Seen the first one before. Second one would be better if Derpy didn't look so fat. Why use perfect vector art for Trixie but not for Derpy? All you would need to do is add the hat.
http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence Under "Applicability of the strict mass–energy equivalence formula, E = mc²"
The equation takes care of system where said mass is "moving" (hence the P - momentum term). The classic E=mc^2 hold true if E is just the rest energy of the system (nothing is moving). The E in E = sqrt((mc^2)^2+(pc)^2) is the total energy of the system.
m = mr/((1-(v^2/c^2))^0.5) ........mr is rest mass and v is relative velocity
We can substitute the above reconfiguration of the energy formula to get:
E/c^2 = mr/((1-(v^2/c^2))^0.5)
Now we square the equation:
E^2/c^4 = mr^2/(1-(v^2/c^2))
We rearrange this equation to:
E^2(1-(v^2/c^2)) = mr^2c^4
Multiply the E^2 through the parenthesis and manipulate:
E^2-(E^2v^2/c^2) = mr^2c^4
Substitute in E^2 = m^2c^4 into the second E^2 to get:
E^2-(m^2c^4v^2/c^2 = mr^2c^4
The c^2 on the bottom cancels out:
E^2-(m^2v^2c^2) = mr^2c^4
Because mv = p (which is momentum), then m^2v^2 = p^2 and:
E^2-(p^2c^2) = mr^2c^4
More rearrangement yields:
E^2 = (pc)^2 + mr^2c^4
A little more manipulation yields Trixie's equation:
E = (p^2c^2 + mr^2c^4)^0.5
From this, we can see that even stationary objects with mass mr will have energy dependent on a factor of c^4, and when the object moves and thus gains a momentum p then it will increase in energy. This also hints at the fact that objects in relative motion have a greater observed mass. Ponies.
E^2 = p^2 c^2 + m^2 c^4 is the generalized form of E = mc^2 for an object in motion. The "math fail" comment was just in regards to the fact that sqrt(a^2 + b^2) is not equal to a + b; exponents are not distributable across addition and subtraction operations.
Trixie's is for moving particles, Derpy's is for stationary particles (I think). Therefore, Trixie's is more useful in real-life situations. Or something
Derpy's equation is for particles at rest only, correct, but Trixie's equation accounts for particles in any state of motion, rest included.
At rest, momentum would be 0, meaning p^2c^2 = 0, making the equation just E = sqrt(0 + m^2c^4), or E = sqrt(m^2c^4), or just plain old E = mc^2 once again. Trixie's math is more great and powerful.
I have officially learned more physics from ponies than I have from anything else. I should probably start me some college... NAH. I'll just watch more ponies.
The only thing I'd add is just the interesting tidbit that the equation Trixie wrote is commonly used in high energy physics, such as in linear accelerators like the LHC, because both energy and momentum are conserved in the interactions and involve relativistic speeds.
@Aecratis Cool, didn't know that. I wonder what Trixie is planning on doing with her knowledge of high energy phenomenon...
Also, the LHC isn't a linear accelerator. I think it's called a synchrotron. There's actually a series of four rings, three to inject/prepare the particles for the main ring, and then the main ring ultimately instigates the particle collisions with all the detectors equipped.
Nevermind. I see that the original constraints of the problem are all positive and E, M, or c^2 could never be negitive so you don't have to worry about negative values. Derp!
Ah, sorry, I always forget that it's not technically a "linear" accelerator. Good thing I'm not really thinking of going into HEP.
But yeah, it uses one linacc and two synchotrons successively to increase the beam energy. The large ring is primarily for beam storage, focusing and detection.
Kitty? for Luna?!...well i guess she needs a caress name too just like ''Tia'' or ''Celly'' hmm...kitty...that reminds me, most of the ponies when sitting on their butts, do indeed look like cats while in that posture
We have E^2 = p^2 * c^2 + m^2 * c^4, which is unsimplifiable (and mathematicians and physicists tend to avoid radicals when possible). The only simplification that can happen is in the particular case of an object at rest, where p=0, giving E^2 = 0 + m^2 * c^4 = m^2 * c^4, thus E = mc^2.
I have... no honest idea how you came up with E = pm^3, either. I've never seen any common math mistake (like the Freshman's Dream, (a + b)^2 = a^2 + b^2, which is incorrect) that could result in that.
The square root would counteract P^2, M^2, and C^2, turning them into P, M, and C. However, the C is added to the other C under the square root radical, Which is transformed into C^2, to make C^3. I guess this makes P+M C^3 (Space indicates multiplication, so they arent done as a group)But It's still close to what I said earlier.
71 comments:
what would i do if i was last
I'm so confused...
1st comic: D'awwww
2nc comic: lol
FIRST
Ugh, I like the at rest one better.
My eyes, my EYES!
I get to take stuff like that soon.
so for the second comic, E=PC+MC^2?
I dont get it
that is a terrible drawing of derpy and i should know she's my mailpony
That's... That's not trolling. That's just mean.
...kitty?
