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Determining Compression of a Spring involving Spring Constants

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data
    A 10g marble is launched horizontally from a spring of K = 20 N/m. If the marble ended up with a launch speed of 40m/sec, how much (in cm) was the spring compressed by?


    2. Relevant equations

    [itex]F=kx[/itex]
    [itex]E=\frac{1}{2}kx^2[/itex]

    3. The attempt at a solution
    To find how much the spring was compressed by, I know that you must solve for x in either equation. But I am unsure what values F or E would be. F =ma, but no acceleration, displacement, or time interval is given. ΔE= FΔd, but still force is required.
     
  2. jcsd
  3. Nov 24, 2012 #2

    rock.freak667

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    Homework Helper

    The elastic potential energy of the spring when compressed to a distance 'x' will be converted into kinetic energy.

    Do you know how to find the kinetic energy of an object given its mass and velocity?
     
  4. Nov 24, 2012 #3
    [itex]\frac{1}{2}mv^2 = \frac{1}{2}kx^2[/itex]

    [itex](0.01)(0.4)^2 = 20x^2[/itex]

    [itex]0.0089 m = x[/itex]

    [itex]8.9 cm = x[/itex]

    I wrote that the initial velocity was 40m/s, should have been 40cm/s. Would this solution be correct though?
     
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