h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Just take my word for it - you made sense.
The pull-ups were no big deal - I'm always game for a pointless challenge, and when I was little I wanted to be a SEAL when I grew up, so...

This morning I received an even nastier score on a Kaplan practice test, so the problem may be between the chair and the pencil. Bad rehearsals mean good performance, right? That's what I said right before I flunked my driving test.

Anyway, I delivered my application yesterday in person so I could drop hints about how wonderful I am and hope I don't drop them to someone who's going to file me away and forget about me. It all sounded promising enough. Fingers crossed, and that stuff.

Thanks for the help and stuff. I'll keep you posted if anything exciting happens.

Just dropping in for a quick question for Pailaway Physics Help:

The transfer of heat equation: mass x specific heat x change in temperature [Tf - Ti] = Q

When you throw two things together that have different temps their equilibrium will be the answer to the equation
Q1 = Q2

Except my final_temperature variables keep canceling out. And I get an answer that doesn't make sense. And it's an algebraic error so the books never show that part of the process, and there's one on almost every test and ... OK, not that bad. But I do feel like a dunce and can't figure it out.

Can you help?

Sure. If I understand your question properly, here's the answer:

First, it important to get the signs right, and I'll bet this is where your difficulty is. Say there two substances, call them 1 and 2, each having masses and specific heats m1, c1 and m2 c2. If they have different initial energies, then one will heat up and the other will cool down. So, substance 1 has initial temperature T1 and substance 2 has initial temperature T2, but they end up at the same temperature Tf. Therefore, the signs will need attention. We shall arbitrarily say that substance 1 will heat up and substance 2 will cool down.

Here's the balance then

m1*c1*(Tf-T1) = m2*c2*(T2-Tf)

and if we end up with a negative sign when returning to this, then it was the other way around. Now then, on to simplifying.

m1*c1*Tf - m1*c1*T1 = m2*c2*T2 - m2*c2*Tf

(m1*c1+m2*c2)*Tf = m1*c1*T1 + m2*c2*T2

Tf = (m1*c1*T1 + m2*c2*T2)/(m1*c1+m2*c2)

which you will come to recognize as a weighted average.

The two special cases are

m1=m2 and c1=c2 so that
Tf = (T1+T2)/2 which is a simple average.

and T1 = T2 = Ti so that
Tf = Ti, which means they were already in equilibrium.

Does that help?

Btw, feeling like a dunce is perfectly normal and does not mean that you are one. The good news is that as you gain experience, it will take more and more difficult problems to make you feel like a dunce.

Did you know that Einstein felt like a dunce about mathematics?

Come to think of it, I do too.

The thing is that Einstein was a dunce at a level that I wouldn't even understand.

Just nattering.

Question: Why do you have Tf-T1 and T2-Tf - because one initial temp is rising and the other falling?

Wasn't Einstein the one who dunced 4th grade math? I didn't do that, though I dunced up quite nicely last night. Did an equation six times, got three different answers, none matched the back of the book. So I ate a cookie, guzzled a few bars of chocolate, downed some water, knocked off a few pull-ups, and thought that maybe a Psy.D wouldn't be so bad. Then I went up and noticed that the back-of-the-book answer was the equation of the tangent line. So the Psy.D was retired.

On the brighter side, most of my mistakes have to do with careless rewriting, so there's hope.

I met the tutor on Friday. I think it was the first time someone asked him how to factor a cubic function, draw a tan graph, and simplifying complex expressions with fractional exponents in a single session. Except he made the fractional exponents thing look so simple that I didn't bother jotting it down and I'm lost again. But no prob. Test isn't until Tuesday. Maybe I'll try to dig up the professor this time. Wish me

Yes, I have Tf-T1 and T2-Tf because one temp will rise and the other will fall. If you set it up as Tf-T1 and Tf-T2 instead, you will end up with a (m1*c1-m2*c2) in the denominator and, besides being wrong, you know what it leads to don't you? DIVISION BY ZERO! hahahahah

