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AAMC Self Assessment Physics, multiple questions

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tshank

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Physics #106

What is the magnitude of the horizontal component of air resistance on the projectile at any point during the flight? (Note: Vx= horizontal speed.)

Can someone explain the answer to this one? Their explanation is that ultimately PVx^2 is the same as (Vx/V)PV^2 Wouldn't that get you (P)(V)(Vx) not PVx^2? I thought those were different numbers since V and Vx are different values.







PS #52

Consecutive resonances occur at wavelengths of 8 m and 4.8 m in an organ pip closed at one end. What is the length of the organ pipe? (Note: Resonances occur at L = n(lambda)/4, where is the pipe lneght, lambda is the wavelength, and n = 1, 3, 5…..)

176925-8ba33de5baf27a4fb71dda63782fc522.jpg

Their explanation is attached (not their error of putting 0.8 m in the first line, should be 8 m) and it includes putting in n and n+2 for the equations. Can someone explain how or why we were supposed to put (n+2)(4.8) and not (n+2)(8)?

Is the thinking, longer wavelength, shorter resonance? I have no idea.








PS #56:

Is there a simpler way to come to the same conclusion for this? They seem to complicate bernoulli's principle and give a convoluted answer when I think it is probably really simple.





PS #61:

Can anyone explain which equation we were supposed to use, I think I used to wrong one. It doesn't make sense to me that their explanation has why its (Pi/4) x (1.0 x 10^-2)^2 and not (1/2) x (1.0 x 10^-2/2)^2 I just don't see where the 5Pi comes from.
 

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popopopop

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106.) I got it right, but I just went by the equation listed for the wind resistance since I know gravity is my Y component and X component horizontally isn't going to change. I guess initially V is the same as your Vx since you're shooting it horizontally and time of flight will only depend on gravity.

52.) Don't know, but solving it your way gives a -5 for n if that means anything in this question.

56.) I need to review my fluids again lol.

61.) It's just volume flow rate = area x velocity. The math works out, you get 1.5 x 10^-5, but 5pi = 15~ so it's 10^-6. Tricky question if you aren't careful.
 
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popopopop

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For 56, I rearranged P = 1/2pv^2 and solved for v. Apparently that's a thing? I never learned about these terms in class.

http://en.wikipedia.org/wiki/Stagnation_pressure

I got the answer right when I first did it and didn't hit guess, so I guess that's a method? Please correct me if I'm wrong. I certainly didn't solve it using AAMC's method.
 

tshank

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For 56, I rearranged P = 1/2pv^2 and solved for v. Apparently that's a thing? I never learned about these terms in class.

http://en.wikipedia.org/wiki/Stagnation_pressure

I got the answer right when I first did it and didn't hit guess, so I guess that's a method? Please correct me if I'm wrong. I certainly didn't solve it using AAMC's method.
Thanks for your responses. I appreciate it. Yeah, I think you actually did us their method, just simplified it though. You had P = pgh = 1/2pv^2 right? Same as their explanation essentially. Plug 5 in for h, isolate v, the p's cancel, and you are left w/ v = square root of 2gh. = 10.
I think they applied the law of stagnation by saying the v at the top is negligible, and therefore zero, so good on you for doing it intuitively.

61) After looking at it again, you're right. Just math. :( Shoot.

106) It makes sense now after reading it again.

52) Yes, doing it my way comes up with the wrong answer. But I don't know the rational to doing it the correct way. Any thoughts? Thanks.
 

justadream

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#52

Wavelength = 4L / n where n goes up by 2

Shorter Wavelength is associated with larger n

Thus:

4.8 = 4L / n+2 ===> 4L = 4.8 (n+2)

8 = 4L / n ===> 4L = 8n

Set the two expression for 4L equal to each other:
4.8(n+2) = 8n
n = 3

Plug n back into either equation:
4L = 8*3
4L = 24
L = 6
 

tshank

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#52

Wavelength = 4L / n where n goes up by 2

Shorter Wavelength is associated with larger n

Thus:

4.8 = 4L / n+2 ===> 4L = 4.8 (n+2)

8 = 4L / n ===> 4L = 8n

Set the two expression for 4L equal to each other:
4.8(n+2) = 8n
n = 3

Plug n back into either equation:
4L = 8*3
4L = 24
L = 6
Thanks for your post and explanation. Yes that makes sense. But how did you know that the shorter wavelength was associated with the smaller n? How do n and wavelength relate to each other within the pipe?
 

justadream

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Thanks for your post and explanation. Yes that makes sense. But how did you know that the shorter wavelength was associated with the smaller n? How do n and wavelength relate to each other within the pipe?

Wavelength = 4L/n for n, n+2, n+4, etc.

Memorize that formula - that applies when you have 1 closed end

As you increase n, wavelength decreases.
 

tshank

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Wavelength = 4L/n for n, n+2, n+4, etc.

Memorize that formula - that applies when you have 1 closed end

As you increase n, wavelength decreases.

Thanks for that tip. But what does n represent? If the wavelength is the same, why does the n change? thanks!
 

justadream

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Thanks for that tip. But what does n represent? If the wavelength is the same, why does the n change? thanks!

I'm not sure how to explain it but n is like representing each possible iteration (maybe "scenario" would be a better word) of the wave.

For the problem at hand:
n = 1 = fundamental iteration
n = 3 = second iteration.

Look up some pictures of it and you'll understand it better.

n doesn't really "change". It's just a different scenario.
 

tshank

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I'm not sure how to explain it but n is like representing each possible iteration (maybe "scenario" would be a better word) of the wave.

For the problem at hand:
n = 1 = fundamental iteration
n = 3 = second iteration.

Look up some pictures of it and you'll understand it better.

n doesn't really "change". It's just a different scenario.
Okay thanks. I thought the wavelength would stay the same in each scenario, but I was wrong. I understand it better now. Thanks for all the comments - it helped! :)
 

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