Force, accleration vectors or not

[alkaspeltzar]

Your right, I can do the problems. I know what a force is, how vectors have both magnitude and direction, and I know that we can break them down via rectangular components in math to make working with them easier. In the end, that is right, it works and follows the book, and I get my answers.

I know I get hung up on things, I guess it is just important that I know how to do it properly. I am not trying to be a physicist, but I would still like the understanding.

thanks for all the help again. Your patience has helped put my mind at ease

 

[alkaspeltzar]

Which is why I said those representations are equivalent.


Bx, etc., are just numbers and thus scalars. Of course, the unit vector is implied.

Doc Al, then why don't we call Bx, By etc in these examples vectors? Aren't they kinda representing them, so at the end of the day, what is the difference?

I guess one thing i am misunderstanding is how we break down vectors into their component notation, in terms of Fx and Fy, which is the scalar components. This is an equal representation of a vector, but if Fx already implies a direction by having "sub x", i don't see the distinction.

 

[alkaspeltzar]

Take a look at the scan out of my book. IT talks about the Scalar components and Vector components.

I understand we break the force into 2 vector components, then for the sake of the alegbra work with the scalar components. But when i look at a scalar componenet, say Fx =-500N, to me that means backwards in the X direction 500 Newtons, so how is that different from the vector Fx=-500Ni?

 

[CWatters]

Sorry to butt in but...

many times for the sake of ease we use component notation, breaking it down into the Fx and Fy components. This many times is done using the equation Fx=Fcostheta and Fy=Fsintheta. It is helpful because now we can use regular algebra since Fx and Fy are scalars.

Fx and Fy are still vectors.

The reason for spliting the original vector into components Fx and Fy is usually because you already have other vectors with components acting in the directions x and y. That allows you to take advantage of the fact that two vectors pointing in the same direction can easily be added together. The same applies to vectors that are the components of other vectors.

For example suppose you have numerous forces acting in random directions on a body. One way to work out the total force is to convert all the vectors to their components in some co-ordinate system (it could be x,y,z or some problem specific system, whatever is most convenient). Then add all the components and convert the result back to whatever form is required.

Just because the components are in the x,y,z directions doesn't make them scalars but it might allow them to be added as if they were scalars.

In some problems this process is best done in two or more stages. eg some vectors are broken down into components in say the i,j,k co-ordinate system and added together. The result is then converted to components in the x,y,z coordinate system where the components of other vectors are added. The result might need to be converted to a third co-ordinate system depending on what the problem requires.

 

[Doc Al]

Take a look at the scan out of my book. IT talks about the Scalar components and Vector components.

I understand we break the force into 2 vector components, then for the sake of the alegbra work with the scalar components. But when i look at a scalar componenet, say Fx =-500N, to me that means backwards in the X direction 500 Newtons, so how is that different from the vector Fx=-500Ni?

I agree with your book. I'd call Fx a scalar, as it's just a number; the vector form would be Fx i. But that's just a technicality. Of course we are talking about representing vectors using their components. (By writing Fx in bold, as Fx, you are merely creating your own vector notation. Thus Fx = Fx i.)

Scalar: 500N
Vector: 500N i

I really think you are making a big deal out of a triviality. Who really cares whether you call Fx a scalar or a vector, as long as you know how to represent a vector in terms of its components and perform all needed operations correctly.

 

[alkaspeltzar]

I don't think i am making a big deal. I keep reading and hearing components are vector then scalars, which is it? I know there are vector componenents and scalar components.


There reason i ask if the scalar components are scalars, is because they ahve both direction referenced thru the "sub x" and are positive or negative...example Fx=-20N, seems to be little difference between it and the vector Fxi, which is -20Ni.

Finally, i have read from multiple sources your can represent a vector thru scalar notation, is that true?

 

[sophiecentaur]

I don't think i am making a big deal. I keep reading and hearing components are vector then scalars, which is it? I know there are vector componenents and scalar components.


There reason i ask if the scalar components are scalars, is because they ahve both direction referenced thru the "sub x" and are positive or negative...example Fx=-20N, seems to be little difference between it and the vector Fxi, which is -20Ni.

Finally, i have read from multiple sources your can represent a vector thru scalar notation, is that true?

It seems to me that you are doing just that, actually.
It is a matter of definition that vectors are specified in terms of Magnitude and direction. The number of Newtons is the Magnitude and i is the direction of a force along the x axis. The use of unit vectors makes life easier in many instances (if you don't use them, you need to use Polar Co ordinates if you want to do actual calculations, for instance - how would you feel about that, in 3D?) so why don't you want to go along with it. If you define and stick to the notation used, there is no confusion and there is no conflict. You don't actually ever have to use unit vectors but you then need to have arrows / lines above / below your symbol - plus Bold type as well.
btw, I find your keyboard use a bit erratic and that's as difficult to cope with as when as people use unit vectors and you seem to be complaining about 'sloppy thinking'.

 

[Chestermiller]

I kinda agree with some of the others that you seem to be becoming obsessed with this and seem to be over-analyzing it. Numerous experts have indicated that it is important to use vector notation as well as resolving things into component form. My suggestion is that you tentatively accept what they are saying and move on. Continue to do problems both ways, and continue getting practice in solving problems until, maybe, you get a better idea of what they are driving at. If not, you can always stop using the vector approach, and continue exclusively with the component approach. But I don't think this will happen. I think that eventually you will realize the power of the vector approach.

Chet

 

[alkaspeltzar]

Thanks, i am sorry for the keyboard, sometimes it comes from my phone.

I know there is vector and components/scalar form, and i should understand both. I was simply trying to understand the differences and why we do/represent one versus another. I understand how to deal with vectors as vectors, but i also understand how to work/represent vectors in scalar notation. I guess that is all that matters for problem solving. Thanks for the help. I will take what i have learned and do it.