OG Spoiler Question Physics

[treeclimbingmonkey]

Does my reasoning make sense or is there a more simple way to approach this question?

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[FrameshiftAndrew]

I honestly really like this question because it's a great example of how you can solve it the easy way or the hard way. Here's how I would describe the easy way: Poiseuille's law here tells us that all things being equal, flow will decrease dramatically as radius constricts because flow is proportional to radius to the fourth (!) power. Therefore, as the pipe gets more and more blocked, we'd need a lot more energy to maintain a constant flow (this is a step using somewhat intuitive reasoning about physics, rather than a mathematical proof, but physical intuition can be useful for the MCAT). Which answer choice corresponds to this? A and B are immediately out, because there's no a way on earth this would be linear. If you're really crunched for time and you have no idea how to solve the problem, you could even guess at this point and it wouldn't be the worst thing in the world. To distinguish C and D, let's look at what they're saying: C is a nonlinear relationship, but it's one where we would reach a steady state in terms of a constant energy needed to maintain flow even as the radius shrinks more and more. That's not at all what corresponds to our intuitive reasoning based on flow scaling to radius to the fourth power, so eliminate it. This leaves D, which tells us that exponentially more energy will be needed to push a constant flow across a continually shrinking radius, which is exactly what we expect conceptually. No need for any equations even.

 

[treeclimbingmonkey]

I honestly really like this question because it's a great example of how you can solve it the easy way or the hard way. Here's how I would describe the easy way: Poiseuille's law here tells us that all things being equal, flow will decrease dramatically as radius constricts because flow is proportional to radius to the fourth (!) power. Therefore, as the pipe gets more and more blocked, we'd need a lot more energy to maintain a constant flow (this is a step using somewhat intuitive reasoning about physics, rather than a mathematical proof, but physical intuition can be useful for the MCAT). Which answer choice corresponds to this? A and B are immediately out, because there's no a way on earth this would be linear. If you're really crunched for time and you have no idea how to solve the problem, you could even guess at this point and it wouldn't be the worst thing in the world. To distinguish C and D, let's look at what they're saying: C is a nonlinear relationship, but it's one where we would reach a steady state in terms of a constant energy needed to maintain flow even as the radius shrinks more and more. That's not at all what corresponds to our intuitive reasoning based on flow scaling to radius to the fourth power, so eliminate it. This leaves D, which tells us that exponentially more energy will be needed to push a constant flow across a continually shrinking radius, which is exactly what we expect conceptually. No need for any equations even.

Thank you so much!

 

[FrameshiftAndrew]

You're very welcome!!