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Non-Uniform Circular Motion: Locomotive Rounding a Curve

  1. Oct 28, 2011 #1
    1. The problem statement, all variables and given/known data

    As a locomotive rounds a circular curve of radius 2.10 km (which would be 2100 m to keep all the units the same), its speed is increasing at a rate of 0.440 m/s2. An instrument in the cab (an accelerometer) indicates that the magnitude of the locomotive's total acceleration at a particular instant is 0.760 m/s2. What is the locomotive's speed at that instant?

    After I got it wrong the first few times, I was also given the hint: "The total acceleration is the VECTOR sum of the centripetal acceleration and the tangential acceleration."

    2. Relevant equations

    The equations I have in my notes regarding non-uniform circular motion are:
    Radial Acceleration: Ar = -(mv^2)/R

    Tangential acceleration: At = d|v|/dt

    and Total Acceleration: Atot = √(Ar^2 + At^2)


    3. The attempt at a solution

    To solve, would it be correct to do the following:

    Ar = √(Atot^2 - At^2)

    And then sub that number into

    V = √((RAr)/(-m)

    But, if I were to do that, I would get the square root of a negative number, which is an irrational number, which I can't have as a velocity?

    Is there a better way to go about this question? What am I doing wrong?
     
  2. jcsd
  3. Oct 28, 2011 #2

    Doc Al

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    Staff: Mentor

    The negative sign just indicates that the acceleration is towards the center. Just worry about the magnitude.

    Otherwise your approach is fine.
     
  4. Oct 28, 2011 #3
    But there is no 'm' given in the question, and I don't know how to get radial acceleration any other way.
     
  5. Oct 28, 2011 #4

    Doc Al

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    Staff: Mentor

    Oops, I didn't see that. Your equation is not quite right:
    That's the centripetal force. The radial acceleration is just v^2/R.
     
  6. Oct 28, 2011 #5
    I must have copied it incorrectly during class. Thank you!
     
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