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carlj0nes

  • one year ago

By using a Scaled phasor Diagram determine the resultant force when the following currents are added. (I will attach a picture in the comment). What I need is from the method I have used clearly explain the method/technique used and to validate the solution/ method by using an alternative mathematical method.

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  1. carlj0nes
    • one year ago
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  2. Michele_Laino
    • one year ago
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    here we can try to develop your formulas

  3. Michele_Laino
    • one year ago
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    please wait I'm computing your sum...

  4. Michele_Laino
    • one year ago
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    here are my steps:

  5. Michele_Laino
    • one year ago
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    \[\begin{gathered} 20\cos \left( {60\pi t} \right)\cos \left( {\pi /4} \right) - 20\sin \left( {60\pi t} \right)\sin \left( {\pi /4} \right) + \hfill \\ \hfill \\ + 30\cos \left( {60\pi t} \right)\cos \left( {\pi /10} \right) - 30\sin \left( {60\pi t} \right)\sin \left( {\pi /10} \right) = \hfill \\ \hfill \\ = \cos \left( {60\pi t} \right)\left\{ {20\cos \left( {\pi /4} \right) + 30\cos \left( {\pi /10} \right)} \right\} - \hfill \\ \hfill \\ - \sin \left( {60\pi t} \right)\left\{ {20\sin \left( {\pi /4} \right) + 30\sin \left( {\pi /10} \right)} \right\} \hfill \\ \end{gathered} \]

  6. Michele_Laino
    • one year ago
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    now, we can write: \[\left\{ \begin{gathered} 20\cos \left( {\pi /4} \right) + 30\cos \left( {\pi /10} \right) = A\cos \alpha \hfill \\ 20\sin \left( {\pi /4} \right) + 30\sin \left( {\pi /10} \right) = A\sin \alpha \hfill \\ \end{gathered} \right.\]

  7. Michele_Laino
    • one year ago
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    using the subsequent values: \[\cos \left( {\pi /4} \right) = \sin \left( {\pi /4} \right) = \frac{1}{{\sqrt 2 }}\]

  8. Michele_Laino
    • one year ago
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    and:

  9. Michele_Laino
    • one year ago
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    \[\begin{gathered} \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \hfill \\ \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \end{gathered} \]

  10. Michele_Laino
    • one year ago
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    I rewrite those values:\[\begin{gathered} \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \hfill \\ \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \end{gathered} \]

  11. Michele_Laino
    • one year ago
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    \[\begin{gathered} \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \end{gathered} \]

  12. Michele_Laino
    • one year ago
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    \[\Large \begin{gathered} \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \hfill \\ \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \end{gathered} \]

  13. Michele_Laino
    • one year ago
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    I hope you see them correctly

  14. Michele_Laino
    • one year ago
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    we can rewrite those equations as below: \[\Large \left\{ \begin{gathered} \frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4} = A\cos \alpha \hfill \\ \hfill \\ \frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4} = A\sin \alpha \hfill \\ \end{gathered} \right.\]

  15. Michele_Laino
    • one year ago
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    then we square both of those equations and we add them together, so we can write: \[\large {A^2} = {\left( {\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4}} \right)^2} + {\left( {\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4}} \right)^2}\]

  16. Michele_Laino
    • one year ago
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    whereas divding side by side those equations, we find: \[\Large \tan \alpha = \frac{{A\sin \alpha }}{{A\cos \alpha }} = \frac{{\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4}}}{{\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4}}}\]

  17. carlj0nes
    • one year ago
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    @Michele_Laino thank you for your help. Sorry to be a pain but would you be able to hand write the first part for me and upload a picture just so i can try to understand some of the terminology of what you have put. e.g. hfill and \

  18. Michele_Laino
    • one year ago
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    no, I'm sorry I'm not able to hand write my answer, nevertheless I'm able to write a PDF file, and attach it using the "Attach FIle" button

  19. Michele_Laino
    • one year ago
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    from my preceding 2 formulas, you can find both the amplitude A, and the angle \alpha, so you can write your answer as follows: \[\Large {i_1} + {i_2} = A\cos \left( {60\pi t + \alpha } \right)\]

  20. Michele_Laino
    • one year ago
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    please wait, I'm doing that computation...

