Frictionless Equilibrium of Block and Wedge System

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    Block Inclined Wedge
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Discussion Overview

The discussion revolves around the equilibrium of a block and wedge system, specifically analyzing the forces acting on the wedge when the system is at rest. Participants explore the implications of friction and the conditions under which the block remains stationary on the wedge, considering both rough and smooth surfaces.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant introduces a problem involving a block resting on a wedge and asks about the frictional force exerted by the floor on the wedge when the system is at rest.
  • Another participant notes that for the system to be in equilibrium, the net force must be zero and questions what forces act on the system, including the necessary frictional force from the floor.
  • Some participants argue that since the system is balanced and only the weight of the block and wedge acts downward, no frictional force is exerted by the floor on the wedge, as there is no frictional force from the wedge on the floor.
  • One participant clarifies that the only force the floor applies is the normal force, asserting that no frictional force is needed to maintain equilibrium.
  • There is a question regarding whether the block would remain stationary if the floor were smooth, to which participants agree that it would, as no frictional force is required in this scenario.

Areas of Agreement / Disagreement

Participants generally agree that no frictional force is needed for the system to remain in equilibrium, but there is some uncertainty regarding the implications of different surface conditions (rough vs. smooth) on the block's stability.

Contextual Notes

Participants do not fully explore the implications of the wedge's angle or the potential for the block to slide if conditions change, leaving some assumptions unaddressed.

Guppy
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Hello, I am new member here.
I would like to know how should I handle this question:

A block of mass 2.5kg rests on the rough surface of a wedge, which in turn rests on a rough horizontal floor. What is the frictional force exerted by the floor on the wedge if the whole system is at rest?

The height of the wedge is 30cm and the length is 40cm (Side view)
 
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Consider that the system of "block + wedge" is in equilibrium: the net force on it must be zero. Besides the force that the floor exerts, what forces act on that system? And what frictional force must the floor exert to couteract those forces?
 
The system of Block & Wedge is in equilibrium, so the whole system is balanced, and the only force acting on the floor is the Mg of the whole block & wedge system, therefore no frictional force is exerted by the floor on the wedge as there is no frictional force exerted by the wedge on the floor, isn't it?

By the way, if it's a smooth floor, the block will also stay the same way as the above case?
 
Guppy said:
The system of Block & Wedge is in equilibrium, so the whole system is balanced, and the only force acting on the floor is the Mg of the whole block & wedge system, therefore no frictional force is exerted by the floor on the wedge as there is no frictional force exerted by the wedge on the floor, isn't it?
This is true. Here's how I would word it. Other than the floor (which merely exerts a passive force), the only force on the system (block + wedge) is gravity. Since the weight of the system acts straight down, the only force that the floor applies to counter it is the normal force--no frictional force is needed.

By the way, if it's a smooth floor, the block will also stay the same way as the above case?
Yes. Since no frictional force is needed, it doesn't matter if the floor is smooth or not. (Things would change if the mass were able to slide down the wedge.)
 
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