What Range of Hanging Mass Keeps the Block Stationary on an Incline?

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SUMMARY

The discussion focuses on determining the range of hanging mass (m) that keeps a block of mass M = 107.0 kg stationary on an inclined plane with an angle of 17.6°. The coefficients of static and kinetic friction are μs = 0.40 and μk = 0.20. The analysis involves calculating the forces acting on the block to establish the conditions under which it remains stationary or slides down or up the incline when nudged. The solution requires applying Newton's laws and friction concepts to find the critical values for m.

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  • Understanding of Newton's laws of motion
  • Knowledge of static and kinetic friction coefficients
  • Familiarity with inclined plane physics
  • Ability to solve equations involving forces and mass
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  • Calculate the forces acting on the block on an incline using free-body diagrams
  • Learn about the conditions for static and kinetic friction in detail
  • Explore the effects of varying angles on friction and motion
  • Study the equilibrium conditions for systems involving multiple masses
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Homework Statement



A block of mass M = 107.0 kg on an inclined plane is attached to another block of mass m via a string, as in the figure below. The coefficients of static and kinetic friction for the block and the incline are μs = 0.40 and μk = 0.20 and the plane is inclined 17.6° with horizontal. (a)Determine the range of values for m, the mass of the hanging block, for which the block will not move unless disturbed, but if nudged, will slide down the incline.
(b) Determine a range of values for m for which the block will not move unless nudged, but if nudged will slide up the incline.

Homework Equations





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