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Static Friction and Circular Motion problem

  1. Apr 16, 2007 #1
    1. The problem statement, all variables and given/known data
    Part 1: Rounding a flat, unbanked curve, which has a radius (r), the coefficient of static friction between the car and the road is 0.5. Find the max speed you can take the curve without sliding.

    Radius (r) = 25 m

    I'll be using (Us) to denote the coefficient of static friction.

    Part 2: If the curve is banked at some angle (theta), find theta so that no frition is required to make the curve.

    2. Relevant equations
    fsmax = Us * N
    N= mg
    NcosTheta = mg
    NsinTheta = mv²/r


    3. The attempt at a solution
    For the first part, I concluded that any sideways motion would be the sliding of the car. So static friction has not exceeded maximum friction. So Us < Fsmax. Since theres no vertical motion, N = mg. I figured when the car is about to skid (the max speed) Us = Fsmax.

    I came up with the equation: V = √(Us * r * g). Plugging in the #s I got √(.5 * 25m * 9.81m/s²). Which gave me an answer of 11.07 m/s.

    Does that sound right?

    I'm much more confused with part 2 of the equation. Im assuming the velocity is needed to figure out the angle, so apparently the velocity from part 1 is used. I came up with the equations listed above

    NcosTheta = mg
    NsinTheta = mv²/r

    But if theres no friction at all, wouldnt the angle then have to be zero? I'm really lost on the 2nd part of this problem, but confirmation on the first part would be helpful also.

    Thanks.
     
  2. jcsd
  3. Apr 16, 2007 #2
    look at the two equations you have, what can you do with them? Do you see any common variables on both equations? Do those common variables effect the angle? What does the force of friction do? what direction is friction force facing?
     
    Last edited: Apr 16, 2007
  4. Apr 16, 2007 #3
    Re part two. No, not flat. Look at oval auto racing, they have banks, not because the tires lack friction but everyone wants faster. Is there a way to use that principle so that gravity helps offset the tendency to lose control?
     
  5. Apr 16, 2007 #4
    The common variables are the Normal force and the mass, neither of which would effect the angle. The thing I could think of would be combining the equations, since sin divided by cos equals tangent. The normal forces would cancel out resulting in the equation

    tanTheta = v² / rg

    But where does friction play a role in this? The way I see it if friction is supposed to be zero, even if it was part of the equation, it would zero that side of the equation and force the angle to be zero.
     
  6. Apr 16, 2007 #5
    Maybe it's the way I'm looking at it, but if there's no friction, the car would slide immediately. So isn't it impossible to take a curve without friction, even if it is banked at an angle?

    Is this a trick question :confused:
     
  7. Apr 16, 2007 #6
    drawing a FBD really helps. Try that way, that may help
     
  8. Apr 16, 2007 #7
    Alright, I think I got an answer.

    tanTheta = V²/rg = Us*m*g

    Theta = Tan -1 (V²/rg) = 26.6 degrees.

    Since mass isn't really a factor, I tested the answer with the equation tanTheta = Us*m*g. Us = tanTheta / m*g.

    tan26.6 / 800kg(arbitrary)*9.81m/s² = Us = .00006 which is basically insignificant.

    Does this look okay?
     
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