  21. Michele_Laino
    • one year ago
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    I got: \[\Large \begin{gathered} A = 48.67Amperes \hfill \\ \alpha = 0.5\;radians \hfill \\ \end{gathered} \]

  22. Michele_Laino
    • one year ago
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    so we can write: \[\Large {i_1} + {i_2} \cong 48.7\cos \left( {60\pi t + 0.5} \right)\]

  23. Michele_Laino
    • one year ago
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    please note that we have the subsequent equivalence: \[\Large 0.5\;{\text{radians}} = 28.75\;{\text{degrees}}\]

  24. carlj0nes
    • one year ago
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    That would be helpful if you could put it as a PDF as im not use to how this is laid out. I normally have to type it up in word and it takes ages (see attached). That was why I suggested handwritten as it what i find easiest. But we all have our preferences.

  25. UsukiDoll
    • one year ago
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    @Michele_Laino you deserve more than 2 medals D:! All that Latex!

  26. Michele_Laino
    • one year ago
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    thanks! :) @UsukiDoll

  27. carlj0nes
    • one year ago
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    Michele does

  28. Michele_Laino
    • one year ago
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    @carlj0nes ok! I start to write your PDF file, please wait, it will take some time

  29. UsukiDoll
    • one year ago
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    texmaker and then use Latex --> PDF I think it was F5 . I forgot.

  30. carlj0nes
    • one year ago
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    just a note at the beginning should that of been 32 cos not 30 cos

  31. Michele_Laino
    • one year ago
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    That's right! I use TexMik with TeXnicCenter

  32. Michele_Laino
    • one year ago
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    ok! I update my answer with your value @carlj0nes

  33. carlj0nes
    • one year ago
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    just a note at the beginning should that of been 32 cos not 30 cos

  34. Michele_Laino
    • one year ago
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    here is my PDF file:

  35. Michele_Laino
    • one year ago
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    what do you think about that file?

  36. UsukiDoll
    • one year ago
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    I saw "in order to that" @______@

  37. Michele_Laino
    • one year ago
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    is it correct? @UsukiDoll

  38. UsukiDoll
    • one year ago
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    doesn't sound right

  39. Michele_Laino
    • one year ago
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    why?

  40. UsukiDoll
    • one year ago
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    "In order to [do] that"

  41. Michele_Laino
    • one year ago
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    ok! thanks! I'm updating my file @UsukiDoll

  42. UsukiDoll
    • one year ago
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    A simple computation shows us...

  43. UsukiDoll
    • one year ago
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    [Therefore,] we can write

  44. UsukiDoll
    • one year ago
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    compute [the following] ratio

  45. Michele_Laino
    • one year ago
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    following the suggestions by @UsukiDoll I have rewritten my file, here is it:

  46. UsukiDoll
    • one year ago
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    [Then],

  47. UsukiDoll
    • one year ago
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    known angles [we have], [Next,] we get,

  48. UsukiDoll
    • one year ago
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    comma splice! period after Amplitude A A simple computation (no s) Again, after a simple computation, we get: delete So. add[ As a result, ]the requested sum of the two currents is

  49. Michele_Laino
    • one year ago
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    here my new updated version of the preceding PDF file, I have to be grateful to @UsukiDoll for her suggestions and comments to my english grammar!

  50. UsukiDoll
    • one year ago
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    I still see that comma splice

  51. Michele_Laino
    • one year ago
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    please what is a comma splice?

  52. UsukiDoll
    • one year ago
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    I'll take a screenshot and use paint to add my marks AHHAAHAHHAHAHA

  53. Michele_Laino
    • one year ago
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    ok!

  54. UsukiDoll
    • one year ago
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    comma splice is a comma between two complete sentences. It's the most aggravating error for English Professors to see on essays

  55. Michele_Laino
    • one year ago
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    ok! Please show where is the comma splice in my file

  56. UsukiDoll
    • one year ago
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  57. carlj0nes
    • one year ago
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    Thank you for all you help it is much appreciated. I am about to post another question and i would like to invite both of you.

  58. UsukiDoll
    • one year ago
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    I have to sleep early. I have to help shop blah

  59. UsukiDoll
    • one year ago
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