Seen the first one before. Second one would be better if Derpy didn't look so fat. Why use perfect vector art for Trixie but not for Derpy? All you would need to do is add the hat.
D'awww looks like Luna's going to end up with another fannon nickname.
Wow Trixie, the lengths you go...
@Anonymous
U R DOING IT WRONG!
Silly Trixie, there's no P in E=MC2 !
1st comic: SO sweet! X3
2nd comic: lacking some Troll-Face :P
^2 = (m0^2 * c^4) + (p^2 * c^2)
#1: D'awwww
/)^3^(\
#2: Problem, Trixie haters?
For the second comic: http://en.wikipedia.org/wiki/Four-vector#E2_.3D_p2c2_.2B_m2c4
@Anonymous
Math FAIL. :P
@Anonymous
While I'm no physics major, P stands for momentum which is a product of mass and velocity (P=M*c). Factor out c and you get
E=c*(P^2+(M*c)^2)^0.5
Simplify more and E = c*(P^2+P^2)^0.5 = c*(2*P^2)^0.5 = c*P*(2)^0.5
I don't understand how the root two is taken care of in Trixie's equation, or am I missing something? She should have divided everything by 2^0.5
Well played Trixie.
May I suggest the honorary name: "The Great and Powerful Trollxie"?
No? I'm gonna do it anyway.
Wait, how is derpy holding the chalk?
The best thing about that second comic is that its actually somewhat true (Physically speaking)
Oh, so THAT was why I hated Trixie so much. *Hugs Derpy* Have a muffin :D
@GabuEx
Why dont you try doing this shit then. and maybe actually explain the comic rather then throwing out retarded insults
Kitty?
@Anonymous
http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
Under "Applicability of the strict mass–energy equivalence formula, E = mc²"
The equation takes care of system where said mass is "moving" (hence the P - momentum term).
The classic E=mc^2 hold true if E is just the rest energy of the system (nothing is moving).
The E in E = sqrt((mc^2)^2+(pc)^2) is the total energy of the system.
E = mc^2
E is energy, m is mass, c is the speed of light
Well that can be rearranged to m = E/c^2
Using the relativistic mass formula:
m = mr/((1-(v^2/c^2))^0.5) ........mr is rest mass and v is relative velocity
We can substitute the above reconfiguration of the energy formula to get:
E/c^2 = mr/((1-(v^2/c^2))^0.5)
Now we square the equation:
E^2/c^4 = mr^2/(1-(v^2/c^2))
We rearrange this equation to:
E^2(1-(v^2/c^2)) = mr^2c^4
Multiply the E^2 through the parenthesis and manipulate:
E^2-(E^2v^2/c^2) = mr^2c^4
Substitute in E^2 = m^2c^4 into the second E^2 to get:
E^2-(m^2c^4v^2/c^2 = mr^2c^4
The c^2 on the bottom cancels out:
E^2-(m^2v^2c^2) = mr^2c^4
Because mv = p (which is momentum), then m^2v^2 = p^2 and:
E^2-(p^2c^2) = mr^2c^4
More rearrangement yields:
E^2 = (pc)^2 + mr^2c^4
A little more manipulation yields Trixie's equation:
E = (p^2c^2 + mr^2c^4)^0.5
From this, we can see that even stationary objects with mass mr will have energy dependent on a factor of c^4, and when the object moves and thus gains a momentum p then it will increase in energy. This also hints at the fact that objects in relative motion have a greater observed mass. Ponies.
Trixie is a smart-ass >.>
If only that was Java instead of physics...
@Anonymous
Chill, dude, it was just a little gentle ribbing.
E^2 = p^2 c^2 + m^2 c^4 is the generalized form of E = mc^2 for an object in motion. The "math fail" comment was just in regards to the fact that sqrt(a^2 + b^2) is not equal to a + b; exponents are not distributable across addition and subtraction operations.
I don't get that second one, what is going on in it?
@Ddude28
Trixie's equation is a more specialized version of the energy-mass equivalence (or something)
see Sedaheht
....So how is it insulting Derpy?
I wonder what Twilight could pull out of her metaphorical hat if she had a shot at the blackboard...
@Anonymous
Trixie's is for moving particles, Derpy's is for stationary particles (I think). Therefore, Trixie's is more useful in real-life situations. Or something
Looking at the second comic, I cant help but think "DAMN! I wish MY chalk had different fonts and sizes!"
@Kill me, I'm a PONY
Derpy's equation is for particles at rest only, correct, but Trixie's equation accounts for particles in any state of motion, rest included.
At rest, momentum would be 0, meaning p^2c^2 = 0, making the equation just E = sqrt(0 + m^2c^4), or E = sqrt(m^2c^4), or just plain old E = mc^2 once again. Trixie's math is more great and powerful.
@Sedaheht
+5 internets for explaining the formula and a bonus +1 internet for putting the gratuitous "Ponies" at the end.
Finally, hard evidence of why Trixie should be liked by no one!
...Well, besides everything else we've ever seen Trixie do.
