This question tests application of Hooke's law to predict spring force at different positions. The spring force is a restoring force that opposes displacement and points toward equilibrium, with its direction given by the negative sign in F_s = -kx. The magnitude is proportional to displacement, so if force is -2.0 N at x = +0.04 m, doubling the displacement to +0.08 m doubles the magnitude while keeping the negative direction. This yields F_s = -4.0 N, as the spring constant k remains consistent. Choice D, +4.0 N, is a distractor that mistakes the sign convention, suggesting a force away from equilibrium. For transferable skills, practice using known force-position pairs to find k, then apply it to new positions for verification.

This question explores how spring force magnitude varies with displacement in Hooke's law. The restoring force acts opposite to displacement, pulling or pushing toward equilibrium with magnitude |F| = k|x|. Doubling the displacement from +0.03 m to +0.06 m doubles the stretch, thus doubling the force magnitude at release. This proportionality holds as long as the spring remains ideal and within elastic limits. Choice D erroneously claims zero force for stretching, confusing it with equilibrium. A transferable tip is to use proportional reasoning: multiply force by the displacement ratio for quick comparisons in similar scenarios.

This question examines the direction of the spring's restoring force when the spring is compressed. The restoring force always acts to restore the system to equilibrium, pushing outward when the spring is compressed. At x = -0.12 m, the compression means the force on the block is to the right, or positive x-direction, to expand the spring back to x = 0. The force magnitude is proportional to the displacement's absolute value, but direction is key here, following F = -kx which yields a positive force for negative x. Choice A distracts by suggesting the force is to the left, confusing compression with stretching. Remember, to solve similar issues, visualize the spring's state and confirm the force opposes the displacement vector.

This question evaluates the correct expression for spring force using Hooke's law. The restoring force is directed opposite to the displacement, toward equilibrium, and its vector form is F_s = -kx, where the negative sign ensures opposition. For x = -0.05 m, this yields a positive force (to the right), proportional to the displacement magnitude. The expression accounts for both magnitude and direction without depending on velocity. Choice C distracts by using velocity v instead of position x, which applies to damping, not ideal springs. When facing formula-based questions, recall Hooke's law and substitute values to verify direction and proportionality.

This question probes how spring force magnitude scales with changes in displacement according to Hooke's law. The restoring force opposes displacement and directs toward equilibrium, whether the spring is stretched or compressed. Its magnitude |F| = k|x| is directly proportional to the displacement from equilibrium, independent of velocity or other factors. Changing from x = +0.05 m to x = +0.15 m triples the displacement, thus tripling the force magnitude. Choice D incorrectly ties the force to velocity, which is not a factor in Hooke's law for ideal springs. A general strategy is to compare ratios of displacements to forecast force changes, ensuring you focus on magnitude separately from direction.

This question assesses understanding of spring forces in AP Physics 1, comparing magnitudes at symmetric positions. The restoring force magnitude depends on |x|, not the sign of x, as |F_s| = k|x|. Moving from +0.20 m to -0.20 m keeps |x| the same, so magnitude remains unchanged. The direction flips, but the question asks about magnitude. Choice A is incorrect because doubling does not occur; sign change affects direction, not magnitude. A transferable strategy is to focus on absolute displacement |x| when questions concern force magnitude, separating it from direction.

This question assesses understanding of spring forces in AP Physics 1, comparing forces at different positive displacements. The restoring force is proportional to displacement and always points toward equilibrium. At x = +0.05 m, |F_s| = k0.05 m; at +0.25 m, it's k0.25 m, five times larger, and both point left. The direction remains leftward for positive x. Choice D is incorrect because force is not zero; it increases with displacement. A transferable strategy is to calculate the ratio of displacements to determine how force magnitudes scale in similar positions.

This question assesses understanding of spring forces in AP Physics 1, particularly calculating force magnitudes. The restoring force is proportional to displacement, with |F_s| = k|x| from Hooke's law. At x = +0.10 m, the magnitude is 3 N, so k = 3 N / 0.10 m = 30 N/m. At x = +0.30 m, |F_s| = 30 N/m * 0.30 m = 9 N. Choice A is incorrect because it ignores the proportionality, suggesting no change in magnitude. A transferable strategy is to find k from one position and apply it to others, ensuring consistent use of Hooke's law.

This question assesses understanding of spring forces in AP Physics 1, specifically the direction of the restoring force when a spring is displaced from equilibrium. The restoring force of an ideal spring always acts to return the system to its equilibrium position, opposing the displacement. According to Hooke's law, the force is given by F_s = -kx, where the negative sign indicates it is opposite to the displacement x. Thus, when the block is at x = +0.10 m, the force points to the left, in the -x direction. Choice C is incorrect because the force is not zero; even though the block is at rest, the spring is stretched and exerts a force proportional to the displacement. A transferable strategy is to always determine the direction of the spring force by checking if the displacement is positive or negative and recalling that it points toward equilibrium.

This question assesses understanding of spring forces in AP Physics 1, specifically the direction during compression. The restoring force opposes the displacement, pushing back toward equilibrium when compressed. For a negative displacement like x = -0.12 m, F_s = -k(-|x|) = +k|x|, directing the force to the right. This proportionality to displacement ensures the force magnitude matches k|x|. Choice C is incorrect because springs exert force when compressed, not just when stretched. A transferable strategy is to visualize the spring's state—compressed or stretched—and note the force always points toward the equilibrium position.