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Hi! I'm struggling with this problem from my Mechanics book. It's actually an Engineering book, but this problem actually seems like an elementary Physics problem - if it's not, someone please move it to the appropriate forum. I tried my best to translate it clearly, but if it's ambiguous or unclear, let me know. Please just indicate what principles/ideas I'm missing here - I really want to work on this by myself as much as I can. I'll come back if I still get stuck and need more help.
An horizontal bar, length 2L, is supported by a homogeneous disk, of weight P and radius R. The friction coefficient between the bar and the disk and between the disk and the ground is μ. (I've redrawn the problem from my textbook. Sorry, it's poorly done, but I hope you can still get what the problem is about. The picture is here https://docs.google.com/document/d/1yOec6udxJKYkh58MUUIY1ktfeKcu0OAR5jPHjXKxi4U/edit). The force 2P on the bar is applied in its mid-point.
1) What is the maximum torque that can be applied to the disk, clockwise, so that it still maintains the equilibrium?
2) What is the maximum horizontal force F that can be applied from right to left at the center of the disk, so that it still maintains equilibrium?
3) Applying a force F=μP (still from right to left) at the center of the disk, what is the maximum (clockwise) torque that can be applied to the disk so that it still maintains equilibrium?
Answers:
1) T = 2RμP
2) F = 2μP
3) T = 3RμP
F = μN and Archimedes' principle.
I'm struggling with all three items, which is a shame for me, who used to perform well in Physics. The bar is obviously applying a force P on the disk, so that the normal force between the disk and the ground is 2P. I know that the maximum static friction force that may occur between two surfaces is F = μN, but I really don't see how I can determine if this maximum force is reached in either the top or the bottom of the disk. If one simply supposes that friction is maximum on both surfaces, we would get F = 3μP (μP at the top and 2μP at the bottom of the disk) for the second item, so that clearly isn't the case. What should I do to solve this? I've tried putting some "dummy" horizontal +G and -G at the top and at the bottom, so I had a binary acting on the system (whose torque would be 2RG) and no net extra force on the system, but I reached nowhere in parts 1 and 3.
Homework Statement
An horizontal bar, length 2L, is supported by a homogeneous disk, of weight P and radius R. The friction coefficient between the bar and the disk and between the disk and the ground is μ. (I've redrawn the problem from my textbook. Sorry, it's poorly done, but I hope you can still get what the problem is about. The picture is here https://docs.google.com/document/d/1yOec6udxJKYkh58MUUIY1ktfeKcu0OAR5jPHjXKxi4U/edit). The force 2P on the bar is applied in its mid-point.
1) What is the maximum torque that can be applied to the disk, clockwise, so that it still maintains the equilibrium?
2) What is the maximum horizontal force F that can be applied from right to left at the center of the disk, so that it still maintains equilibrium?
3) Applying a force F=μP (still from right to left) at the center of the disk, what is the maximum (clockwise) torque that can be applied to the disk so that it still maintains equilibrium?
Answers:
1) T = 2RμP
2) F = 2μP
3) T = 3RμP
Homework Equations
F = μN and Archimedes' principle.
The Attempt at a Solution
I'm struggling with all three items, which is a shame for me, who used to perform well in Physics. The bar is obviously applying a force P on the disk, so that the normal force between the disk and the ground is 2P. I know that the maximum static friction force that may occur between two surfaces is F = μN, but I really don't see how I can determine if this maximum force is reached in either the top or the bottom of the disk. If one simply supposes that friction is maximum on both surfaces, we would get F = 3μP (μP at the top and 2μP at the bottom of the disk) for the second item, so that clearly isn't the case. What should I do to solve this? I've tried putting some "dummy" horizontal +G and -G at the top and at the bottom, so I had a binary acting on the system (whose torque would be 2RG) and no net extra force on the system, but I reached nowhere in parts 1 and 3.