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Speed on an Inclined plane

  1. Dec 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider 4 frictionless slides described by the equations

    (1) y = sqrt(x), (2) y = x, (3) y = 2x, (4) y = x2. If you start at rest at y = h and slide down to y = 0, which statement regarding your speed v at y = 0 is correct?

    2. Relevant equations

    (1/2)mv2 = KE
    mgh = PE

    3. The attempt at a solution
    The answer to this question is that all the speeds are equal at y = 0

    I know the question asks for speed and that speed is distance over time, so doesn't that mean their speeds should differ taking 1, 2, 3, and 4 into account?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 5, 2009 #2

    kuruman

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    Speed is "distance over time" only if there no acceleration, i.e. when the object covers equal distances in equal times. I don't know what y = x2 means, but if it describes a slide, there must be acceleration in case (4) also. Try conservaion of mechanical energy and see what that tells you.
     
  4. Dec 5, 2009 #3
    o whoops I meant to put that as x^2

    I solved for v using conservation of mechanical energy but all my v values came out rather different still. I think I might be doing it wrong...
     
  5. Dec 5, 2009 #4

    kuruman

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    Can you show what you did and exactly how your v values came out wrong?
     
  6. Dec 5, 2009 #5
    here's one example

    1.
    mgsqrt(x) = (1/2)mv2

    sqrt(2g(sqrt(x))) = v

    2.
    mgx = (1/2)mv2
    sqrt(2gx) = v
     
  7. Dec 5, 2009 #6

    kuruman

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    In all cases the initial kinetic energy is zero and the final potential energy is zero. So the initial potential energy is equal to the final kinetic energy. That's conservation of mechanical energy. Now answer this question, if in all cases the mass starts at height h, what is its initial potential energy?
     
  8. Dec 5, 2009 #7
    I think I am getting confused by the
    y=sqrt(x), y = x etc.

    so having that aside, if they all start from the same height, that means they should all have the same initial potential energy and thus same final kinetic energy and given this, when you write the equations out, they all have the same velocity?

    is x representing the horizontal distance here?
     
  9. Dec 5, 2009 #8

    kuruman

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    Yes, they have the same speed.

    Yes, it does.
     
  10. Dec 5, 2009 #9
    thank you!
    want to help me on my other recent post? >_<
     
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