I left out the very initial set up and skipped to thinking about the sign, But you can set this problem up so that you don't have to think about the sign. The correct initial statement is that at the start:

Q1 + Q2 = Q
meaning that if you add the energy of the two individual things together things they have a certain total amount of energy, even though they're physically separate.

but if we mix them, then we haven't added or subtracted energy to the whole system, we'll just distribute it differently ie it will transfer between the two things but the total will remain unchanged - so if we take that same equation and look at the difference over time:

Q1f + Q2f = Q at time final - minus
Q1i + Q2i = Q at time zero - equals

(Q1f-Q1i) - (Q2f-Q2i) = (Q-Q) = 0

So, (Q1f-Q1i) = -(Q2f-Q2i) = (Q2i-Q2f)

which is to say

c1*m1*(Tf-T1) = c2*m2*(T2-Tf)



Careless rewriting welcome to the club.

>>he made the fractional exponents thing look so simple that I didn't bother jotting it down<<
Hmmm, yes I have membership in that club too.

on the test - I suspect that you'll not only do quite well, but will probably screw up the grading curve for the rest who'll find themselves in a downward spiral of division by zero if they don't start studying.

Thanks - you've fixed my heating problem. SAT coming up this Sunday.

I assume the last line must be for psyching purposes, like football team stuff:
"We're gonna differentiate those equations!"
"Yeah!"
"We're gonna ace this calculus test!"
"YEAH!"
"We're gonna do so freakin' well we're gonna screw up the grading curve!"
"YEAH!!!"
"LET'S DO IT!"

2 hours to zero hour. Thanks!

That's the spirit!

Divide and Conquer!

I like that. Divide and conquer.

Calculus done (for now) I should have done fine. I checked every example at least twice. Was rather chagrined and amused to find that one careless mistake corrected another in the last question.

Psychology test just fluffed. Physics coming up. All I can say is that if the test is like Princeton Review, I'm sunk. If it's like Kaplan, I have a fighting chance. Either way, Sunday I'll be up at the ungodly hour of 7:30 chewing a pencil and trying to get an 800.

>>one careless mistake corrected another<<

Are you telling me that two wrongs made a right?

...I must rearrange my world-view.

Well, congratulations on the test - and sunday

Two wrongs make a right unless the professor is counting work, which I doubt. He gave us a whole lecture in the beginning about how we shouldn't say that we know the math it's just the numbers that are tripping us up, because if we get the numbers wrong then we're WRONG.

SAT was a bittersweet business. I passed on the physics and flunked on the common sense. There was only a handful of questions that left me scratching my head, which I think is pretty good, but I tried answering those questions while I went back to fill in the bubbles on the answer sheet, and lost track of the time. So I didn't get a chance to fill in all the answers. I'd kick myself, but there's no point. If I get most of what I filled in right, then I can still get an above average score. So it's not a tragedy.

And if you were wondering: the topics were broader than Kaplan, but the questions were somewhat simpler than Princeton Review.

Well, the good news is that in going back to try and answer the handful of questions and then completely losing track of time indicates that your brain is wired about right for engineering, so you can take heart from that. What I mean is, it's only a minor tragedy not to do as quite as well on a particular exam as you know you should have - but it's a major tragedy to be in the wrong field.

Broader than Kaplan but simpler that Princeton Review? I'll have to find samples of each because I'm curious now. What you say indicates that Kaplan is something like - these two things collide, now where do they go?, while PR is more like - if these two things collide, can they also be a wave? (The only problem with having a look at samples of these exams is that I might realize I'm a complete idiot, which is something I prefer to suspect than to know)

This is *high school* physics, Mr. Engineer. If an SAT II test made you feel like an idiot, you'd probably be one. That's something I suspect isn't the case, but I don't know it for sure.

Kaplan asks what the velocity of the items are after collision. Princeton tells you the angle they diverge and expects you to find out something about the difference in kinetic energy or acceleration or something using them.
Or Kaplan will expect you to use individual equations to find out about the individual variables of a satellite, while PR will expect you to combine a couple of equations to tell them things that each equation can't answer on its own.

