Equations of Motion

1. Mar 23, 2014

rcummings89

1. The problem statement, all variables and given/known data
Please see the attached picture for the problem description. Now, I have a solution using the Lagrange method, (it should coincide with Newton's second law, I believe?) I just have a hard time getting my equations of motion to match.

2. Relevant equations
∑Fext - M dv/dt = 0

3. The attempt at a solution
For mass Mo I have
K(x2 - x1) = Mo*x1'' x (where mass Mo moves a distance x1 and mass M moves a distance x2) which agrees with the Lagrange solution

I have trouble matching the remaining equations. For the rolling mass m, I have the external forces as -mg (y-dir) and FN (y'-dir) where x' and y' are at an angle θ depending on the location of the rolling mass.

Then my equation of motion is -mg y + N y' = m[x'' x + (R-r)θ'' y' - (R-r)θ'2 x']

Now I realize that I need to organize everything into the x-y or x'-y' plane but when I do the solution doesn't match; do you see anything that I'm missing?

Finally for mass M

∑Fext = -mg y - K(x2 - x1) x
My professor typically neglects gravity and normal forces acting on carts, so I don't include them here. But I feel like I'm neglecting a force. Should I include the momentum of the rolling mass with the external forces acting on M? Because setting what I have = M*x2'' x doesn't match, and I feel like I'm over-simplifying the problem.

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• problem statement.JPG
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Last edited: Mar 23, 2014
2. Mar 23, 2014

SteamKing

Staff Emeritus
No attached picture.