/sci/ - Science & Math

Vectors, OP.

maybe you should pick up a book that starts with treating forces as the vectors they are.
all of that trigonometry stuff only appears because you treat forces as scalars

>Two forces F1 and F2 going in opposite directions, apparently they >can be expressed as a resultant force F1 - F2.
>Here's the kicker...
>Why?

Let's say F1 is 10N and F2 is 5N

Using the equation for resultant force in question, F1 - F2 that would be 5 - 10 = -5 (N).

Now look at the second example in your image, it's the same, thus you can express resultant force as Force 1 - Force 2. If you keep F1 as left, F2 as right then a positive number means moving to the left, and a negative number is moving to the right.

Obscure reasoning probably, but then I don't see how you're stuck on F1 - F2 = RF

>>2737875
I have used forces as vectors too, I still don't understand why they obey geometric rules.

Is it because you can see using dimensional analysis that the Newton.
[N] = ML/T^2
so 1N sends 1kg mass 1m in 1 second
So they are related to length..
hmm, maybe I answered my own question.
That's correct yeah?

>>2737900

At our level, you should really refer 1N as 0.98kg not 1kg.

>Why do the mechanic laws scientists have invented in order to describe how the universe work actually describe how the universe work?
Because scientists are clever

>>2737909
What?
I was not referring to gravity, just the basic definition of a Newton.

>How does mechanics work?
>I am studying it at the moment, but the more I think about it the less I feel I understand.
>I am studying it at the moment,
>studying it at the moment
>at the moment
>the moment
>moment

>>2737939
lol'd

>>2737845
think about the vectors being in a coordinate system, any 2-dimensional vector can now be described by giving the x-axis and y-axis values. so basically they all become triangels, the force vector being the hypotenusa(sp) from where you can count the values of the other sides(?) of the triangle

sorry english is my 4th language :)

What you are asking about is the principle of superposition and was probably first written down by Newton (3rd law).

It has to do with linearity and of course has its boundaries.

In your example, this little block or whatever the hell it is, is probably rigid enough not to deform under the forces that are acting on it - hence the superposition of the forces

a) make sense
b) make this problem easy to solve

It is also an important feature, since it keeps the forces acting on your "items" linear, and we all know, linear problems are much easier to handle.

The trigonometry part is founded on this too, simply because if you are able to apply the superposition principle on your system, you can just decompose every force into smaller parts, which in sum give you the total force. The rest is geometry.

>>2737939

>>2737900
No, it accelerates a 1kg mass to 1metre per second in 1 second.

F = 1N
m = 1kg
a = 1ms^-2
u = 0
t = 1

v = u + at
= 1ms^-1

it displaces it by 0.5m

s = ut + 1/2 * a * t^2
= 0 + 1/2 * 1 * 1
= 0.5m

>>2737939

>>2737845
Think about this way op.
If we understood how stuff worked without mathematics, we wouldnt need mathematics.
Math is just a tool to understand the world, and it freaking works, even if you dont understand it.

We find it to be the true by experiment.
Pic semirelated.

>>2737845
Just shut up and calculate

>>2737980
I do understand the mathematics, I just don't understand why it can be applied to this situation.

Sure it works, but why does it work?
Why don't two parallel forces combine and cause a perpendicular force, or a force at 30 degrees to the horizontal?

Perhaps it's an unanswerable question, just the way the world is?

DISREGARD MECHANICS

ACQUIRE ELECTRICITY AND MAGNETISM

ok, now u are just trolling

>>2737997
Why you say?
This is why:
http://www.youtube.com/watch?v=wMFPe-DwULM

>>2738002
Fucking Feynman. I could listen to that man for ages and not get tired.

>>2737997
If two parallel forces had combined in a perpendicular force, you would have been taught it along with the equations enabling to predict how.
If it weren't possible to predict how the universe work logically, then evolution wouldn't have given us a brain to do logic.

>>2738053
I suppose as someone who usually studies pure matheamtics I got a bit lost in the "why", expecting a satisfying explanation, but now I understand why I wont get one.

Just gonna have to learn to take some things for granted I guess.

Forces are the mathematical representation of certain behaviours in nature. They are not `real`, natural, or intuitive. They obey the mathematical fundamentals, and you shouldn't be surprised.

Next up: electrons don't exist as objects in nature, but are the mathematical representation of electrical force

>>2738082
>why do things happen the way they do
Because they do, dude. It's as simple as that.

>Next up: electrons don't exist as objects in nature

Oh yes they do.

>>2738082
Newton discovered it. Forces seem to act linearly. Therefore we can use superposition to calculate the sum of all forces and treat it as one.
Experiments show that it is right.

There isn't a "higher" explanation to it, and if there is, I haven't heard it yet.

i'm sometimes doubtful about the basic concepts of physics too op, but here's my take:
physics uses arbitrary quantities like forces, work, energy, momentum... they are not things that EXIST, but they are quantities that help making calculations.
A force is, BY DEFINITION mass X acceleration.
Where acceleration is the derivative of speed.
Therefore, taking out the mass that is constant, a force is just related to speed, and it's easy to understand that speeds sum themselves as in OP's pic.

Newton's laws are the result of experimentation, not mathematical derivation. It's inductive, not deductive.

>>2738271

I have a question then: If all of these laws are inductive, how do we get around the problem of induction? Is there a way to do that, or are we taking empirical laws on faith?

>>2737997
>>Perhaps it's an unanswerable question, just the way the world is?

It's not unanswerable: It's just the way nature works.

You could also ask "why do photons exist?", which would yield the same answer.

>>2738424
It's not "on faith". It's empirical, just as you said. So far, nobody has found a way to mathematically deduce the rules of motion. They're called laws and all, but scientists know that they aren't perfect.

>>2738424
>how do you get around the problem of induction
you can't. you can vindicate it, justify it, make up definitions of 'random' or 'probable', but there is no way to prove it.

Because forces act in the same way as lengths, it's just the way shit is.

I can think abstractly about a universe with completely different laws of physics and mathematics, or a universe without what we consider "physical laws" that is just bizarre and chaotic but it's all in my imagination and has little practical usage concerning questions like "why does existence occur" and all that.