- #1
Raziel2701
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Homework Statement
A marble of mass M and radius R rolls without slipping down the track on the left from a height h1, as shown below. The marble then goes up the frictionless track on the right to a height h2. Find h2. (Use the following as necessary: M, R, and h1.)
http://imgur.com/sZIyQ
The Attempt at a Solution
[tex]Mgh_1=\frac{1}{2}*Mv^2 +\frac{1}{2}*I*\omega^2[/tex]
[tex]\frac{1}{2}*Mv^2 +\frac{1}{2}*I*\omega^2=Mgh_2 +\frac{1}{2}mv^2[/tex]
I don't know why but these equations for conservation of energy are not giving me the right answer which is supposed to be:
[tex]\frac{5}{7}h_1 +\frac{2}{7}R[/tex]
So I know that my conservation of energy equations are incorrect but I don't know where nor why.
I'm setting potential at the top to be equal to kinetic at the bottom, and the kinetic at the bottom to be equal to potential at h2 plus linear kinetic since there is no rotational kinetic because the track is frictionless. Yet I'm not getting anywhere with those because that velocity at h2 is different than the velocity at the bottom, so I have three unknowns and two equations.
I'm using the moment of inertia to be 2/5 MR^2 and also the relationship that w=v/r to simplify things. Bottom line is, are my conservation of energy equations correct?