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A box, with a weight of mg = 25 N, is placed at the top of a ramp and released from rest. The ramp measures 4.40 meters horizontally and 3.50 meters vertically. The box accelerates down the incline, attaining a kinetic energy at the bottom of the ramp of 54.0 J. There is a force of kinetic friction acting on the box as it slides down the incline.

a) What is the coefficient of kinetic friction between the box and ramp? & please show work.

  • Physics -

    Equate the work done against friction to the mechanical (potential + kinetic) energy loss. That will allow you to solve for the friction coefficient, Uk.

    The slope of the ramp is arctan 3.5/4.4 , which is 38.5 degrees.

    The hypotenuse of the ramp is 5.622 m

    Show your work for further assistance.

  • Physics -

    I know the work done is

    W = ì X mgcosè X d

    and W is Ui+ W= Kf which is 54-(25*3.3)=-33.5

    so W = ì X mgcosè X d

    and so ì= (W/(mgcosè X d))

    and mg=25N so what is cosè? and i think d is the hypotenuse?

  • Physics -

    im sorry it should be cos theta for all of them

  • Physics -

    and the "i" looking thing is the coefficient of friction

  • Physics -

    It would be easier to do it the way Dr WLS suggested.
    vertical distance down = 3.5 m
    so potential energy lost = mgh=25*3.5 =87.5 Joules
    It has Ke of 54 Joules at the bottom so lost (87.5-54) = 33.5 Joules to friction
    Friction force * length of ramp = 33.5
    length of ramp = sqrt(3.5^2+4.4^2) = 5.62 meters
    so friction force = 33.5/5.62 = 5.96 Newtons
    5.96 = mu*normal force
    5.96 = mu * (25 cos slope)
    cos slope = 4.4/5.62
    mu = 5.96 *5.62/(4.4*25) = .238

  • Physics -

    Ohh I see! Thanks a lot!

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