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Uncertainty Principle

  1. Mar 9, 2004 #1
    Can anyone help me on this??

    In a contest to drop a marble with mass 30 g from the roof of a building onto a small target 50 m below. From uncertainty principle considerations, what is the typical distance by which you will miss the target, given that you aim with the highest possible accuracy? Ignore wind and air resistance.

    [Hint: Let x be the coordinate in the horizontal direction. You should realise that the uncertainty in the position x of the marble when it reaches the ground depends on both the initial uncertainty in the position xi, and the initial uncertainty in the speed vx.]
  2. jcsd
  3. Mar 10, 2004 #2

    Tom Mattson

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    Let the initial position x0 lie in the interval:

    Let the initial velocity v0 lie in the interval:

    Now use the ordinary kinematic equations to figure out the extreme values of x(t) and v(t) when the marble hits the target.
  4. Mar 14, 2004 #3
    Would the uncertainty principle apply to a marble?

    I was always told that it applied to sub-atomic particles. Even atoms were supposed to obey semi-classical formula in my education.
  5. Mar 18, 2004 #4
    I've had a longer think about this question (and I haven't done any active physics for years, please forgive the poorly articulated arguement) but I would expect the following:

    A particle of uncertainty dX has 2/3 chance of being in the region
    x +/- dx.

    Two particles each with an uncertainty of dx in a system (ignoring the interactions) should have a centre with a lower uncertainty. Even if both particles are outside the 2/3 probability, if one is on the extreme left and one on the extreme right, this would cancel.

    So a mole of particles(or say 10^23) should have a centre with almost no uncertainty even without taking into account the structure of the substance.

    I reason that the same is true of particle momenta.

    I think this reasoning is wrong because you are all brilliant and I'm useless (and the marble question sounds like a formal one). But why?

    Sorry this post was put together at lunch in a cafe. I usally have time to make a proper go of it.
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