A small block is attached to the free end of an ideal horizontal spring that is fixed to a wall. The block slides without friction on a straight track. At a particular instant the block is located 0.12 m to the right of the spring’s relaxed (equilibrium) position and is moving leftward toward the wall.
Assume a rightward positive x-axis.
(1) Describe the direction of the force exerted by the spring on the block at that instant and relate it to the block’s displacement from the equilibrium position.
(2) Using the coordinate convention stated, explain why the algebraic sign of the spring force at that instant differs from the sign of the block’s displacement. In your answer, discuss how the sign communicates physical direction.
(3) Identify the displacement values (positive, negative, or zero) that correspond to (i) a negative spring force, (ii) zero spring force, and (iii) a positive spring force for this coordinate choice, and justify each case with reasoning about the system’s tendency to return to equilibrium.