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

[negatifzeo]

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?

 

[Mapes]

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?

 

[negatifzeo]

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.

 

[Mapes]

"Assuming the grater applies the force uniformly to the upper surface..."

 

[negatifzeo]

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?

 

[Mapes]

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.

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

Yep.

 

[negatifzeo]

Thank you very much for helping to clarify this for me!

 

[nvn]

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.

 

[Mapes]

"Normalized" here just means that the load is divided by area to get a parameter (stress) that's independent of area.