Force following same rules as vectors

[xailer]

hiya

I understand vectors perfectly, but still something is bothering me when it comes to forces being represented as vectors

We'd compute the x component of force F with F*cos(alpha), alpha being angle force has with x axis.

Promblem I have with this is why does force follow the same rules vectors do? Meaning if same force has smaller angle with x-axis then x component of force will be greater. Why, unlike vectors, couldn't x-axis be smaller or follow some completely different set of rules?

thank you

 

[alias25]

wel yea if u think about it, cos of a smaller angle is a bigger number than cos of a bigger angle (0< angle< 90) then multiplied by the force ull still have a bigger number for a smaller angle. my proffesional opinion (ie i think this is the case)
force is a vector because F = ma where acceleration is a vector. i guess in a way vectors are equivilant to negitive numbers if u multiply a negitive with a positive u get a negitive (like here mass is scalar and acceleration is vector)
and if u multiply a neg with neg u get positive like P = FV where force and velocity are vectors giving u power which is scalar.

 

[arildno]

hiya

I understand vectors perfectly, but still something is bothering me when it comes to forces being represented as vectors

We'd compute the x component of force F with F*cos(alpha), alpha being angle force has with x axis.

Promblem I have with this is why does force follow the same rules vectors do? Meaning if same force has smaller angle with x-axis then x component of force will be greater. Why, unlike vectors, couldn't x-axis be smaller or follow some completely different set of rules?

thank you

That the resultant (or net) force can be calculated by modelling forces as vectors may be seen as "axiomatic" in the mathematical model we use in order to describe physics.

Whether our mathematical model is "good" or "bad", that is,. for example, that testable predictions following from our model will be confirmed by experience or not, can only be resolved by experiment.

Innumerable experiments bear out that the vector modelling of some sort is, indeed, a very good modelling of forces.

 

[xailer]

Whether our mathematical model is "good" or "bad", that is,. for example, that testable predictions following from our model will be confirmed by experience or not, can only be resolved by experiment.

Innumerable experiments bear out that the vector modelling of some sort is, indeed, a very good modelling of forces.

I had an impression that using vectors for net force was something immediatelly obvious and a common sense for most of you people. So basically vectors are just a means to an end until someone finds other, more precise way of finding components of the force ?

 

[HallsofIvy]

Quite simply, forces follow the same "rules" as vectors because force are vectors! That's the way "force" is defined! Since a force in a given direction causes a different acceleration that a force of equal strength in a different direction, it's impossible that a force not be a vector!

 

[Dorothy Weglend]

hiya
Promblem I have with this is why does force follow the same rules vectors do? Meaning if same force has smaller angle with x-axis then x component of force will be greater. Why, unlike vectors, couldn't x-axis be smaller or follow some completely different set of rules?

Why does a falling mass in a vacuum accelerate in time proportional to t? Why does Newton's Law of Universal gravitation 'work'? These are all 'why' questions, and the answer to them all is: "we don't know". All we know is that the equations reflect a physical reality which we have determined experimentally.

The same thing is true of your questions about forces and vectors. Vectors are used to model forces because the experimental evidence tells us that forces work in this way. Perhaps some day a force will be found which follows a completely different set of rules. Then a new model will have to be found to fit the experimental data for that force. Vectors wouldn't be used, in a case like that.

Dot

 

[lightgrav]

It's not quite so hazy as Dorothy presents it ...
we know "why" for about 2 "layers deeper".

Whenever we eventually find some inteaction
that doesn't behave like a Force, we call it
something else (for example, a "pseudo-vector").

Alias25 was saying that, since location "defines" vector
then Location, displacement, velocity, boost, acceleration
are all vectors also (unless time is not a scalar).

Momentum, impulse, Force are all the same kind;
they will be vectors (unless mass is not a scalar).
That's why you did a lab with Forces on a circular table,
to convince yourself that Forces add like vectors.