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Homework Help: Forces on a Bike

  1. Apr 17, 2005 #1
    A biology student rides her bike around a corner of radius 24 meter at a steady speed of 8.3 m/sec. The combined mass of the student and the bike is 87 kg. The coefficent of static friction between the bike and the road is μs = 0.39.

    a) If she is not skidding, what is the magnitude of the force of friction on her bike from the road?
    Ffric = N *
    b) What is the minimum value the coefficient of static friction can have before the bike tire will skid?
    μmin = *
    0.292 OK
    c) What is the magnitude of the total force between the bike tire and the road?
    Ftotal = N
    1103.19 NO

    Need help with part c.

    Is it something like this F = mg + mv^2/R

    Is this correct.
  2. jcsd
  3. Apr 17, 2005 #2

    Andrew Mason

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    The total force on the bicycle is:

    [tex]\vec F = m\vec g + \vec N + \mu_sN\hat r = m\vec a = \frac{mv^2}{R}\hat r[/tex]

    The forces exerted by the road on the bicycle are [itex]\vec N, \mu_sN\hat r [/itex]. The magnitude of those forces would be the magnitude of the vector sum:

    [tex]m\vec g - \frac{mv^2}{R}\hat r = \vec N + \mu_sN\hat r[/tex]

    Note[itex]\vec N[/itex] and [itex]\hat r[/itex] are perpendicular. What is the magnitude of the resultant force?

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