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Find the spring constant

  1. Jul 27, 2011 #1
    1. The problem statement, all variables and given/known data

    A car with mass m rolls d down a frictionless [tex]\theta^0[/tex] degree incline. If there is a horizontal spring at the end of the incline, what spring constant is required to stop the car in a distance of x?

    3. The attempt at a solution

    [PLAIN]http://img4.imageshack.us/img4/8837/unledxrq.jpg [Broken]

    I am honestly very embarrassed that I can't do these basica problems properly and I am a rising sophomore.

    I tried

    [tex]\sum W = \Delta K[/tex]

    [tex]mg(d\sin\theta) - \int_{x = 0}^{x = x} kx dx = -\frac{1}{2}mv_0^2[/tex]

    I thought that at the top before it collides that

    [tex]-\frac{1}{2}mv_0^2 = -mg(dsin\theta)[/tex]


    [tex]mg(d\sin\theta) - \int_{x = 0}^{x = x} kx dx = -mg(d\sin\theta)[/tex]



    [tex] \int_{x = 0}^{x = x} kx dx = 2mg(d\sin\theta)[/tex]


    [tex] k = \frac{4mgd\sin\theta}{x^2}[/tex]

    Apparently this is wrong and the answer is just mgh = 0.5kx^2.

    I decided to not use LaTeX for the correct answer because I am upset.

    If assume initial velocity is 0 I get it right



    [tex] k = \frac{2mgd\sin\theta}{x^2}[/tex]

    Why? How do I know it started with 0 velocity?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jul 27, 2011 #2

    tiny-tim

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    hi flyingpig! :smile:
    yes :smile:

    (except you really ought to use a different variable inside the ∫, maybe x' or y)
    i don't understand where this comes from :confused:
     
  4. Jul 28, 2011 #3
    It came from at the top of the ramp.
     
  5. Jul 28, 2011 #4

    PeterO

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    This is the simple part.

    Read the question and look for the following:

    An object falls, an object is dropped, a car rolls down a hill, a block slides down a slope, ...

    In all these cases the object is starting with zero velocity.

    When the question starts

    An object is thrown, A projectile is lauched, or similar, it is NOT starting with a velocity of Zero.

    Actually "an object is dropped/falls" can be tricky, since it can sometimes be dropped/fall from a moving point - but then you will realise it is moving so it shouldn't be a problem.
    Examples could be:
    You dropped a book while in a lift traveling up at 2 m/s
    A bomb falls from an airplane traveling at ......
    A bag of nuts falls out of a roller coaster when it speeds over a crest ....

    Good luck

    Peter
     
  6. Jul 28, 2011 #5

    SammyS

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    At the top of the ramp, the car has PE = mgd(sinθ) and KE = 0.

    At the point where the spring has stopped the car, the car has PE = (1/2)k(x2) and KE = 0.

    Therefore,
    mgd(sinθ) = (1/2)k(x2) .​
     
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