One end of a spring is attached firmly to a wall, and a block is attached to the

Question

One end of a spring is attached firmly to a wall, and a block is attached to the other end. When the spring is fully compressed, it exerts a force F on the block, and when the spring is fully extended, the force it exerts on the block is ?F. What is the force of the spring on the block at (a) equilibrium (neither compressed nor stretched), (b) halfway between maximum stretch and equilibrium, and (c) halfway between maximum compression and equilibrium? Carefully consider the signs in your answer, which indicate direction, and express your answers in terms of F. One end of a spring is attached firmly to a wall, and a block is attached to the other end. When the spring is fully compressed, it exerts a force F on the block, and when the spring is fully extended, the force it exerts on the block is ?F. What is the force of the spring on the block at (a) equilibrium (neither compressed nor stretched), (b) halfway between maximum stretch and equilibrium, and (c) halfway between maximum compression and equilibrium? Carefully consider the signs in your answer, which indicate direction, and express your answers in terms of F.

Explanation / Answer

Equilibrium, by definition means no net forces so when the block is at the spring's equilibrium point, the force of the spring on the block is 0.
5b&c) The force that a spring generates is a linear function of the displacement from equilibrium, so at half the displacement, the force will be half that of maximum displacement (but it will have the same sign). So, at half compression, the spring will exert a force of F/2 and at half extension, the spring will exert a force of -F/2.

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