Actually, in some ways it was easier than the stuff I did over the summer, because when the test is 1 hour and there are 75 questions, they can't expect you to spend too much time on each one.
The strange part was that a few chapters of physics that I studied over the summer were totally ignored by PR and Kaplan, and only given cursory attention by the SAT, while topics totally unaddressed by the summer books were given tons of attention by the SAT. And the PR book hinted at tons of more stuff that nobody addressed at all. There's an awful lot of physics out there.

But enough of that. I took the test to make sure I would know everything I needed to know to start college level physics and also in the hope of adding to my chances at a scholarship. The more important half was accomplished.


But thanks for the encouragement. I happen to need it at the mo. Professor kind of mentioned related-rates problems in passing "You set up an equation for the relationship of the variables and solve" and he expects us to be able to move on from there. I'm not managing well. Is there some mathematical 6th sense that must develop, or are there some basic types of relationships that anyone can crib and recycle as needed?

PS: Do all mathematicians have a v-shaped crease between their eyes from concentrating on math problems all the time? If that's a hazard of the job, no wonder women don't go for it in droves.

>>You set up an equation for the relationship of the variables and solve<<

It's actually fairly common for professors to mention things in passing as though you should be completely familiar with them. A very famous mathematician, I've forgotten which one, once said - 'when a paper I'm reading contains the phrase 'this is intuitively obvious' then I know I've got a few hours work before it becomes so to me'

So, there's no 6th sense. Rather, the drill is to press the prof for an explanation, or to press the TA for an explanation. In this way you will learn all those basic types of relationships that anyone can crib and recycle as needed.

The subject you mention, that of related rates, is fundamental to differential calculus and you will have ample opportunity to become familiar with it. In fact, there is surely a chapter devoted to it. Anyway, whenever someone waves their hand and airily says 'oh you know, it's nothing more than related rates' - pin 'em down.

Furrowed brow hmmm? ...No, can't say I know what you mean

The book gave only three examples, one was some seriously weird trig and machine question, so that left two... But I've found a few on the web and have the tutor lined up for tomorrow, so things'll be . Maybe related rates comes up later again, but I want to know how to figure out the length of my shadow when I'm approaching a streetlight NOW. Things like this are IMPORTANT.

I do feel just like that mathematician. Whenever my eyes cross in class, it usually means I'm going to need a good 45 minutes reinventing the wheel. Today I was quite excited to rediscover the relationship between radians and multiples of pi and trig values... Like figuring out a puzzle.


I think I may as well officially hire you as moral support and cheerleader. That's your first paycheck.

I'm Rich!

Related rates will come up later - but in the form of parametric equations, I think. (hee hee)

You never thought engineering would be so lucrative, right?

Parametric...

(yes, you call the parametrics when your equation is all zeroes, but before it goes to infinity)

So, just checking in -

I've been staring at that parenthetical statement for three days (not straight) and can't figure out if it's a bad joke, a good joke, or completely serious. But parametrics don't come in until chapter 9, and we only get up until chapter 6 this semester - so I won't find out very soon.

Update:
Been accepted to a program and offered a 2/3 scholarship, which is good, except for the 1/3 still left to cover.

Found a chemical engineer to ask question to. He assured me that:

"I think chemical engineers make the most money because we're smart, cute, communicative, funny, excellent beer & whiskey drinkers (if you don't have this skill, you'll have to pick it up for professional credibility; smoking cigars is optional, but a big plus) and just great people with whom to hang out."

But overall, even though the company sounds great, it sounds like a fairly dull business.


The Computers Club invited a robot programmer to speak, and I ended up on YouTube all night watching humanoid robots collapse all over themselves on the RoboCup field. It's a field that can use vast improvements.

Did a calculus min/max example three times last night to get three wrong answers; did it three times this morning and got the right answer the second two times. I still don't understand why that happens. There must be a scientific explanation.

correction: