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Dynamics - Normal and Tangential Motion

  1. Feb 11, 2013 #1
    1. The problem statement, all variables and given/known data

    The tires on a car are capable of exerting a maximum frictional force of 1753 lb. If the car is traveling at 75 ft.s and the curvature of the road is ρ=560 ft, what is the maximum acceleration that the car can have without sliding?

    2. Relevant equations

    ƩFn = man

    3. The attempt at a solution

    Ff = 1753 lb
    v = 75 ft/s
    ρ=560 ft
    wcar = 3150 lb

    an = [itex]\frac{v^2}{ρ}[/itex] = [itex]\frac{75^2}{560}[/itex] = 10.04 ft/s2

    I believe that the acceleration would be the magnitude of the tangential and normal acceleration.

    ƩFn = man = [itex]\frac{3150}{32.2}[/itex]*10.04 = 982.2 lb

    1753 = √Ft2 + 982.22

    Solving for Ft = 1452 lb;

    Now solving for at → 1452 = [itex]\frac{3150}{32.2}[/itex]*at
    at = 14.85 ft/s2

    a = √at2 + an2 = √14.852 + 10.042 = 17.90 ft/s2

    I'd appreciate it if someone could verify my work.
     
  2. jcsd
  3. Feb 11, 2013 #2
    I get the same answer as you. I think the question is asking for the maximum tangential acceleration which is 10.04 ft/sec^2.
     
  4. Feb 11, 2013 #3
    Tangential was actually 14.85 ft/s^2.

    And it makes sense too.

    Thanks.
     
    Last edited: Feb 11, 2013
  5. Feb 11, 2013 #4
    I typed the wrong number.......should have typed 14.85 ft/s^2.
     
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