A system consists of a rope of length l and mass m with two blocks of mass M1 and M2 (with M1 < M2) attached to the end points. The block of mass M1 lies on a plane inclined at an angle alpha, while the second block hangs at the other end of the rope. The rope
can slide without friction, but the friction coeffcient between the first block and the plane is non-zero and equal to u.
The system is subject to gravity and initially half of the rope lies on
Compute the minimum value, umin, of the friction coeffcient between
M1 and the plane for which the system remains in equilibrium when
Assume now that u < umin. The system is released and the block of
mass M2 starts to descend. Compute its acceleration when the length
of the portion of rope lying on the plane is x.
The Attempt at a Solution
Right, the only problem I have with this is the fact that the tension varies along the rope.
My plan was to consider each halfs of the rope to be individual strings with individual tensions, and find one tension in terms of the other and the masses, and solve.
But, I'm thinking that if I take one section of the rope, and then a small section after that, and the component of it's weight at that section, then integrate to find the tension at the points pulling the masses, I'll be able to find the forces pulling the masses.