I have officially learned more physics from ponies than I have from anything else. I should probably start me some college... NAH. I'll just watch more ponies.
@Sedaheht
Bravo, very well put.
The only thing I'd add is just the interesting tidbit that the equation Trixie wrote is commonly used in high energy physics, such as in linear accelerators like the LHC, because both energy and momentum are conserved in the interactions and involve relativistic speeds.
lol That first comic is too funny and cute. But it does have Luna. And even without socks, that bumps its cuteness up. :)
And darnit Trixie you showoff.
It should be E^2 in Trixie's panel.
To many comments to read, hopefully some other ponies caught that too.
Luna and Celestia at their finest!
@Aecratis
Cool, didn't know that. I wonder what Trixie is planning on doing with her knowledge of high energy phenomenon...
Also, the LHC isn't a linear accelerator. I think it's called a synchrotron. There's actually a series of four rings, three to inject/prepare the particles for the main ring, and then the main ring ultimately instigates the particle collisions with all the detectors equipped.
...I think. <_<
>mfw Big Macintosh breaks out the tensors and goes general relativity on that flank
@Sedaheht
You, my good sir, win the internet tonight. And a cookie.
To repeat what I said as a comment on the second picture on dA, quantum mechanics. Problem, relativity?
@Sedaheht but if you're taking the square root of E^2, shouldn't you add a +/- to the equation.
Nevermind. I see that the original constraints of the problem are all positive and E, M, or c^2 could never be negitive so you don't have to worry about negative values. Derp!
Don't you use your fancy mathmetics ì_Ã
I aww'd so much that I actually Daww'd on #1
@Sedaheht
Ah, sorry, I always forget that it's not technically a "linear" accelerator. Good thing I'm not really thinking of going into HEP.
But yeah, it uses one linacc and two synchotrons successively to increase the beam energy. The large ring is primarily for beam storage, focusing and detection.
Celestia, you know she's not a cat, right?
Kitty? for Luna?!...well i guess she needs a caress name too just like ''Tia'' or ''Celly'' hmm...kitty...that reminds me, most of the ponies when sitting on their butts, do indeed look like cats while in that posture
The first comic is so adorable!
My brain hurts @_@
I'm only a 14 year old!
And I have to know this in high school?
OOOOOOOOOW
@Swweet
not sure if serious but....if you are, you don't need to know that in high school, dont worry.
First comic is full of d'awwwww. Trixie ypu crazy science troll.
My little trolling : winning is magic !
@Sedaheht
This.
@Everyone else
I made the second panel and just found the first panel, thus did not draw Derpy. It is explained on my DA site.
Trixie's equation is correct for total energy but Derpy's equation is correct for rest energy
math is fun
Fibonacci sequence!
>not related to anything, I just like that sequence.
@Sedaheht
I am now smarter. Thank you sir.
so, am i the only one that understood the second equation like this:
E=PC+mc^2
where PC = Princess Celestia
?
@La Barata Derpy's response: http://s1098.photobucket.com/albums/g375/skomikbewm/?action=view¤t=DERPFINAL.jpg
My Physics teacher used to troll me like that
<.<
>.>
...I hated her.
@Anonymous
Long answer long = http://en.wikipedia.org/wiki/Special_relativity
Long answer short = special relativity.
Uh, Trixie, you do realize that you just said E=P M C^3.
Haven't you studied logarithms?
(9^62773 + 2)^83721= 83721 x log (9^62773 + 2)
log (9^62773 + 2) = log (9^62773) +log ( 2)
log (9^62773 + 2) = 62773 log (9) + log ( 2)
log (9^62773 + 2) = 62773 (0.954242509) + ( 0.301029996)
log (9^62773 + 2) = 59900.966
So:
83721 x log (9^62773 + 2)= (83721)(59900.966)
83721 x log (9^62773 + 2) =5.01496877 × 10^9
Digital sum is
5 + 0+ 1+4+9+6+8+7+7= 47
4+7=11
1+1=2
Problem, Trixie?
@Anonymous, That's not how math works.
We have E^2 = p^2 * c^2 + m^2 * c^4, which is unsimplifiable (and mathematicians and physicists tend to avoid radicals when possible). The only simplification that can happen is in the particular case of an object at rest, where p=0, giving E^2 = 0 + m^2 * c^4 = m^2 * c^4, thus E = mc^2.
I have... no honest idea how you came up with E = pm^3, either. I've never seen any common math mistake (like the Freshman's Dream, (a + b)^2 = a^2 + b^2, which is incorrect) that could result in that.
The square root would counteract P^2, M^2, and C^2, turning them into P, M, and C. However, the C is added to the other C under the square root radical, Which is transformed into C^2, to make C^3. I guess this makes P+M C^3 (Space indicates multiplication, so they arent done as a group)But It's still close to what I said earlier.
So cute and adorabl---- I mean grrrr... Monster trucks and guns grr.. Aww did she just hugged her? AWWWWWWWWWWWWWWWWWWWW xD
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