Mathematics - 2012-10-22 (page 1 of 3)

user19161

00:06

@PeterTamaroff We are more than cousins. =)

Argon

Is the force of friction always the opposite direction of the net force?

user19161

Friction always acts opposite to the direction of motion of the object.

Argon

@JasperLoy What happens if $\mu = 0.3$ so $f_{f} = \mu f_n$ where $f_f$ and $f_n$ are frictional and normal forces respectively.

Then

if $f_n = 1$ for example, we have $f_f = 0.3$

Correct?

Then, if the applied force is $0.2$ N, what happens to the object? Clearly it does not go backwards!

user19161

@Argon There the constant is called the coefficient of friction. It's just a formula, so you are right! Think of it as if you press down an object more onto the floor and try to slide it along the floor, it is harder to slide! The greater the normal reaction the greater the friction.

Argon

@JasperLoy I know that. I was wondering, though, if the applied force < friction

How does this work? On a free body diagram, one would this that the object is accelerating backwards!

user19161

00:18

@Argon Hmm, applied force can never be less than the friction. The object starts to move only when the applied force is more than it, and then the formula applies.

Argon

@JasperLoy So friction suddenly appears when the applied force is greater then it?

user19161

@Argon Ah, I am not sure what happens at the boundary, I have forgotten all my math and LaTeX, and physics is even worse!

Argon

This means that if $f_f = 1$ and the applied force is $0.999999$, the net force is $0.999999$. However, if the applied force increases to $1.000000001$, the net force decreases to $0.000000001$???

This is why math trumps physics.

user19161

@Argon I think friction also works differently when the object is moving and at rest. So that one applies to when moving.

Argon

@JasperLoy Right, $\mu_s$ static friction. I forgot

user19161

00:21

@Argon You should know more than me. Ask your physics teacher! I have an interesting phenomenon to share with you.

user19161

If you drink iced water, do you sometimes see that after a while the ice cubes seem to merge?

Argon

@JasperLoy Sure, ya

user19161

What do you think is happening?

Argon

@JasperLoy Perhaps when the ice is close to each other and there is water between them, the ice freezes this small layer quickly and merges the cubes?

user19161

@Argon Yes, I think so too! Anyway I once asked my physics teacher and he did not say anything, so I suggested this to him and he said, hmm maybe.

Argon

00:25

@JasperLoy There is a fun way to merge ice cubes by sprinkling salt on them and then stacking them. This method uses that phenomenon to fuse together the ice.

The salt melts a bit of ice, and then the cubes freeze this water quickly.

user19161

Also, if you push an object in outer space till it moves at v and then let go. it will move at v forever!

Argon

Yes :)

Newton's first law

user19161

Amazing ain't it? You get motion for nothing!

user19161

Rebecca Black should make a song out of that!

Argon

@JasperLoy I don't know if she is nerdy enough...

But she'd have some interesting lyrics, to be sure!

user19161

00:27

@Argon I think she is a great match for Mr Bieber...

Argon

@JasperLoy You are probably right

user19161

@Argon Is your name Aaron? I heard Marilia call you aaron.

Argon

@JasperLoy Ya

She likes to call me Aaron. And quote songs at me

:)

user19161

@Argon Anyway, my e question still has no answers, I thought it would have OVER 9000 votes by now.

Argon

@JasperLoy I saw it :)

You were disappointed a few hours ago as well.

+1

user19161

00:31

@Argon I noticed this e thing in high school I think. Always thinking about it.

Argon

@JasperLoy I noticed it too. It makes the first digits of $e$ easy to remember :)

user19161

I might delete the question after a while if it has no answers...

Argon

@JasperLoy Why? 5 upvotes is not too shabby!

user19161

@Argon Yes, I once memorised pi to about 40 digits.

user19161

@Argon Cos I like all my questions to have answers of some kind, even if the aswer is Just Because, Justin Bieber.

Argon

00:33

@JasperLoy I'm tempted to answer that.

@JasperLoy I know 19 digits. More then enough

user19161

Sometimes, my questions get an answer that don't really answer the question, but it is good enough so I accept it.

Argon

$\frac{5}{9000} \cdot 100 = 0.0\bar{5}$%. Almost there.

user19161

So I wanna keep a 100 per cent accept rate.

Jonas Teuwen

I wrote a paper, and when I check it again I am like holy monkey... did I write that?

Argon

@JasperLoy The $e$ thing probably is, dare I say, a coincidence.

Holy monkey

user19161

00:35

@JonasTeuwen I can't believe I wrote my undergrad paper, some of the proofs are very hard really, though it may be trivial to others. And I thought of every proof myself except for the one I mentioned in the preface.

Jonas Teuwen

I like this one

$$\left(1 - \frac{\Psi_m}{m!} \right)\psi_m= \sum_{k = 1}^{m - 1} \frac{\Psi_k}{k!} \psi_k$$

@JasperLoy Yes.

