Which Area Should Be Used to Calculate Shear Stress in a Cheese Grater Scenario?

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Discussion Overview

The discussion revolves around the calculation of shear stress in a scenario involving a cheese grater applying a lateral force to a block of cheese. Participants explore which area should be used in the shear stress formula, considering the geometry of the cheese and the nature of the applied force.

Discussion Character

  • Homework-related
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant asks whether to use the area of 24 cm2 or 96 cm2 for calculating shear stress.
  • Another participant suggests that shear stress is the load normalized to the area of the surface upon which the load acts.
  • A participant expresses confusion about the definitions of shear stress and questions whether they contradict each other.
  • There is a discussion about the area of the upper surface being equal to 96 cm2, similar to the bottom surface.
  • One participant mentions uncertainty regarding the term "normalize" and its implications in the context of the discussion.
  • Another participant clarifies that "normalized" means dividing the load by area to obtain a stress parameter independent of area.

Areas of Agreement / Disagreement

Participants express differing views on which area to use for calculating shear stress, with no consensus reached on the correct approach. Some participants agree on the definition of shear stress, while others remain uncertain about the terminology and its implications.

Contextual Notes

There are unresolved questions regarding the definitions of shear stress and the appropriate area to use in calculations, as well as the interpretation of the term "normalize." The discussion reflects varying levels of understanding among participants.

negatifzeo
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Homework Statement


The bottom surface (8 cm x 12 cm) of a rectangular block of cheese (3 cm thick) is clamped in a cheese grater. The grating mechanism moving across the top surface of the cheese, applies a lateral force of 20 N. The shear modulus, G, of the cheese is 3.7 kPa. Assuming the grater applies the force uniformly to the upper surface, estimate the lateral movement of the upper surface with respect to lower surface?


My question is about shear stress. When calculating shear stress, which is force/area, which area do I use here? The 24 cm^2, or the 96 cm^2?
 
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Your other choice is 36 cm^2. But the shear stress is the load normalized to the area of the surface upon which the load acts. Does this answer your question?
 
I think so. I'm having a bit of trouble visualizing which surface the force is applied to from the wording of the problem, but I went ahead and solved using 24 cm^2 as my A.
 
"Assuming the grater applies the force uniformly to the upper surface..."
 
Well this is confusing to me. In my notes it says shear stress deals with the force parallel to the area. But you say it is the load normalized to the area of the surface upon which the load acts. Don't these two definitions contradict each other?
And the area of the upper surface would be equal to 96 cm^2, the same as the bottom surface, right?
 
negatifzeo said:
Well this is confusing to me. In my notes it says shear stress deals with the force parallel to the area. But you say it is the load normalized to the area of the surface upon which the load acts. Don't these two definitions contradict each other?

A parallel (or lateral) load still acts upon an area.

negatifzeo said:
And the area of the upper surface would be equal to 96 cm^2, the same as the bottom surface, right?

Yep.
 
Thank you very much for helping to clarify this for me!
 
It depends on what Mapes means here by the word "normalize." Maybe he means something like "average" (?), but I didn't see that definition in the dictionary under "normalize," so I'm not sure.
 
"Normalized" here just means that the load is divided by area to get a parameter (stress) that's independent of area.
 

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