]\mu[/itex]Fgy

    http://hyperphysics.phy-astr.gsu.edu/hbase/mincl.html#c2

    So the friction force is [itex]\mu[/itex]297.4 N

    However, a better approach is to think about the net force acting down the incline: Fgx-Ffrict = mg sin 35° - [itex]\mu[/itex]mg cos 35°.

    Dividing the force by the mass being accelerated gives the acceleration, so

    a = g sin 35° - [itex]\mu[/itex]g cos 35° = 0.574 g - [itex]\mu[/itex] 0.819 g = 1.35 m/s2


    BTW, this appears to be a homework problem, so please post in the HW forum, Introductory Physics.
     
  4. Nov 4, 2007 #3
    Sorry for posting twice and thanks for the help!
     
  5. Nov 4, 2007 #4

    Astronuc

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    Staff: Mentor

    You are very welcome!

    If one of one's posts goes missing, one can click on one's username and select 'Find More Posts by username', then select the post.
     
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