Physics

The Daytona International Speedway shown below has the following track statistics: Bank turn of 31.0o, a radius of curvature of 1000 ft, and a total length of 2.50 mi. Given that the typical weight of a NASCAR car is 3000 lbs, and that the friction coefficient between the tires and the track is around 0.9-1.3 (use 0.900), estimate the maximum speed of the race car in a banked turn.

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  1. I guess we are doing feet and pounds and such.
    force down on car = 3000 lbs = m g
    car mass = 3000/g
    normal force of weight on track = 3000cos 31
    so max friction force down tangent to track = 3000 cos31*0.9
    component of weight down tangent to track = 3000 sin 31

    acceleration tangent to track = v^2/R * cos 31 down track
    so
    3000 * .9 * cos 31 + 3000 sin 31 = m v^2/R = 3000/g * v^2/R
    .9 cos 31 + sin 31 = (v^2/R) / g = ratio of centripetal to gravitational acc
    (of course in the end the weight does not matter :)
    R = 1000
    g = 32 ft/s^2
    solve for v in feet/second

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  2. Forgot to continue component of centrripetal down slope
    acceleration tangent to track = v^2/R * cos 31 down track
    so
    3000 * .9 * cos 31 + 3000 sin 31 = m v^2/R = 3000/g * v^2/R cos 31
    .9 cos 31 + sin 31 = (v^2/R) cos 31 / g = ratio of centripetal to gravitational acc
    (of course in the end the weight does not matter :)
    R = 1000
    g = 32 ft/s^2
    solve for v in feet/second

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