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Should all three modulus types be memorized. Young's, Shear, and Bulk for the MCAT??? If so can someone just briefly explain Shear Modulus. Thanks
Physics: 3 modulus types
- Thread starter newtonsfriend
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S
Segovia
I would have said don't worry about it a few months ago, but all the recent test takers continue to report that seemingly obscure topics tend to pop up.
I tend to just remember that any modulus is just some sort of Stress/Strain, and since Stress=Pressure, I substitute F/A into the numerator.
Honestly, I generally just use unit analysis to solve these, but since force is a vector, you can differentiate between Young's mod and Shear mod, by whether or not the force applied is perpendicular or parallel to the area. I think it is easiest to understand Shear by understanding how it differs from Young's:
Young's
Clearly, if you are applying a perpendicular force, say tugging on a piece of laffy taffy, the length will deform, e.g. get longer than the original laffy taffy. (This is Young's). Although you would generally see this in a cable holding up an elevator on a passage, the analogy still holds. The "area" having a force applied in this case are the "tips of the taffy" and the force is "normal" to the tips.
Shear
Say, instead of tugging on a piece of taffy, you put an empty cardboard box on the ground. Then some rabid dog, capable of defying the force of gravity, jumps over the box, such that all of his motion is in the horizontal direction. If the dog hits the top of the box, all of his force applied will be parallel to the top of the box.
The dog is not only abnormal, because he is rabid, but the force he applies is not "normal" or perpendicular to the surface of the box. In fact, the force he applies is parallel. It is kind of like he is skimming the surface, as opposed to "tugging the taffy". The deformation (the strain) will reflect this difference. So, whereas tugging the taffy caused a length deformation (deltaL/L), the dog will cause a deformation (delta x/h), which is just another way of saying: How much the dog moved the top of the box in the horizontal direction / height of the box.
Sorry this wasn't brief, but I am avoiding studying.
If anyone notices any errors in my logic, please point it out, because I am explaining this just as much for my benefit as the OP's.
I tend to just remember that any modulus is just some sort of Stress/Strain, and since Stress=Pressure, I substitute F/A into the numerator.
Honestly, I generally just use unit analysis to solve these, but since force is a vector, you can differentiate between Young's mod and Shear mod, by whether or not the force applied is perpendicular or parallel to the area. I think it is easiest to understand Shear by understanding how it differs from Young's:
Young's
Clearly, if you are applying a perpendicular force, say tugging on a piece of laffy taffy, the length will deform, e.g. get longer than the original laffy taffy. (This is Young's). Although you would generally see this in a cable holding up an elevator on a passage, the analogy still holds. The "area" having a force applied in this case are the "tips of the taffy" and the force is "normal" to the tips.
Shear
Say, instead of tugging on a piece of taffy, you put an empty cardboard box on the ground. Then some rabid dog, capable of defying the force of gravity, jumps over the box, such that all of his motion is in the horizontal direction. If the dog hits the top of the box, all of his force applied will be parallel to the top of the box.
The dog is not only abnormal, because he is rabid, but the force he applies is not "normal" or perpendicular to the surface of the box. In fact, the force he applies is parallel. It is kind of like he is skimming the surface, as opposed to "tugging the taffy". The deformation (the strain) will reflect this difference. So, whereas tugging the taffy caused a length deformation (deltaL/L), the dog will cause a deformation (delta x/h), which is just another way of saying: How much the dog moved the top of the box in the horizontal direction / height of the box.
Sorry this wasn't brief, but I am avoiding studying.
If anyone notices any errors in my logic, please point it out, because I am explaining this just as much for my benefit as the OP's.- Joined
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wow...are u physics major? that was excellent. The illustrations actually really helped; I understand it now! haha i wish u were taking my PS section...i despise it. Thanks for the help.
S
Segovia
Honestly, I had to read up on that topic before trying to explain it, so it helped me as much as it helped you. I am not a physics major; I think a physics major would probably do an integral or something to solve these. Anyway, I heard that thermal expansion showed up on a recent administration, and this topic is quasi-related, so better safe than sorry. Thanks for asking the question.
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Ya I dont know anything about TPR so I cant comment on that, but my friend used EK for his prep and he said a lot of formulas that they said should not be memorized were actually tested....so I would memorize.
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i am doing badly on my physical sciences practice tests. average score is a 7. i just can't seem to get the materials into my head. i took physics during my sophomore year, but our physics department sucks. we didn't have to memorize/ learn to use any equations. everything was theory-based. we just had to reason everything out.
so, i am struggling with all the calculations/ equation manipulations that we have to do in the PS section.
any suggestion on how i can study?
so, i am struggling with all the calculations/ equation manipulations that we have to do in the PS section.
any suggestion on how i can study?
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If you need help remembering the formulas, I really like the mnemonic TPR gave.
dL = (F*L)/(E*A) (Young's modulus, stress)
dL = (F*L)/(A*G) (Shear modulus, strain)
From these, you can also solve for E or G, which is just E = (F/A)*(L/dL) = (P*L)/dL
To relate the two, remember that "Stress is strainy" (stress = strain * E), where E is Young's modulus.
There's no good mnemonic for the Bulk modulus, but it's just -(V*dP)/dV.
dL = (F*L)/(E*A) (Young's modulus, stress)
dL = (F*L)/(A*G) (Shear modulus, strain)
From these, you can also solve for E or G, which is just E = (F/A)*(L/dL) = (P*L)/dL
To relate the two, remember that "Stress is strainy" (stress = strain * E), where E is Young's modulus.
There's no good mnemonic for the Bulk modulus, but it's just -(V*dP)/dV.
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For the record, I took a TPR class and the physics professor specifically said we didn't need to memorize these. I memorized them anyway, better to be safe than sorry... Anyway, a few points I use to remember Young's vs. Shear:
Young's modulus: a higher Young's modulus means that the material is difficult to compress or stretch when a perpendicular force is applied. Since we're talking about stretching or compressing, it makes sense that you'd set the equation equal to Delta L.
Just remember the FLEA equation mentioned above and rearrange to solve for F/A (which makes sense if you think about stress and pressure being the same idea)
Shear Modulus: Deals with a parallel force, which will deform the particular face of the object that the force is acting on. Picturing a parallelogram really helps me with this. The face being sheared is obscured and moves a distance x. A material with a large shear modulus is difficult to bend.
Hope this helps!
Young's modulus: a higher Young's modulus means that the material is difficult to compress or stretch when a perpendicular force is applied. Since we're talking about stretching or compressing, it makes sense that you'd set the equation equal to Delta L.
Just remember the FLEA equation mentioned above and rearrange to solve for F/A (which makes sense if you think about stress and pressure being the same idea)
Shear Modulus: Deals with a parallel force, which will deform the particular face of the object that the force is acting on. Picturing a parallelogram really helps me with this. The face being sheared is obscured and moves a distance x. A material with a large shear modulus is difficult to bend.
Hope this helps!
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Something to remember is that your equations only work for ductile materials. Anything else and you're sol
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Way more in depth than the MCAT is going to ask about. You really just need to know the different situation that each modulus deals with, and the modulus = stress/strain idea.
