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JenniferSmart1

  • 2 years ago

Why is kx=25N instead of -kx=25N?

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  1. JenniferSmart1
    • 2 years ago
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  2. JenniferSmart1
    • 2 years ago
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    @Outkast3r09

  3. JenniferSmart1
    • 2 years ago
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    shouldn't F=-kx?

  4. JenniferSmart1
    • 2 years ago
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    @CliffSedge ?

  5. Outkast3r09
    • 2 years ago
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    Ahh this my physics teacher went over

  6. JenniferSmart1
    • 2 years ago
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    cool! Now you can explain it to me :)

  7. Outkast3r09
    • 2 years ago
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    the negative explains how that force is acting upon the spring

  8. Outkast3r09
    • 2 years ago
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    it depends on the what you're trying to find

  9. Outkast3r09
    • 2 years ago
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    if you're trying to find the force the spring is exerting on the mass or the mass exerting on the spring

  10. JenniferSmart1
    • 2 years ago
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    Hmmm let's see|dw:1353379482698:dw|

  11. Outkast3r09
    • 2 years ago
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    |dw:1353379572781:dw|

  12. JenniferSmart1
    • 2 years ago
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    well I guess we're stretching to a certain length, so the first figure?

  13. JenniferSmart1
    • 2 years ago
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    I mean the first figure you drew

  14. Outkast3r09
    • 2 years ago
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    the figures are the same

  15. Outkast3r09
    • 2 years ago
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    it depends on whether you're trying to find the length of the spring or the position of the mass

  16. JenniferSmart1
    • 2 years ago
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    Uhm I think we want my figure because In your figure we have to consider the gravitational force and the restoring force. I don't think they want to consider the gravitational force

  17. Outkast3r09
    • 2 years ago
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    if it asked abouthe spring itself it'd be negative

  18. Outkast3r09
    • 2 years ago
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    there is two ways this question can be answered 1) How long did the spring stretch from initial 2) What is the position of the mass after initial. They're the same thing

  19. Outkast3r09
    • 2 years ago
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    so since it's asking for position of the mass it's this|dw:1353379915405:dw|

  20. JenniferSmart1
    • 2 years ago
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    why is it positive? because it is going in the direction that we designated as positive?

  21. Outkast3r09
    • 2 years ago
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    yes

  22. Outkast3r09
    • 2 years ago
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    technically this question can have 2 answers + answer and a - answer depending on how you set up your axis

  23. JenniferSmart1
    • 2 years ago
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    OH I see! |dw:1353380068540:dw| Like so?

  24. JenniferSmart1
    • 2 years ago
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    Now I can say that F=kx

  25. JenniferSmart1
    • 2 years ago
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    right?

  26. JenniferSmart1
    • 2 years ago
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    no the other way around, I should probably make the restoring force positive...

  27. Outkast3r09
    • 2 years ago
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    |dw:1353380229463:dw|

  28. Outkast3r09
    • 2 years ago
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    yeah the picture they used was probably a free falling mass

  29. Outkast3r09
    • 2 years ago
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    and saying that the sum of the force of gravity + any other force = F

  30. JenniferSmart1
    • 2 years ago
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    Yeah that makes more sense. so they probably had up as positive and down as negative.

  31. Outkast3r09
    • 2 years ago
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    yes but it really just depends on what you define it... if your teacher marks you wrong and your diagram says otherwise just clear it up with him

  32. JenniferSmart1
    • 2 years ago
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    yep

  33. JenniferSmart1
    • 2 years ago
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    so why is k(0.2) why 0.2? How did they come up with x=0.2?

  34. JenniferSmart1
    • 2 years ago
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    never mind

  35. JenniferSmart1
    • 2 years ago
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    LOL

  36. JenniferSmart1
    • 2 years ago
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    that's the displacement haha

  37. Outkast3r09
    • 2 years ago
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    yes the displacement will still be posive

  38. JenniferSmart1
    • 2 years ago
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    hmm interesting: (this the DE part of my calc II book) \[2\frac{d^2x}{dt^2}+128x=0 \text{ has the solution }x(t)=c_1cos8t+c_2sin8t \] yeah that's easier that doing it manually....