That is excellent!

user19161

In fact, some of the proofs are so hard that I have difficulty following except at times my mind is very clear.

Jonas Teuwen

If you work a bit with it more regularly you will even not bother writing it down as it is so trivial.

user19161

It is in more or less Bourbaki style, so someone would probably take 4 times the length to write.

Jonas Teuwen

I'd do for some: \begin{proof} Similar to the above, hence we omit the proof. \end{proof}.

user19161

00:38

@argon Are you going to be a mathematician when you grow up? I am making you sound like a small kid now....

Jonas Teuwen

When I grow up I am going to be the ruler of the universe.

2

Argon

@JasperLoy Doubt it. I like math, but I'm no good at it

user19161

@JonasTeuwen I would say: This is trivial and is left as an exercise for the reader.

Jonas Teuwen

Skip the trivial.

And then make the theorem really hard.

user19161

@Argon But you asked me about Canadian universities, no?

Jonas Teuwen

00:39

"Left as an exercise for the interested reader."

Bang! Nagata-Smirnov-Bink.

Argon

@JasperLoy Yes. I'm going to be taking math, but not majoring or anything.

I want good math courses.

user19161

@Argon Aw, I think you can do math, just a gut feel from the vibes you send me through the LCD.

Argon

@JasperLoy I don't know if you can trust the LCD.

:)

I always have to try in math and check stuff over a billion times. I have friends who can do this stuff no problem, no double checking, and get perfect.

The only reason I know what to do is because everything we do it really trivial and repetitive.

kahen

YES! meta.math.stackexchange.com/a/4393/1269 - finally a mathjax script for chat that works for greasemonkey

Jordan

Anyone know about linear regression? According to my assignment the slop in y = mx + b is defined as the summation of $x_i y_i$ what does that mean?

kahen

00:44

no more silliness with having to have a bookmark

user19161

@kahen What is greasemonkey?

Argon

@JasperLoy Isn't it a Firefox addon or something?

user19161

@Jordan Nice to see you again...

kahen

An addon for Firefox that lets you write javascript to be injected on websites adding functionality or changing layout

here is one that lets you download youtube videos for example: userscripts.org/scripts/show/25105

Argon

@Jordan Good to see you back!

Jordan

00:45

@JasperLoy Hello, I took a break from math :P but I am trying to get back into it before my next semester

user19161

@Jordan It means you add all of them like $x_1y_1+...+x_ny_n$.

Jordan

@JasperLoy I add what though, the multiplication of xy so it is like $x*y$?

user19161

The sum is taken as $i$ goes from the bottom index to the top index.

kahen

hmm... it isn't automatically updating as more lines in chat are added. that's kind of a bummer

Jordan

Ok thanks I think I get it

user19161

00:48

@kahen Should be auto, so that is not good.

user19161

But after refreshing you need to click again.

Argon

01:13

@JasperLoy I presume you were/are in math in university?

user19161

01:27

@Argon Yes, were.

user19161

@Argon I just accepted your answer. I will accept another if there is a better one.

Alexander Gruber

@BenjaLim not really, is it requied for group cohomology?

Argon

@JasperLoy That's fine

I thought I'd put you out of your misery. :)

user19161

@Argon So now we both get some points for this stupid thing, hehe.

Argon

@JasperLoy Let's complain to people that we thought we'd be getting THOUSANDS of +1s!

user19161

01:39

@Argon Yeah, considering how some of the highly upvoted questions are of this flavour too!

Link

Hi

user19161

Another mechanics question?

Link

What's new guys?

nope

user19161

Phew!

Link

I understand forces :D

much easier than kinematics was

Argon

01:40

@Link I don't :)

user19161

@Argon You only understand forces when you can sense a disturbance in the force.

Argon

@JasperLoy :) Jedi mind tricks

user19161

@Argon How long more before you go to university?

Link

Hmm, I was solving Project Euler problems the other day, I was surprised when I got it using just a piece of paper and a calculator :D

user19161

@Argon Hey wanna change your avatar to something else instead of the default one? Just a thought.

Link

01:42

I love math.

@JasperLoy, yours is a blue square....

Argon

@JasperLoy A bit less then 2 long years.

@JasperLoy I thought about it. But then I saw I had to register something and got too lazy.

I don't know what I'd make it to anyways.

user19161

@Argon Oh it's really fast, less than 5 minutes.

Argon

You've convinced me :)

I'll be back (in the terminator voice)

user19161

The default ones are a bit hard to recognise.

Link

With guns, and ammo!

Rajesh D

01:45

Here

jmi4

@JonasTeuwen it is, I just hadn't been making the connection between the fibers of the target of a homomorphism $\phi$, the cosets, and the translates of the kernel of said homomorphism.

Argon

@JasperLoy I think I changed it

There we go :)

peoplepower

@Argon the question is, can you breathe?

Argon

@peoplepower I'm not allowed to :)

@JasperLoy What inspired you to use a blue square as your avatar?

user19161