Understanding superposition of forces and its consequences

1. May 21, 2012

aaaa202

This isn't really a single question, but rather a series of speculations, where you can hopefully help me understand some of the things.

Soo.. Classical mechanics are, at least on basic level, based on the euclidean geometry, which allows you to add forces as vectors. Often this means that we can solve a problem that involves forces by inserting a proper coordinate frame and breaking the forces into their horizontal and vertical components.
Now, this is something that I have more or less accepted to be a truth in nature, although I do know that in relavistic mechanics space is not euclidean, but let's forget about that for now.

What I want to ask about, is some of the consequences of force superposition that always makes me speculate and that I never have a proper answer to. On the picture attached, I have drawn a pendulum bob connected to the wall by a string. In class one learns how to break the weight of the pendulum into a force that pull along the string, and into a force that pulls perpendicular to the string. By doing so you can show that the force is approximately proportional to the amplitude for small angles etc.

I just want to ask why you know that this is the correct way to break down the force. How does the weight of the pendulum "know" that it must pull along the string? For me this can't just be a consequence of the postulate that space is euclidean. Can someone explain what happens on microscopic level that supports, that you actually can break the force into those components and not just any two components?

2. May 21, 2012

tiny-tim

hi aaaa202!

are you simply asking why we can break forces, and force equations, into their x and y (and z) components?

then yes, it is because space is locally euclidean, ie a linear vector space

(even complicated spaces have a euclidean tangent space at any point, and so are still locally euclidean)

force is defined as a vector, and for two forces (or sums of forces) to be equal, their components must be equal, in any direction …

so long as vectors can be defined (eg in a tangent space), this works by definition

3. May 21, 2012

aaaa202

hmm well, I was more asking for: Why is it that the force on the pendulum bob MUST be broken into the components I have drawn for the physics to make sense.

Of course it is rather lunatic to propose any other components due to your everyday experience. Yet it is just weird for me that the pendulum bob somehow "knows" that it must pull along the string. If you think about it:
In reality it is only pushing the string directly down, so why would it choose to pull on the string like that rather than any other weird way. I could understand if there existed some kind of principle that said that a force will always act towards causing a reaction (in this case from the string).

Okay, this is in some way just gibberish from my mind, and your answer will probably not have changed, so I will just anyways have to accept that.

By the way: Thanks for all the help you give me - you are by far the #1 helper on here imo :)

4. May 21, 2012

tiny-tim

it has no idea the string is there, except that it receives a pull from the string

the make-up of the string determines the direction of that pull
there is … it's good ol' newton's third law … the bob only exerts a force equal and opposite to the force on it, and since that has to be along the string, that's the line along which the bob exerts its force too

5. May 22, 2012

azizlwl

The pendulum bob knows that 2 forces acting on it, the earth and the string.
The string just can apply centripetal force and the earth down.
If both strong enough the bob will break apart.

Since both forces do not cancel each other, there's resultant force.

The job now is to substitute these 2 forces to other quantities for easier calculation.
Now we have different environment where FBD rules. No gravity.

6. May 22, 2012

Zubeen

What actually happens is ,
after studying Newton's laws of motion, they become so much synchronized and correct with the world that we can see, that any thing( regarding motions ) can be answered using these laws.
and now we are so much used to it that we can apply it to any condition, without knowing any thing, but since we are applying it using Newton's laws, they must be correct and should be exactly what is happening, because newtons laws can't be violated (conditions apply ).
that is the case what we do in the pendulum picture.
we know that gravity is pulling the bob with some force, but since the bob doesn't gets down so there must be another force in opposite direction equating with the weight of the bob ( as per Newton's laws of motion ). Which can only be provided by the string.
but since the bob accelerates perpendicular to the string, there should be force in that direction too, witch is a component of the force by string.
So here everything is about newtons law, by applying them, you can the way in which force should be split up.
Zubeen