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Homework Help: Incline Problem with spring

  1. Mar 10, 2010 #1
    1. The problem statement, all variables and given/known data

    The ball launcher in a pinball machine has a spring that
    has a force constant of 1.20 N/cm The surface
    on which the ball moves is inclined 10.0° with respect
    to the horizontal. If the spring is initially compressed
    5.00 cm, find the launching speed of a 100-g ball when the
    plunger is released. Friction and the mass of the plunger negligible

    2. Relevant equations

    Ki + Ws + Wg = Kf

    3. The attempt at a solution

    W = integral kx
    but i don't understand where gravity comes into play. I'm trying to understand the concept, the solution manual works it out as 1.68 m/s and they use cos 100 don't understand that either
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Mar 10, 2010 #2
    I would do this problem by using conservation of energy. The energy in a spring is given by E = (1/2)kx^2, so plugging in your spring constant and initial compression gives you the initial energy, Ei.

    Now all that energy goes into the pinball. The energy of the pinball is given by E = (1/2)mv^2 + mgh, where h is altitude. (There's where the gravitational acceleration comes into play). That's the final energy, Ef. Just equate Ei and Ef and then solve for v. h will represent the difference in altitude between the compressed position and the equillibrium position--so h=5cos(10°).
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