Science questions not worth a thread I: I'm a moron!

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How do you calculate the length of a parabola?

You need to solve the curve integral.

A parabola y = x^2 you can parametrize as c(t) = (t, t^2)
Then you have to calculate the norm of the derivative of c:
|c'(t)| = sqrt(1 + 4t^2)

And then integrate over that: Integral from a to b over sqrt(1 + 4t^2) dt
 
Well... I'm going to assume that the parabola in question is a parabola of the form

y=ax^2+bx+c

In that case, you'd use the arc-length formula, which is...

L=∫_a^b sqrt(1+(dy/dx)^2) dx

Here, dy/dx = 2ax+b so...

L=∫_a^b sqrt(1+4a^2 x^2 + 4abx + b^2) dx

Where a and b are the two endpoints of the parabola you're measuring. And just to let you know, the indefinite integral for that problem has the solution...

∫ sqrt(1+b^2+4abx+(2ax)^2) dx = (sqrt((2ax)^2+4abx+b^2+1)(2ax+b)+arsinh(2ax+b))/(4a)

Where arsinh(2ax+b) is the inverse hyperbolic sine of 2ax+b.

Does that help?
 
What cleaners can ammonia be safely mixed with? Spic & Span?

Federal law basically prohibits mixing any household chemicals together!!!!!!!!!!!!!!!!!!

Read the label.
 
Yeah, I'm a bit beyond that. What I need to know is what will land me in the hospital :p
 
You can simply fill a spoon full of Ammoniak into your cleaner. The released energy can in no way be high enough to hurt you. In the unlikely case that you see a strong chemical reaction, you should propably not mix them. ;)
 
I know next to nothing about physics so forgive me for this question.


What are the exact mechanics behind gravity and how does it work? Are there nuclear particles that determine mass or some other force?

I thought i heard somewhere that scientists don't exactly know how gravity worked but i thought they knew some specifics about it.
 
I know next to nothing about physics so forgive me for this question.


What are the exact mechanics behind gravity and how does it work? Are there nuclear particles that determine mass or some other force?

I thought i heard somewhere that scientists don't exactly know how gravity worked but i thought they knew some specifics about it.

magnets
 
I know next to nothing about physics so forgive me for this question.


What are the exact mechanics behind gravity and how does it work? Are there nuclear particles that determine mass or some other force?

I thought i heard somewhere that scientists don't exactly know how gravity worked but i thought they knew some specifics about it.

Scientists, afaik, don't understand how gravity "works". I'm sure there are plenty of competing theories and I'm sure gravitons are in a few of those theories.
 
Oh, you have asked a difficult question.

To be honest, we have some idea of how gravity works. It's sort of a dip in the space-time fabric, I guess.

The real question is, how does mass work?
 
I was just curious since we just did projectile motion in AP Physics but we never went over stuff like flight distance (which is important sometimes, right?). But it certainly looks like your answer is comprehensive! :lol:

You can calculate the length with no knowledge of the explicit formula also: Just approximate it with small right triangles, little like when you're finding the area under it. Now you're just interested about the lengths of the hypotenuses of the triangles, and their sum. When the number of triangles increases, the sum approaches the mentioned integral:

\int [1+(f'(x))^2]^(1/2) dx.
 
I know next to nothing about physics so forgive me for this question.


What are the exact mechanics behind gravity and how does it work?

The current description of gravity is General Relativity. In a nutshell mass and energy bends spacetime and objects just move along "straight lines" (actually geodesics) in this curved spacetime, which is percieved as an accelerated motion for an external observer.

Until now there has been no evidence against this description, although some predictions still await direct confirmation (gravity waved for example)

Are there nuclear particles that determine mass or some other force?

A lot of mass in our world is actually just binding energy between sub-nuclear particles. The mass of the proton is about 100 times the mass of its constituent quarks, the rest is binding energy, which effectively acts as mass.

However, (most) sub-nuclear particles do have mass, which is created by coupling to the Higgs field. The gauge boson of this field, the Higgs boson is indeed some sort of particle that determines the mass of other particles (and itself).

The problem with these descriptions of mass is that the underlying theories have to ignore gravity, so the connection between this mass and the mass relevant for gravity is not exactly clear.

I thought i heard somewhere that scientists don't exactly know how gravity worked but i thought they knew some specifics about it.

With GR we do have a theory of gravity that has not been falsified in any way, yet. What we do not have is a quantum theory of gravity, as all attempts to unify GR and quantum field theory have either failed or do not give any testable predictions. So we have no idea what happens, when quantum gravity effects become relevant. But experimentally we are a long way from realizing such conditions.

So in other words: We can explain every gravity effect we can see, but we have no idea what happens in very extreme conditions.

(Note that the explanations can only go to a certain level. At one point there will always be formulas, constants or assumptions with no explanation why these things are what they are)
 
You know how KE=.5*m*v^2
How do you get from that to the formula for Average Kinetic Energy of gases: KE=3/2*R*T*n
 
You use the formula for the root-mean-square speed of molecules.

v(rms) = sqrt(3 R T / M)

Where R is the gas constant, T is the temperature, and M is the molar mass.
 
You know how KE=.5*m*v^2
How do you get from that to the formula for Average Kinetic Energy of gases: KE=3/2*R*T*n

This is a results of statistical mechanics. At first you have to calculate the partition function (basically a sum over all possible states at a certain energy) for the ideal gas with the help of E=1/2 m*v^2. The easiest way is then to calculate the entropy from the partition function and use the definition for he temperature to get that formula.

The harder way is to calculate the velocity distribution form the partition function, then determine the rms velocity by integration and put it again into E=1/2 m*v^2.

So in a nutshell, you take E=1/2 m*v^2, apply statistical mechanics to it and arrive at that mean kinetic energy.
 
Why would you do all that when you can use the approximate, but highly accurate formula for the root-mean-square speed that I provided that, incidentally, gives the other formula he mentioned?

It's a whole lot easier my way.
 
Why would you do all that when you can use the approximate, but highly accurate formula for the root-mean-square speed that I provided that, incidentally, gives the other formula he mentioned?

It's a whole lot easier my way.

Because if you want to know where a formula comes from it does not help to let an equivalent formula drop from the sky.

Your formula is right, but you did not mention how to get that formula and it does not make apparent, that there is a much deeper connection between the kinetic energy of a single particle and the average kinetic energy of an ideal gas.
 
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