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Force, accleration vectors or not

  1. May 18, 2013 #1
    Taking highschool physics, i have learned that force and acceleration are vectors. But i have noticed prior to this, we have never worried about them as such. Most of the problems simply treat them like any other measurment or value, ignoring direction. Almost like scalars.

    So my question is, can we do this since for most problems it is just simpler and until we have more complexity with varying directions, we just work with force as purely 20lbs, 200 newtons, ignoring the direction? Same with acceleration, we talk about it simply a some number of meter/second squared. Even the book will write its answers as"the force is 22.5lbs"...no direction.

    Do people many times use the words force and acceleration as synomymous with the force or acceleration magnitude? Proabaly just the way it is

    Thanks
     
    Last edited: May 18, 2013
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  3. May 18, 2013 #2

    Doc Al

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    Sometimes it just doesn't matter. Sometimes the direction is obvious. Sometimes all you need is the magnitude.
     
  4. May 18, 2013 #3
    When the direction of the velocity vector is changing along the trajectory, this translates into a component of acceleration (and net force) in the direction perpendicular to the velocity vector. The acceleration vector is equal to the rate of change of velocity vector along the trajectory. This is when it is important to include the directions of the vectors in the physical analysis.
     
  5. May 19, 2013 #4

    CWatters

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    Most of the time you will need to treat them as vectors.

    Relatively simple problems such as those involving balls thrown vertically upwards involve vectors but you may not have realised it - for example the initial velocity is in one direction (upwards) and the acceleration is acting in the oposite direction (downwards). You may not have realised that by assigning up or down as positive you are treating them as vectors.
     
  6. May 19, 2013 #5

    CWatters

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    Sometimes the direction is implied, for example gravity usually (but not allways) acts downwards. Best get into the habit of specifying the direction with your answers when possible.
     
  7. May 19, 2013 #6
    Okay CWatters, tell me if i have this right.

    Acceleration and force strictly speaking are vector quantities, but many times since direction is implied or not important, we just simply work with them generally. This is why we often talk about the magnitude of force as a force, likewise with acceleration right?

    But at the end of the day, we should try to include direction to be proper?

    Would you agree?
     
  8. May 19, 2013 #7
    It's much more than that. Consider the following:
    Suppose you have a particle continually moving around the circumference of a circle at a constant speed. The particle keeps orbiting the center of the circle for all time. Here are some questions:

    Is the particle accelerating? If you decide that the particle is accelerating, what is the direction of its acceleration vector?

    Do you now see why it is important to include the directions of the velocity vector and the acceleration vector in your analysis?
     
  9. May 19, 2013 #8
    I get it is more than that. I am just wondering if my reasoning is correct as to why my text book simplfies force and acceleration. That is all i am asking.

    I agree, they should include direction but some many times my book leaves it as vague/understood.
     
  10. May 19, 2013 #9
    Maybe your book isn't so hot, or maybe it's geared for the most elementary level. Is this a freshman physics course, or is it high school level? If it is freshman level, it should more clearly explain why including the directions of vectors is important, and present ample examples and problems to emphasize this.

    Chet
     
  11. May 19, 2013 #10

    Doc Al

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    What might prove helpful to you is for you to post a few problems from your book (in the Intro Physics HW section, not here) along with your solutions. (Obviously, choose ones where you think there's an issue.) Then we can comment on why or why not the direction of the force was needed. (Sometimes, even when the direction is needed to solve the problem, all they ask for is the magnitude.)
     
  12. May 20, 2013 #11

    CWatters

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    No. I would say most of the time you have to treat them as vectors. For example it's very common for velocity and acceleration to act in different directions.

    I agree it would be interesting to see an example from your book. If you post it into the Intro Physics Homework section please post a link to it here.
     
  13. May 20, 2013 #12
    That's why forces are described in systems like Cartesian coordinates.
     
  14. May 20, 2013 #13
    Examples from the Book

    Okay, I have attached examples from the book. I know how to get to the answers, that is not what I want to know.

