JenniferSmart1 3 years ago Why is kx=25N instead of -kx=25N?

1. JenniferSmart1

2. JenniferSmart1

@Outkast3r09

3. JenniferSmart1

shouldn't F=-kx?

4. JenniferSmart1

@CliffSedge ?

5. Outkast3r09

Ahh this my physics teacher went over

6. JenniferSmart1

cool! Now you can explain it to me :)

7. Outkast3r09

the negative explains how that force is acting upon the spring

8. Outkast3r09

it depends on the what you're trying to find

9. Outkast3r09

if you're trying to find the force the spring is exerting on the mass or the mass exerting on the spring

10. JenniferSmart1

Hmmm let's see|dw:1353379482698:dw|

11. Outkast3r09

|dw:1353379572781:dw|

12. JenniferSmart1

well I guess we're stretching to a certain length, so the first figure?

13. JenniferSmart1

I mean the first figure you drew

14. Outkast3r09

the figures are the same

15. Outkast3r09

it depends on whether you're trying to find the length of the spring or the position of the mass

16. JenniferSmart1

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

18. Outkast3r09

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

so since it's asking for position of the mass it's this|dw:1353379915405:dw|

20. JenniferSmart1

why is it positive? because it is going in the direction that we designated as positive?

21. Outkast3r09

yes

22. Outkast3r09

23. JenniferSmart1

OH I see! |dw:1353380068540:dw| Like so?

24. JenniferSmart1

Now I can say that F=kx

25. JenniferSmart1

right?

26. JenniferSmart1

no the other way around, I should probably make the restoring force positive...

27. Outkast3r09

|dw:1353380229463:dw|

28. Outkast3r09

yeah the picture they used was probably a free falling mass

29. Outkast3r09

and saying that the sum of the force of gravity + any other force = F

30. JenniferSmart1

Yeah that makes more sense. so they probably had up as positive and down as negative.

31. Outkast3r09

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

yep

33. JenniferSmart1

so why is k(0.2) why 0.2? How did they come up with x=0.2?

34. JenniferSmart1

never mind

35. JenniferSmart1

LOL

36. JenniferSmart1

that's the displacement haha

37. Outkast3r09

yes the displacement will still be posive

38. JenniferSmart1

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

It's convention to designate potential energy as negative. The reaction force of the spring is opposite the positive applied force.

40. CliffSedge

More clearly: The negative sign of F=-kx means that the spring force is opposite to the applied force on the spring.

41. JenniferSmart1

potential energy as positive...the restorative force?

42. JenniferSmart1

Yes that makes sense

43. JenniferSmart1

I had to reread the last sentence you wrote several times, but it makes sense now

44. JenniferSmart1

but where did they get the 8 in sin and cos 8t

45. CliffSedge

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

The 8 is based on the period of the spring - that is determined by the spring constant, k, and the attached mass.

47. CliffSedge

$$\large T=2\pi \sqrt{\frac{m}{k}}$$ T^-1 is the frequency of oscillation.

48. JenniferSmart1

yep, sounds good. I googled it LOL $T=2\pi \sqrt{\frac mk}$

49. CliffSedge

The "8" in the cosine function usually goes by the name, omega, $$\large \omega$$. Might want to look that up too.

50. JenniferSmart1

so the formula is $x(t)=c_1cosTt+c_2sinTt$

51. JenniferSmart1

so T is $\omega$

52. CliffSedge

$$\large . . . cos(\omega t) . .$$ No, ω is related to T.

53. JenniferSmart1

Oh $\omega=\sqrt{\frac km}$

54. CliffSedge

Right!

55. JenniferSmart1

$x(t)=c_1cos\omega t+c_2sin\omega t$

56. CliffSedge

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

leaning more towards engineering....physics formula sheet :P

58. JenniferSmart1

omega doesn't seem to have units

59. CliffSedge

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

omega should have units of s^-1, it's a frequency.

61. CliffSedge

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

63. JenniferSmart1

according to my friend wiki

64. JenniferSmart1

so s^-1 should be sufficient, i can leave the radians part out in my notation?

65. CliffSedge

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

66. JenniferSmart1

Oh I see

67. JenniferSmart1

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

Thanks everyone!!!!