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a slide loving pig slides down a certain 44° slide in twice the time it would take to slide down a frictionless 44° slide. What is the coefficient of kinetic friction between the pig and the slide?

  • physics -

    The force of friction on the slide is

    mg*mu*cosTheta, and the component of gravity down the slide is mgsinTheta

    F=ma=m(vf/time) but vf with friction is 1/2 that of no friction (why? average velocity is 1/2 that of no friction).

    so, with friction...
    mgSinTheta-mg*mu*Costheta=m Vf/time
    =m 1/2 V'/2 t' where the ' means no friction.
    g sinTheta-g*mu*cosTheta=V'/4t'

    now without friction..
    mg sinTheta -nofriction=m v'/t'
    or v'/t'=g sinTheta
    now back into the friction equation.
    g sinTheta-mu*g*CosTheta=g sinTheta/4
    dividing both sides by g cosTheta
    tanTheta-mu=tantheta /4
    mu=3/4 tanTheta

    check that.

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