Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Homework Helper

    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

  6. Jul 28, 2011 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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.

    mgd(sinθ) = (1/2)k(x2) .​
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook