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March 26, 2017

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A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius R=4 cm. The plane of the coin is tilted at an angle of θ=45∘ with respect to the horizontal plane (see the figure below). Find the coin's period T in seconds, that is, the time it takes for the coin to go around the circle of radius R. The radius of a U.S quarter is r=1.2 cm.

  • physics - ,

    Newton’s 2nd law
    vector(ma) = vector(mg ) +vector( N) +vector(Ffr)
    Projections:
    ma=F(fr)
    0=N-mg

    mv²/r =μN
    N=mg

    mv²/r = kN = μmg
    μ=v²/gr.

    tanα =F(fr)/N = μmg/mg = μ = v²/gr.
    v=sqrt{gr•tanα}

    T=2πR/v= 2πR/ sqrt{gr•tanα} = …

  • physics - ,

    nope, 0.733 is wrong

  • physics - ,

    wait, Elena, what is are R and r? Are they the same ones that I used?

  • physics - ,

    R=0.04 m
    t= 0.012 m
    The solution is correct.May be there is mistake in calculations (or in your answer)...

  • physics - ,

    net torque on the coin, answer not just force balance

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