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uriwolln
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A board lies on top of 2 uniform cylinders that lie on a fixed plane inclined at an angle theta. The board has mass m and each of the cylinders has mass m/2. The system is released from rest. If there is no sipping between any of the surfaces, what is the acceleration of the board. Solve using force and torque.
http://img192.imageshack.us/img192/4955/diagramwt.jpg Since I have been having some problems using the torque method I figured ill use the Lagrange one. But the thing is, the answer I am getting through this method is wrong.
I have tried using the Lagrange equations for that.
where by, let's say the positions of the objects the left cylinder, right cylinder and board respectively as follows:
(R[itex]\gamma[/itex]cos[itex]\theta[/itex] , H - R[itex]\gamma[/itex]sin[itex]\theta[/itex])
(Scos[itex]\theta[/itex] + R[itex]\gamma[/itex]cos[itex]\theta[/itex] , H - Ssin[itex]\theta[/itex] - R[itex]\gamma[/itex]sin[itex]\theta[/itex])
(xcos[itex]\theta[/itex], H - S/2 sin[itex]\theta[/itex] + Rsin[itex]\theta[/itex] -Xsin[itex]\theta[/itex])
[itex]\gamma[/itex] being the angle of which the cylinder rotates
after integration I get the velocities.
then I plug into L=T - V, and from that to derive the equation of motion.
Which in the end I get the acceleration to be a=3/2gsin[itex]\theta[/itex]
Whereas it should be a = 6gsin[itex]\theta[/itex]
I would very much like help with both of the methods.
Thanks
http://img192.imageshack.us/img192/4955/diagramwt.jpg Since I have been having some problems using the torque method I figured ill use the Lagrange one. But the thing is, the answer I am getting through this method is wrong.
I have tried using the Lagrange equations for that.
where by, let's say the positions of the objects the left cylinder, right cylinder and board respectively as follows:
(R[itex]\gamma[/itex]cos[itex]\theta[/itex] , H - R[itex]\gamma[/itex]sin[itex]\theta[/itex])
(Scos[itex]\theta[/itex] + R[itex]\gamma[/itex]cos[itex]\theta[/itex] , H - Ssin[itex]\theta[/itex] - R[itex]\gamma[/itex]sin[itex]\theta[/itex])
(xcos[itex]\theta[/itex], H - S/2 sin[itex]\theta[/itex] + Rsin[itex]\theta[/itex] -Xsin[itex]\theta[/itex])
[itex]\gamma[/itex] being the angle of which the cylinder rotates
after integration I get the velocities.
then I plug into L=T - V, and from that to derive the equation of motion.
Which in the end I get the acceleration to be a=3/2gsin[itex]\theta[/itex]
Whereas it should be a = 6gsin[itex]\theta[/itex]
I would very much like help with both of the methods.
Thanks
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