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The block in the figure below lies on a horizontal frictionless surface and is attached to the free end of the spring, with a spring constant of 35 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 2.7 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. Assume that the stopping point is reached

MY questions is how do you find the maximum kinetic energy of the spring during the blocks displacement?

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Typically, in this kind of problem, the spring is idealized as massless. Thus, it is only the mass attached to the spring that can possess kinetic energy. –  Alfred Centauri Oct 26 '12 at 23:24

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  1. You know that the restoring force of the spring is F=-kx where k is the spring constant and x is the displacement of the spring (negative because it acts in the direction opposite to the displacement x of the spring).

  2. You are given an applied force of 2.7N that causes displacement in the positive x direction.

  3. Using a free-body diagram you should find the net force on the block. You should see that there is no net force in the y direction and that along the x direction, you have the spring force and the applied force acting in opposite directions. The magnitudes of the spring force and the applied force are equal at the stopping point.

  4. Now you can find the displacement x.

  5. Force applied over a distance results in work. Work is a form of energy. Do you know the equation for work?

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except this isn't the KE of the spring, it's the KE of the block. See the comment. –  Ron Maimon Oct 27 '12 at 3:41

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