1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Engineering Dynamics Normal Date
Finding the density inside a tank as air escapes Dec 12, 2017
Surface runoff Jun 30, 2017
Angular Momentum Incorrect Graph? May 13, 2017
Simplified Air-Conditioning Calculations Feb 25, 2017