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Distance traveled in a circular motion

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data

    A car starts from rest and accelerates around a flat curve of radius R = 31.7 m. The tangential component of the car’s acceleration remains constant at at = 2.97 m/s2, while the centripetal acceleration increases to keep the car on the curve as long as possible. The coefficient of friction between the tires and the road is μk = 0.851. What distance does the car travel around the curve before it begins to skid? (Be sure to include both the tangential and centripetal components of the acceleration.)


    2. Relevant equations

    F=(mv^2)/r
    F=ma
    F=μN


    3. The attempt at a solution
    mv^2/r=μN
    mv^2/r=μmg
    μg=v^2/r
    v^2=rμg
    v^2=v(initial)^2+2ax
    rμg=2ax
    x=rμg/(2a)
    x=(31.7)(.851)(9.81)/(2(9.81))
    x=44.55m
    This is how i attempted the problem, but am apparently incorrect. What am i doing wrong?
     
  2. jcsd
  3. Oct 28, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The static friction that acts at the tyres has to cover the total accelerating force which includes both centripetal and tangential acceleration.

    ehild
     
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