Weakest Point of Cylinder in Pressure Piston Homework

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Homework Help Overview

The discussion revolves around identifying the weakest point in a cylinder and piston system under pressure, specifically focusing on the failure modes of different surfaces of the cylinder. The context is set for A-level physics students, with an emphasis on understanding material strength and stress distribution.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the comparison between flat and curved surfaces, questioning whether to consider different regions or failure modes. There is also discussion about the thickness of the cylinder wall and its impact on stress. Some participants suggest starting with simpler shapes, like spheres, to understand failure mechanisms.

Discussion Status

The discussion is active, with participants raising questions about the assumptions regarding wall thickness and material properties. Some guidance has been offered regarding the need to consider hoop and axial stresses in evaluating cylinder failure, though there is no consensus on a specific approach yet.

Contextual Notes

Participants note that the material for both flat and curved surfaces is uniform and that the joint strength is equivalent to the material itself. There is an acknowledgment of the challenge posed by the homework, with references to the adequacy of AS-level physics knowledge.

FG314
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Homework Statement


In a cylinder & piston system, where is the weakest point on the cylinder (the point that will break under increasing pressure)?
You may assume the joint between edges are as strong as the material.
This is homework for A-level students.

Homework Equations


P = F/A
Surface Area of Flat Surface= πr2
Surface Area of Curved Surface = 2πrl

The Attempt at a Solution


F = PA, if 2l > r, then curved surface will face more force and will break first?
 
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I'm not sure that the idea is to compare flat with curved. Maybe you are just supposed to consider different regions and/or different failure modes of the curved surface.
The failure mode of the flat surface is complicated. It depends on how the piston flexes.
Anyway, it isn't total normal force on the component that matters. Start with something simpler, like a sphere, and consider how it will fail.
 
Does the cylinder wall have a thickness, or is it infinitely thick? Is the stress in the cylinder wall higher if the wall is thin or if it is thick? What course is this from? Is it Strength of Materials? Do you know how to calculate the stress in the cylinder wall? If so, what are the principal stresses on the inside and the outside of the wall?

Chet
 
Chestermiller said:
Does the cylinder wall have a thickness, or is it infinitely thick? Is the stress in the cylinder wall higher if the wall is thin or if it is thick? What course is this from? Is it Strength of Materials? Do you know how to calculate the stress in the cylinder wall? If so, what are the principal stresses on the inside and the outside of the wall?

Chet
It is a homework that is supposed to be challenging and makes us think, AS level physics knowledge should be adequate. material for flat and curved surface is the same, with uniform thickness, and the joint is as strong as the material itself.
 
FG314 said:
It is a homework that is supposed to be challenging and makes us think, AS level physics knowledge should be adequate. material for flat and curved surface is the same, with uniform thickness, and the joint is as strong as the material itself.
Have you learned about the concept of principal stresses?

Chet
 
Chestermiller said:
principal stresses
nope. only basic pressure, and young modulus.
 
FG314 said:
nope. only basic pressure, and young modulus.
It seems like you don't have enough knowledge yet to solve this problem properly. There is going to be a hoop stress in the cylinder wall, and there is going to be an axial stress. These need to be taken into account in evaluating the failure of the cylinder wall. You would also need a failure criterion expressed in terms of the principal stresses.

Chet
 
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