Just me or are these really difficult?

[azor ahai]

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I suck at the PS section. I spend too much time on calculations and it wrecks me. Here are some examples. I just want to know what the general consensus is on these - are they actually as hard as I think they are?

http://imgur.com/uNUlZwO,JXT2UXR,fE75Ik1,YB3cym2,Sp5hVP4

first image, #1 - effusion rates. they're inversely proportional to that compound's molar mass. except the difference in the molar masses for these are so similar that rounding doesn't work. evaluating rad(4/2), rad(20/18), rad(39/37) and rad(20/16) - how can one even do this under timed conditions?

#2, i came to either A or D since they're mutually exclusive but chose wrong.

second image, the solution doesn't make any sense. i get that i am looking for the greatest difference in the center of mass beign displaced from its vertical position at its resting state. don't knwo what to do from there.

third image, they give you poiseielle's formula but that is a LOT of calculations with many different variables. am i supposed to just plug and chuck all of these? under a time limit?

fourth image, the solution isn't even given (some typo). i figured it's either B or D, but no nothing about how energy of the EM signal relates to cost. clueless here.

fifth image, i spent like 10m on this trying to figure out the math. didn't even know how to approach this. and the choices are all so similar. i guessed right but still - 10m!

 

[blkgrnblkylw]

they seem very hard. what are the answers?

 

[Odi]

Gave them a shot timed, not sure if correct in my answers or reasoning...

1) D. You want the combination that produces the greatest difference in their mass ratios. D has 4 Hydrogen atoms substituted for 4 Deuterium atoms. The other answers have a lesser number of H's for D's so D must have the greatest difference in masses.

2) D. By process of elimination.

3) D. In option D M2 has a greater difference in heights in that scenario (I think) so you'd want M2 at the low side.

4) C. The r^4 in the equation makes it unlikely that B or D are the answers. Quick math between the other two says C.

5) B. Process of elimination. The other answers are untrue (I think), even if I don't know jack **** about cost.

6) D. Guess and move on lol.

What are the answers?

 

[azor ahai]

Gave them a shot timed, not sure if correct in my answers or reasoning...

1) D. You want the combination that produces the greatest difference in their mass ratios. D has 4 Hydrogen atoms substituted for 4 Deuterium atoms. The other answers have a lesser number of H's for D's so D must have the greatest difference in masses.

2) D. By process of elimination.

3) D. In option D M2 has a greater difference in heights in that scenario (I think) so you'd want M2 at the low side.

4) C. The r^4 in the equation makes it unlikely that B or D are the answers. Quick math between the other two says C.

5) B. Process of elimination. The other answers are untrue (I think), even if I don't know jack **** about cost.

6) D. Guess and move on lol.

What are the answers?

1) A. I put D too with that same line of reasoning. but it's the overall mass that matters. D2 has double the mass of H2, none of the others come close.

2) correct. how did you choose between a and d by process of elimination? i found it difficult to prove mathematically. i know mass is inversely proportional to the square of velocity when KE is constant. momentum requires mass to be inversely proportional to velocity if momentum is to be kept constant, and therefore it is not constant. holy crap, i think i just figured it out.

3) correct. it seems so much more simple when i treated it as a simple pendulum - is that what you did? i was too psyched out by the double pendulum. i couldn't unconvince myself that they had the same change in height because they both had the same proportional change in height. it's height at equilibrium is x, and its height in all the examples is xrad(2) (because of the 45-45-90 triangle). only afterward did i realize simply that if x increases, so does what x stand for - its height and thus potential energy.

4) correct again. good job on eliminating B and D because squares of numbers less than 1 et smaller. i didn't figure that out until i was waist deep in math.

5) correct. i got this right but i spent more time trying to prove why B is right than why D is wrong. all waves experience constructive and destructive interference, and wavelengths/frequencies have nothing to do with it.

