Greg S. answered • 12/04/20
Science & Math Tutoring from a Scientist (MIT SB, NU PhD)
Use conservation of energy. As the block falls, it can do work corresponding to mgh, where h is the change in height, on the system. This work will be divided between the rotational energy of the pully, the moving block, generation of heat from friction and (don't forget) the motion of the falling mass. The math may be a little gross, but at all times the sum of the work done by friction, and the energy imparted to the moving block, mass and pully should add up to the change in potential energy of the falling mass. Again, don't forget that the kinetic energy due to the motion of the falling mass must also be included.
Greg S.
If you're just starting, this is a pretty complex problem to give you. Before tackling a problem that includes angular momentum and rotational energy--or a problem where you have to add up work done in various systems, you usually have been through kinematics, forces, work, momentum, and conservation of energy in simpler systems. With all that in place, my explanation should have made sense. That said, let me illustrate the principles with a simpler system: for instance, with a massless pully and string where a mass m1 falls through distance h while also pulling on a mass of m2 on frictionless horizontal surface. As m1 falls, it does work = to it's change in potential energy, mgh on the entire system. Since the moving system has kinetic energy of (1/2)(m1+m2)v^2, you can set that = to mgh to find the final speed of the system after it falls some distance h. This problem is similar, except you have to account for all the places that energy goes. To both moving blocks, the work done against friction, and the energy imparted to the pully. I have to tutor in 30 minutes for 2 hours; after that I'll take a crack at showing you how this whole thing works out. I just don't want to do all the work and simply give you the answer without a full explanation. Your goal will be to fully understand all the parts of this. Given the complexity of this problem, you can expect more like it from your instructor.12/05/20
Greg S.
Perhaps it is too late now, but I have worked this out completely for you now. However, it needs a video answer which I cannot do here. Contact me if still need the answer.12/05/20
Greg S.
Perhaps it is too late now, but I have worked this out completely for you now. However, it needs a video answer which I cannot do here. Contact me if still need the answer.12/05/20
Daniel M.
We just started this topic so I have literally no idea what you just said. I have a tutor and I'm working on concepts but right now I just need to see what I have to do so I can figure it out with more practice. Thank you though.12/05/20