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Spring / ramp energy problem

  1. Mar 12, 2010 #1
    1. The problem statement, all variables and given/known data

    A 200-g block is pressed against a spring of force constant 1.40 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of the ramp inclined at 60.0deg to the horizontal.

    Using energy considerations, determine how far up the incline the block moves before it stops (a) if there is no friction between the block and the ramp and (b) if the coefficient of kinetic friction is 0.400.

    2. Relevant equations

    Delta KE = Delta PE

    3. The attempt at a solution

    Okay, since the system is conservered with no fricition, I can assume that
    initial energy = final energy, and we can rewrite it as
    PE initial (of the block at the highest point) = KE final (of the spring as it gets compressed for 0.01 meter)

    PE initial = KE final
    X is the length the block travels from its original position
    (mg*sin60 * X) = 1/2 * k * (0.01m^2)

    And then I was wondering why do we assume that the initial KE of the block is zero? The problem did not state that there was no initial velocity for the block.
     
  2. jcsd
  3. Mar 12, 2010 #2

    rl.bhat

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    Homework Helper

    Energy store in the spring is
    E = 1/2*k*x^2.
    When the block detaches from the spring, stored energy in the spring in converted into PE and KE. The PE is m*g*x*sinθ, where x is the compression of the spring.
    Now you get the initial velocity. final velocity is zero. Find the distance traveled by the block along the ramp.
     
  4. Mar 12, 2010 #3
    hi, thanks. i was so dump did not consider its reverse condition.
    thanks!
     
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