6) ha. i do the discretes in the first 13m and this was one of them. i ended up spending like 10m on this problem alone and rushed through the rest with eroding confidence i do remembering coming to an intuitive answer. the change in [X] decreases every time not the [X] but the change in [X]. from t0 to t1 it drops by like 42, from t1 to t2 it drops by like 20, and from t2 to t3 i would expect a drop of 10 - but that ends up being t4. so how about a drop midway of 5? that'll give you around 31, but you see that the drop is always less than what you expect. 30.6 is too close to the expected drop, and 28.3 is on the lower end. that's the answer. i guessed right, but this one point i paid for twenty fold.

 

[erythrocyte666]

1) A. I put D too with that same line of reasoning. but it's the overall mass that matters. D2 has double the mass of H2, none of the others come close.

2) correct. how did you choose between a and d by process of elimination? i found it difficult to prove mathematically. i know mass is inversely proportional to the square of velocity when KE is constant. momentum requires mass to be inversely proportional to velocity if momentum is to be kept constant, and therefore it is not constant. holy crap, i think i just figured it out.

3) correct. it seems so much more simple when i treated it as a simple pendulum - is that what you did? i was too psyched out by the double pendulum. i couldn't unconvince myself that they had the same change in height because they both had the same proportional change in height. it's height at equilibrium is x, and its height in all the examples is xrad(2) (because of the 45-45-90 triangle). only afterward did i realize simply that if x increases, so does what x stand for - its height and thus potential energy.

4) correct again. good job on eliminating B and D because squares of numbers less than 1 et smaller. i didn't figure that out until i was waist deep in math.

5) correct. i got this right but i spent more time trying to prove why B is right than why D is wrong. all waves experience constructive and destructive interference, and wavelengths/frequencies have nothing to do with it.

6) ha. i do the discretes in the first 13m and this was one of them. i ended up spending like 10m on this problem alone and rushed through the rest with eroding confidence i do remembering coming to an intuitive answer. the change in [X] decreases every time not the [X] but the change in [X]. from t0 to t1 it drops by like 42, from t1 to t2 it drops by like 20, and from t2 to t3 i would expect a drop of 10 - but that ends up being t4. so how about a drop midway of 5? that'll give you around 31, but you see that the drop is always less than what you expect. 30.6 is too close to the expected drop, and 28.3 is on the lower end. that's the answer. i guessed right, but this one point i paid for twenty fold.

For the bolded on in case you're looking for the derivation: KE = 1/2mv^2 = 3/2RT --> mv^2 = 3RT --> v = sqrt(3RT/m)
p = mv = m x sqrt(3RT/m) = sqrt(3RTm^2/m) = sqrt(3mRT)
hence, momentum is directly proportional to sqrt of mass

 

[Odi]

@azor ahai

Definitely fell for the trick in the first problem lol. I knew the combination with the greatest ratio difference was the correct answer but fell for the sorcery of thinking option D was that choice. Setting up the fractions like you did would have saved me instead of doing it my head.

For number 2 any gas at the same temp will have the same kinetic energy. When you set up 1/2mv^2 equal for both hydrogen and deuterium you can rearrange the equation in terms of their velocities to get:

Vh / Vd = sqrt (Md / Mh) ... Deuterium mass is 2 and hydrogen is 1 so you get Vh / Vd = sqrt 2 ...hydrogen will be moving sqrt 2 times faster

And to check their momentum just plug it all in.

Momentum of hydrogen is MhVh = 1 x sqrt 2 Vd .... since Vh = sqrt 2 x Vd from the top equation
Momentum of deuterium is MdVd = 2 x Vd

You can see now written in this fashion that 2 is a bigger factor than 1 x sqrt 2 meaning deuterium has greater momentum. All choices are satisfied, D must be wrong.

For 3 I just treated it like a pendulum. The higher up the pendulum, the less change in height an object will experience when the pendulum swings. That's why M2 should be at the bottom, it'll have a greater change in height and thus a greater change in potential energy.

6 was weird. If I honestly saw that on the MCAT I would realize right away it's a problem I do not know the answer to. I would guess and keep moving, if I had time, I'd come back to it.