- #1
CAF123
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Homework Statement
A uniform flexible chain of mass M and length L is hung under gravity over a frictionless pulley of radius a and moment of inertia I whose axle is at a fixed height above the ground. Write down the Lagrangian of this system in terms of a generalized coordinate l denoting the displacement below the axle of one end of the chain. Assume that L is sufficiently long that some part of the chain hangs freely from both sides of the pulley.
Homework Equations
L = T-V, V the potential energy term (which I should take to be of the form -mgz, where z is the distance of the CoM of the system from the fixed point and zero potential reference point there.
The Attempt at a Solution
Let ##l## be the distance of one end of the chain from the axle. Let ##l'## be the distance of the other end from the axle. Then ##l + l' + a\pi = L##. I don't see a way to incorporate the fixed height in (H), unless I introduce more parameters namely the height of the two ends above the ground ##z_1## and ##z_2## in which case ##z_1 + l = H## and ##z_2 + l' = H##.
I am not really sure how to model the kinetic energy term. One point cannot have the entire mass of the string.
Thanks.