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Interesting Electric Field and Spring Problemf

  1. Jul 28, 2008 #1
    1. The problem statement, all variables and given/known data
    A block having mass m and charge +Q is connected to an insulating spring having constant k. The block lies on a frictionless, insulating horizontal track, and the system is immersed in a uniform electric field of magnitude E as shown in the diagram. If the block is released from rest when the spring is unstretched (at x = 0),

    (a) by what maximum amount does the spring expand?
    (b) what is the equilibrium position of the block
    (c) show that the block's motion is simple harmonic and determine its period
    (d) repeat (a) assuming that the coefficient of kinetic friction between the block and the surface is mew K.


    2. Relevant equations
    a few, F = qE = ma = -kx

    3. The attempt at a solution

    I'm only starting to attempt part (a), the block has a force QE to the right and a restoring force kx to the left.

    So I equated the forces thus: QE = kx and solved for x to obtain x = QE/k.

    This isn't the solution for (a), but it is for (b). The solution for (a) is 2QE/k

    It's driving me crazy trying to find where the 2 came into calculations. Working backwards from (b) I see that the equilibrium position is half of the maximum expansion. But how so?
  2. jcsd
  3. Jul 28, 2008 #2
    Right, that's the answer for B because at the equilibrium position, the restoring force of the spring is equal to the electric force. That's why at equilibrium, Fnet is 0 so the acceleration of the block is also zero.

    For part A, consider the relationship between the potential energy of the spring at the point of furthest expansion and the work the electric force must do to get the block to that point.
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