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Velocity released from a spring

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Everything is on a frictionless horizontal surface. If a block is compressed against a spring for some distance x meters and then released, what is the velocity of the block the moment it loses contact with the spring?


    2. Relevant equations
    W_s = -(1/2)kx^2 [if reference point is 0m]
    W = (1/2)m(v_f)^2 - (1/2)m(v_i)^2


    3. The attempt at a solution
    So if we take the compression of the spring to be our 0 point, then when it is released, the block travels x meters when it is fully released by the spring. The work done by the spring on the block is going to be negative. But since the initial velocity is 0, we get the equation: -(1/2)kx^2 = (1/2)m(v_f)^2. If you try to solve this for the velocity, you have to take the square root of a negative number. What am I doing wrong here?
     
  2. jcsd
  3. Nov 29, 2012 #2

    Doc Al

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    Staff: Mentor

    Why do you think that the work done by the spring will be negative?

    Which way does the spring push? Which way does the block move?
     
  4. Nov 29, 2012 #3
    The displacement is in the same direction as the force of the spring pushing on it, so it should be positive, but then why does the textbook say that the work done by a spring is always -(1/2)kx^2 if the starting position is taken to be the 0 point?
     
  5. Nov 29, 2012 #4

    Doc Al

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    Staff: Mentor

    The work done by the spring is negative when you compress it from 0 to x and positive when it decompresses from x to 0 (which is what is going on here).

    I prefer to think in terms of the energy stored in the spring, which is simply 1/2kx^2.
     
  6. Nov 29, 2012 #5
    It says that the work done is negative because the block or the system DOES work ON the spring AGAINST its restoring force.
     
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