.45 joules
the answer choices are
1) 8360 joules
2) 50,000 joules
3) 100,000 joules
4) 4,180 joules

Umm, well I am not a Jellsprout, nor do I identify as one (I can't speak for Bmwsu), so I feel no obligation to answer the question (which I wouldn't even know where to begin to do so, btw). I never really pegged you for a blacksmith/apprentice blacksmith, so I'll assume this is a homework problem. If Jellsprout doesn't come on it time, just try your best to come up with a good answer. It's only homework. I'd be much more concerned if you had to craft a sword for the fief's knight on a deadline. You don't, right?

well it's a take-home test, but ya, I see what you're saying. thank you

Silly Yaya... the temperature for smelting iron is MUCH higher.  

lol

It's 0.46 J g^-1 K^-1
Dimensions are very important, especially when dealing with specific heats. Otherwise nobody would know if you are using the mass or molar specific heat. It also really helps solving the problem.

Look:

c = 0.45 J g^-1 K^-1
Now multiply this with the temperature difference:
c * dT = 0.45 * 40 J g^-1 K^-1 K
K^-1 * K = 1, so those cancel.
Now we multiply by the mass:
c * m * dT = 0.45 * 40 * 50 J g^-1 g
Again g^-1 g = 1, so they cancel.
And we are left with:
c * m * dT = 0.45 * 40 * 50 J = 880 J = Q

This is far lower than any of the given answers, so I assume that you messed up the units somewhere, like saying g instead of kg somewhere.
It is also important to consider that a specific heat drops for lower temperatures, that would make the required heat even lower than it is now. It doesn't drop until cryogenic temperatures either, so that isn't really something we need to worry about here.

Math always looks so much more complicated to me when you don't have superscript.

Math always looks way too complicated for me. #Math iz dumb

I've said it before, I'll say it again. This forum needs LaTeX math support.

Can you explain how physics differs when working in 4 or more dimensions?

It depends on the specific branch. Generally, just compare physics in 2D (like on a flat surface or in a very thin cavity) to physics in 3D and you'll notice the difference.
Some noticeable changes would be that, because the number of degrees of freedom increases, you'll need more energy to heat something up. Something else is that many things that depend on 1/r^2 such as gravity or the electrostatic force will now depend on 1/r^3. Basically, electric force then would be similar to magnetic force now.

Fundamentally, nothing will change. All the symmetries (and by extension, all conservation laws) will still be there, so all the fundamental laws will be the exact same. It is only that these will now lead to different results.

Alternatively, consider 3D space but put a white hole (an inverse black hole) in there. Now the space becomes 4D!

Train goes to the destination. If we increase its speed by 10 km/h, the ride will be 1 hour shorter. If we decrease the speed by 10 km/h, the ride will last 4 hours longer. What's the distance between the starting point and the destination? (in km)
Task from today's math olympiad, I didn't do that one even though I'm sure there were harder ones, but that one still makes me curious. (hope You will get it) I didn't do well year ago when the "Need for Speed" competition was started here at the Interguild and Kro just released Not Worth The Gold, but this time I'm not satisfied either.

Let us take v as the velocity in the original situation, x as the distance and t as the time in the original situation. Then we have the following three equations:

(1) x = v * t
(2) x = (v + 10) * (t - 1) = v * t + 10 * t - v - 10
(3) x = (v - 10) * (t + 4) = v * t - 10 * t + 4 * v - 40

Three equations, three unknowns, simple business. It is a shame the system isn't linear, so we have to put some more work into the thing.
First we use (1) to isolate v:

(4) v = x/t

Now we fill this into (2):

(5) x = (x/t) * t + 10 * t - (x/t) - 10 = x + 10 t - x/t - 10

Subtract x and multiply with t:

(6) 10 t^2 - 10 t - x = 0

This is a simple quadratic equation::

(7) t = 1/2 +/- sqrt( 1/4 + x/10)

We will only consider the positive solution, as that is the only physically realistic one.

Fill (4) and (7) into (3):

(8) x = x - 10 * (1/2 + sqrt( 1/4 + x/10)) + 4 x / (1/2 + sqrt( 1/4 + x/10)) - 40

This simplifies to:

(9) 0 = -10 * (1/2 + sqrt( 1/4 + x/10))^2 + 4x - 40 (1/2 + sqrt(1/4 + x/10) )= 3x - 25 - 50 sqrt(1/4 + x/10)

Now we add 25 - 3x and take the square of both sides:

(10) (25 - 3x)^2 = 625 + 9x^2 - 150x = 2500 (1/4 + x/10) = 625 + 250 x
(11) 9 x^2  - 400x = 0

This gives us two possible solutions. x=0, which is clearly not a good solution, and 400/9 km. The time in the original situation would then be 8/3 h and the speed 50/3 km/h.
A quick check, 80/3 * 5/3 = 400/9 and 20/3 * 20/3 = 400/3, so this is correct.

I confirm
source: http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
I support


<long quote>
I confirm

I verified this way up to the moment with the quadratic equation and it all seemed to be correct, sweet! Yeah, there had to be some another way to do it too, since they aren't able to put any quadratic functions into the tasks yet for 14-16 aged students (I know it already though so it would come handy at times like here...) Waiting for the results so I know how they expected us to do this task (I'd put the solution here by occasion if You have no idea too). At the time of the olympiad, I've written down the exact same equations You've written here, but yeah it wasn't linear and every side of every equation was equal to each other (thought they *could* get reduced together), and since there wasn't too much time left I didn't manage to simplify those equations. ;/ Thank you very much for the help!

in ages 14-16 you still don't study quadratic equations? what kind of maths do you learn then?????

They learn Polish hand magic.

You learn about the quadratic equation in grade 11 here. And that's only in smart people maths. Fortunately, most people take smart people maths.

Quadratic equations are taught sometime between the 16-18 age and at the moment they're teaching us about the arithmetic and algebraic basics together with the basics of planimetry and stereometry once again. ._. I'm pretty sure I'm already doing it all quite well for a long, long time, but it's only me and two or three other people in the school, every other student directly adds 5 * sqrt(2) + 5 and thinks it's 10 * sqrt(2)... And when the last stage of the regional olympiad comes with only few people classified for it, we get some "crazy" tasks about the speed, time and the distance no one thought about with such stuff and there are only maybe 6 winners out of 200.000 (probably way more) students from the region who had the possibility to take part in it and win it. So no, rarely someone happens to be good at maths in this country. Poland. ;3

What??? You don't learn quadratic equations until 16??? I learned them last year, what.

i feel like that was 6th grade or something... so age 11?

I think I learned them when I was 14 but I'm in the B set (I suck at maths)

I am dazzled

what kind of math is it possible to learn for 10 years without getting to a quadratic equation

oh my gawd

and I thought my educational system sucked.

I think I learnt quad in 6th or 7th grade; and that was well before I started doing all these extravagant stuff. by grade 11 I was almost halfway through a degree; that is exceptional, I know, but seriously, studying a subject which can be covered in *one* line only in grade 11, that's like whaaaat

Not only that, they say polish education system is actually one of our best advantages. Completely surprised you all have already learned about stuff like that so early. So even though life gave me some really good mathematical skills, nice to know it was never well explicated. Poland.

because most people don't care about maths beyond working out their taxes and adding up. Is that really so bad to you? I love history, but I don't expect people to know much beyond the basics unless they're interested