|
Ok, this is not about an experiment that was cool or some experiment where our prof did something great. This is about a theory me and my partner managed to proof because of some craziness we did.
So, we did an experiment on pendulums and blah blah where the Period (T) is given by the equation:
T = 2 pi; sqrt(L/g), where L is the length of the string and g is the gravitational constant.
So we calculated stuff and the like, and we were asked to graph length (it started from 100 cm and ended at 20 cm) vs period and we got a curve. Then our prof asked us to get the graph of T^2 = (4) (pi) (L/g) and we got a line with the equation T^2 = 4.003x where x was our length.
Then there was a guide question asking us the importance of the slope, then we did some calculations and got....
So starting from our equation:
T^2 = 4.003L (since x is L)
then consider this: (pi^2) / g is very near 1.
so we can get:
T^2 = (4) (rounding 4.003 off) (L) (pi^2) / g
T^2 = (4)(pi^2) (L/g)
then getting the square root:
T = 2 (pi) sqrt (L/g)
we managed to get the theory by multiplying our equation by (pi^2)/g which is very near 1. I showed our solution and our friends were hyped up the madness we did. Hahaha. To some degree this solution is correct, right?
|
|
|
|
|
|
|
this is so Japanese to meh
|
|
|
Equation for... Yamato Cannon?
|
This happened in our class too, it's just a fluke 
|
I don't understand anything, I feel dumb knowing nothing about physics and mathematics. I make up for it in knowledge in history, religion and philosophy but it feels like there is no future in that.
|
Germany2896 Posts
No idea what you are doing. The formula T=2*pi*sqrt(L/g) is obvious from the linear differential equation describing the problem for small angles.
(pi^2)/g which is very near 1
It is not even the same dimension as 1. So wtf???
|
|
|
I don't want to brag but I understood that lol
|
is this the ion cannon equation?
|
On February 18 2009 23:00 MasterOfChaos wrote:
No idea what you are doing. The formula T=2*pi*sqrt(L/g) is obvious from the linear differential
equation describing the problem for small angles.
It´s not bad to get it out of an experiment.
To SkyLark: nice work, some comments:
Think about it, if pi^2 would not be nearly equal to g, you could still add in a factor to make it equal. You can always multiply by one. What you did here was an approximation (pi^2 ~= g, 4.003~=4). So in a way your approach was correct and it obviously must lead to the right conclusion. (though you are a bit "lucky" that the errors in both of your approximations cancel each other out)
On the other hand, you could take the formula T=2*pi*sqrt(L/g) as given and actually measure g at your location from the slope (4.003 or whatever) of your curve. As you have seen, it´s very close to pi^2 though.
edit: haha you DID get that slope from experiment, didn´t you? Otherwise what you did is circular reasoning ^^
|
i believe the way T = 2pi sqrt l/g was originally derived was by assuming that sin x = x, x being the angle, which was small. your way works too though. i think you can approximate g/pi^2 = 1, especially if you're near sea level.
|
That's totally not how you are supposed to do it if you were doing a serious experiment, but whatever. The point of any experiment is to verify a theory. So basically you take the T = 2 pi; sqrt(L/g) as a given. Then you try to figure out the value of "g" from the slope you got. Compare the value of gravity to the actual value of gravity and see if it matches up within the possible error. If it matches up, then your experiment supports the theory. If it doesn't match, then the theory is wrong or you need to explain some experimental error.
I don't know what level of class you are taking so it might not matter at all.
|
and then?i don't understand the hype...
|
United States24776 Posts
People laugh but figuring stuff out in that kind of environment can be exciting. I've had moments like that before.
|
|
|
17066 Posts
CRAZINESS!!
+ Show Spoiler +(and to be honest, I love having those moments...nothing as cool as yours though :D...mainly we just messed around with the lab set ups and left an hour early. I wish we could've independently "derived" some equations like you did haha)
|
sqrt ==> squirt <.< >.> ^^
|
On February 18 2009 23:44 Maenander wrote:Show nested quote +On February 18 2009 23:00 MasterOfChaos wrote:
No idea what you are doing. The formula T=2*pi*sqrt(L/g) is obvious from the linear differential
equation describing the problem for small angles. It´s not bad to get it out of an experiment. To SkyLark: nice work, some comments: Think about it, if pi^2 would not be nearly equal to g, you could still add in a factor to make it equal. You can always multiply by one. What you did here was an approximation (pi^2 ~= g, 4.003~=4). So in a way your approach was correct and it obviously must lead to the right conclusion. (though you are a bit "lucky" that the errors in both of your approximations cancel each other out) On the other hand, you could take the formula T=2*pi*sqrt(L/g) as given and actually measure g at your location from the slope (4.003 or whatever) of your curve. As you have seen, it´s very close to pi^2 though. edit: haha you DID get that slope from experiment, didn´t you? Otherwise what you did is circular reasoning ^^
yeah the slop was from the experiment itself..:D
|
|
|
|
|
|
EPT![[image loading]](http://img24.imageshack.us/img24/1649/poster73587195bv6.jpg)
