- #1

rcummings89

- 19

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## Homework Statement

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.

## Homework Equations

∑F

_{ext}- M dv/dt = 0

## The Attempt at a Solution

For mass M

_{o}I have

K(x

_{2}- x

_{1}) = M

_{o}*x

_{1}''

**x**(where mass M

_{o}moves a distance x

_{1}and mass M moves a distance x

_{2}) 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 F

_{N}(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

∑F

_{ext}= -mg

**y**- K(x

_{2}- x

_{1})

**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*x

_{2}''

**x**doesn't match, and I feel like I'm over-simplifying the problem.

Thanks in advance

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