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TheoMech - rolling a ball down a curve

  1. Mar 14, 2005 #1
    This isnt a homework question (im not in school) but its nearly one for a Theomech class, or maybe just dynamics. Maybe I'm just not seeing it.

    Assume you have a hill thats defined by some part of a function y=f(x) (like exponentially decreasing, or a sine wave)

    and you put an object on top and let it move down the curve.
    assume no friction, there is some gravity force in the y direction only.

    What are the independent forces of the object at a given x direction?

    so im looking for Fx(x,f(x)) and Fy(x,f(x)) so get the force given some euation describing the curve and a position.

    Would I use lagrangian mechanics to pull out the accel in each direction? or what...

    Last edited: Mar 14, 2005
  2. jcsd
  3. Mar 14, 2005 #2
    heres what ive come up with so far

    assuming the equation f(x), the vector describing the direction of increase from the current point xo, would be :

    Vi = {f(xo+dx) - f(xo), xo} (haha, ive seen that somewhere before.....)

    ok, so the normal force would be orthogonal to this vector.

    Vn = -dx*i + (f(xo+dx)-f(xo))*j

    so Fn = |Fn|*Vn
    and Fn_x = -dx

    wait wait wait, so this DOESNT feel a force in the X direction? I mean if take the limit and dx->0... am I doing this the wrong way?

    Its basically looking at the gradient of something... why dont i remember this stuff...
  4. Mar 14, 2005 #3
    If you are referencing your x-axis perpendicular to g, then no there is no force in the x direction. Personally, I would set the axis such that x is along the average of the function of the path of decent, y being perpendicular, g will be a resultant of two vectors, Gx and Gy. I'm not really sure what your trying to do though, so...
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