    What is want to know is this:
    1. In example 4.7, they begin by talking about the forces in the problems, as you see in bold letters with arrows denoting vector quantities. But as they progress, they simply look at the x and y components, which are magnitudes. They start talking about Ax as acceleration, but as far as I can tell, that is really only the magnitude of the acceleration in the x direction, so why do they call it acceleration?

    2. In example 4.4, they just simply talk about acceleration and force without direction..why?

    So those are my question. Why do they sometimes leave out directions as in ex. 4.4? And is it normal when breaking down the vectors, looking only at the components/magnitudes, to refer to them and call them Force, or tension.

    Please review my example and read the remarks below. I guess I get confused because if it force is a vector, they should talk about it as one all the time and sometimes it isn't.

    Thanks
     

    Attached Files:

  15. May 20, 2013 #14
    Here is another example, 4-2. They define the force vector at the beginning as F=Fxi, where Fx is the magnitude.

    But then step #3 asks use to find the force(Fx). I agree that forces really should be described with both their strength/magnitude and direction, but many times we generally refer to the magnitude as just "force" too. At least that is what this book is doing?

    Is this just an English shortcut the book is using that is confusing me? Maybe that is all it is, fudging the words..

    Thanks for all the help. I appreciate the conversation.
     

    Attached Files:

  16. May 20, 2013 #15

    sophiecentaur

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    But Fx DOES specify direction. i.e. the force in the x direction. Are you familiar with resolving vectors?
     
  17. May 20, 2013 #16
    Yes, I understand resolving vectors. And I get that Fx does show direction....but it is not a vector according to my book, only the scalar magnitude of the force along x-axis.

    So that is where the confusion comes in. IS Fx a vector? If not, as the book says it is the component of F along the x axis which is a scalar, why do they still refer to it as force?

    They should say, find the magnitude of force along x-axis,,Fx instead of find the force Fx. I believe that would be less confusing
     
  18. May 20, 2013 #17

    sophiecentaur

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    If you look in Example 4-2 you will see the actual vector defined as Fxi where i is a unit vector in the direction x. So Fx is a scalar. Having done that then they really don't need to spell it out all the time.
    I think, by now, that you understand what it's all about but may still be annoyed at the way they're writing it down? It doesn't seem all that sloppy to me. They do put an arrow over F when they are referring to the vector force.
     
  19. May 20, 2013 #18
    I agree with that Sophiecentaur, the actual vector is Fxi, and when trying to find it, you need to calculate the magnitude of Force in the x-direction, using the equation fx=mAx. At that point they should say THAT, find the magnitude of force, fx, but instead, they don't need to spell it out. By saying find the force, referring to Fx you know what they mean.

    I guess that was my question and you have answered it. Don't get to caught up on the words, sometimes we leave out details because it is already understood and doesn't need to be spelled out. That explains why in my other example, 4-4, they simply just called out force and acceleration without direction, because it was unnecessary in that problem. I am trying to be to perfect. Sorry for the confusion. THanks for the help
     
  20. May 20, 2013 #19
    It was very helpful to see your examples. I can now see where you are coming from.

    If the motion is in a straight line, and/or the only relevant forces and accelerations depend on only one spatial variable, then it is not important to account for the vectorial nature of forces, velocities, and acceleration. However, if there exist forces and accelerations in more than one direction that need to be included in the analysis, then to solve your problem, you need to resolve the equations into components. Even though the force balance can usually be expressed exclusively in vectorial form (i.e., in terms of bold letters with arrows over them), when you solve a practical problem, you usually need to resolve the forces and accelerations into component form to get a mathematical solution to your problem. Think about trying to solve some of your problems without doing this.

    Chet
     
  21. May 21, 2013 #20

    sophiecentaur

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    I can't see the contents of the pages previous to p95 but are you sure they don't mention the idea of unit vectors, in the directions of the xyz axes? If they do, then I can't see why you have had any problem. There is nothing in those examples that could be construed as confusing or even 'imperfect' if they have already told you what i stands for. If they haven't introduced unit vectors then they are being really really sloppy.
    Life's too short and paper is too scarce for people not to be using well-known abbreviations. Where would you stop, if you qualified and defined everything before making a statement?
     
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