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Engineering Dynamics: Normal-Tangential Components

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data
    A race boat is traveling at a constant speed v0 = 130 mph when it performs a turn with constant radius ρ to change its course by 90°. The turn is performed while losing speed uniformly in time so that the boat's speed at the end of the turn is vf = 116 mph. If the magnitude of the acceleration is not allowed to exceed 2g, where g is the acceleration due to gravity, determine the tightest radius of curvature possible and the time needed to complete the turn.


    2. Relevant equations
    ρ(x) = ([1 + (dy/dx)2]3/2)/(absvalue(d2y/dx2))

    *edit* an = v2

    a = atut + anun

    v = vut

    at t = 0;
    ut = -sin90i + cos90j
    3. The attempt at a solution

    So the distance traveled by the boat is 1/4 of a circle, s = rθ = ρ([itex]\pi[/itex]/2)

    converting mph to ft / s
    v2 = v02 + 2 ac(s - s0)
    [(170.13)2 - (190.67)2] / 2(32.2 ft/ s ^2) = s
    s = 57.5 ft = 17.5 meters


    ρ = 57.5 ft * 2 / pi

    I feel like I'm missing something BIG because it can't be this simple.
     
    Last edited: Feb 12, 2012
  2. jcsd
  3. Feb 12, 2012 #2

    PhanthomJay

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    The equation you have written assumes tangential acceleration only at -1g. You want the total resultant acceleration (centripetal plus tangential, vectorially added) not to exceed 2g's.
     
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