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Heisenberg Uncertainty Principle homework Question

  1. Jul 31, 2009 #1
    Sorry about not using symbols but I haven't learnt how to do that yet.

    1. The problem statement, all variables and given/known data

    A woman is on a ladder of height H. She drops small rocks of mass m toward a point target on the floor.

    Show that according to the Heisenberg Uncertainty Principle, the average miss distance must be at least

    delta(x final) = sqrt [h/pi*m] * sqrt sqrt [2H/g]

    where h is the planck's constant,
    pi is 3.14
    m is the mass of the rock
    H is the height from which the rock is dropped
    g is the acceleration due to gravity.

    Assume that delta(xfinal ) = delta(x initial) + (delta(v))*t
    Also justify the assumption.

    2. Relevant equations

    delta(x) * delta(p) < or = [h/4*pi]

    delta(p) = m * delta(v)

    v= u +at
    s= 0.5(u + v)t
    s= ut +0.5at^2
    v^2= u^2 +2as

    3. The attempt at a solution

    I did a couple of substitutions and got something like t=sqrt[2H/g] and delta(v)=sqrt[2gH] but I can't seem to get the equation needed. Tried for 2 hours and can't seem to understand it all. Please help? Or at least give some hints. Also, I don't know how to justify the assumption above.
     
  2. jcsd
  3. Aug 26, 2009 #2
    Nvm. I found a similar answer in another thread.
     
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