  39. CliffSedge
    • 2 years ago
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    It's convention to designate potential energy as negative. The reaction force of the spring is opposite the positive applied force.

  40. CliffSedge
    • 2 years ago
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    More clearly: The negative sign of F=-kx means that the spring force is opposite to the applied force on the spring.

  41. JenniferSmart1
    • 2 years ago
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    potential energy as positive...the restorative force?

  42. JenniferSmart1
    • 2 years ago
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    Yes that makes sense

  43. JenniferSmart1
    • 2 years ago
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    I had to reread the last sentence you wrote several times, but it makes sense now

  44. JenniferSmart1
    • 2 years ago
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    but where did they get the 8 in sin and cos 8t

  45. CliffSedge
    • 2 years ago
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    As others mentioned above, it's a sign convention. You define what direction you want to be positive and anything opposite to that is negative. The norm, though is to treat spring force as negative/opposite to any force acting *on* the spring.

  46. CliffSedge
    • 2 years ago
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    The 8 is based on the period of the spring - that is determined by the spring constant, k, and the attached mass.

  47. CliffSedge
    • 2 years ago
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    \(\large T=2\pi \sqrt{\frac{m}{k}}\) T^-1 is the frequency of oscillation.

  48. JenniferSmart1
    • 2 years ago
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    yep, sounds good. I googled it LOL \[T=2\pi \sqrt{\frac mk}\]

  49. CliffSedge
    • 2 years ago
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    The "8" in the cosine function usually goes by the name, omega, \(\large \omega\). Might want to look that up too.

  50. JenniferSmart1
    • 2 years ago
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    so the formula is \[x(t)=c_1cosTt+c_2sinTt\]

  51. JenniferSmart1
    • 2 years ago
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    so T is \[\omega\]

  52. CliffSedge
    • 2 years ago
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    \(\large . . . cos(\omega t) . . \) No, ω is related to T.

  53. JenniferSmart1
    • 2 years ago
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    Oh \[\omega=\sqrt{\frac km}\]

  54. CliffSedge
    • 2 years ago
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    Right!

  55. JenniferSmart1
    • 2 years ago
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    \[x(t)=c_1cos\omega t+c_2sin\omega t\]

  56. CliffSedge
    • 2 years ago
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    Yes, you can either derive that using the Diff.Eq. or look it up on a physics formula sheet. (Depends on if you are more mathematician or engineer ;-) )

  57. JenniferSmart1
    • 2 years ago
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    leaning more towards engineering....physics formula sheet :P

  58. JenniferSmart1
    • 2 years ago
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    omega doesn't seem to have units

  59. CliffSedge
    • 2 years ago
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    That would be my choice too, but know that the way the physicists got those formulas in the first place was to solve the DEs (or rather to get their math dept. grad students and TAs to do the solving for them..)

  60. CliffSedge
    • 2 years ago
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    omega should have units of s^-1, it's a frequency.

  61. CliffSedge
    • 2 years ago
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    Or .. is at least based on a frequency, something in the derivation might make the units cancel, but I'm pretty sure it's just the reciprocal of the time period, T.

  62. JenniferSmart1
    • 2 years ago
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    radians per second

  63. JenniferSmart1
    • 2 years ago
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    according to my friend wiki

  64. JenniferSmart1
    • 2 years ago
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    so s^-1 should be sufficient, i can leave the radians part out in my notation?

  65. CliffSedge
    • 2 years ago
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    Yes, because radians are dimensionless (it's derived from length ÷ length), that's what the 2π conversion factor is in there for.

  66. JenniferSmart1
    • 2 years ago
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    Oh I see

  67. JenniferSmart1
    • 2 years ago
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    why is c_2 zero? shouldn't it be ...so when we say\[ x(0)=8c_2 cos8t\] does that mean \[0=8c_2 cos8t=8c_2cos(0)=8c_2(1)=c_2\] yep that seems right LOL

  68. JenniferSmart1
    • 2 years ago
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    Thanks everyone!!!!

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