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Vector Components physics homework

  1. Feb 16, 2009 #1
    Determine the x and y components. A 40 lb force vector that makes an angle of 120 degree counterclockwise from the -y direction.

    I did Ax= (40)(-cos120 degree) and Ay= (40)(sin120 degree)

    I got the right answer, I just want to make sure that this is the correct way of solving the problem.
     
  2. jcsd
  3. Feb 16, 2009 #2

    AEM

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    I read your earlier thread with Tiny_Tim and noticed that you wanted a rule as to when to use the formulas he suggested. When I was teaching, I used to tell my students to draw a careful diagram and label the angles the vector makes with each axis and work then use trigonometry to find the projection of the vector on to the axes. I think that way you will make fewer mistakes.
     
  4. Feb 16, 2009 #3
    Okay. Thank you. Also, was the way I solved the problem correct?
     
  5. Feb 16, 2009 #4

    AEM

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    Well, you said that you got the right answer, but I'm puzzled. Isn't your vector in the first quadrant making a 30 degree angle with the x axis?

    Your solution is appropriate for a vector that makes an angle of 120 degrees with the Positive X axis.
     
    Last edited: Feb 17, 2009
  6. Feb 17, 2009 #5
    Yes, it is. I must have done something wrong with the equation. How would I fix it?
     
  7. Feb 17, 2009 #6

    robphy

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    The x-component of A is [tex]\hat x \cdot \vec A[/tex] (which is equal to [tex](1)|A|\cos\theta_{\mbox{\small between $\vec A$ and $\hat x$}}[/tex]).
    The y-component of A is [tex]\hat y \cdot \vec A[/tex] (which is equal to [tex](1)|A|\cos\theta_{\mbox{\small between $\vec A$ and $\hat y$}}[/tex]).

    You can also express the components as
    [tex]A_x=A\cos\theta[/tex]
    [tex]A_y=A\sin\theta[/tex]
    where [tex]\theta[/tex] is the counterclockwise angle from the positive-x axis.
    Note that this angle is in the range [tex]0\leq \theta < 360^\circ[/tex] (and so [tex]-1\leq \cos\theta\leq 1[/tex] and [tex]-1\leq \sin\theta\leq 1[/tex]).

    The above are the best facts to remember.
    If you need to work with other angles, you need to draw a good picture and express the given angle in terms of the angles above [and possibly use some trig identities, especially if you want a general formula using some other choice of angles or axes].

    So, for instance, if you are given a counterclockwise angle [tex]\phi[/tex] with respect to the -y axis, what is the corresponding counterclockwise angle [tex]\theta[/tex] from the +x-axis?
     
  8. Feb 17, 2009 #7
    It would be the same numbers for both however the positive x direction, both the x and y component would be positive and for the negative y direction, both the x and y component would be negative. Thank you for your help.
     
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