This question tests understanding of spring forces and their restoring nature. When a spring is stretched to the right from equilibrium (positive displacement), it exerts a restoring force back toward equilibrium, which is leftward (negative direction). The spring force follows Hooke's law: F = -kx, where the negative sign indicates the force opposes displacement. Since x = +0.10 m (positive), the force F = -k(0.10) is negative, meaning leftward, and its magnitude is proportional to the displacement x. Choice A incorrectly assumes zero force because the block is at rest, but spring force depends on position, not velocity. The key strategy is to remember that spring forces always point toward equilibrium and are proportional to displacement from equilibrium.

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 evaluates knowledge of Hooke's law and how spring force magnitude depends on displacement. The restoring force in an ideal spring is always directed toward the equilibrium position, counteracting the displacement whether the spring is compressed or stretched. In compression, such as at x = -0.06 m, the force pushes the mass to the right, and its magnitude is given by |F| = k|x|, directly proportional to the absolute value of displacement. Thus, doubling the displacement from -0.03 m to -0.06 m doubles the force magnitude. Choice D is a distractor that wrongly implies the force is zero during compression, ignoring Hooke's law proportionality. A useful strategy for these problems is to calculate the ratio of displacements to predict force magnitude changes without needing the spring constant.

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 investigates changes in spring force when displacement reverses sign. The restoring force always opposes displacement, switching direction to point toward equilibrium as the sign of x changes. From x = +0.02 m to x = -0.02 m, the force shifts from negative (left) to positive (right), but magnitude remains k*0.02 in both cases due to equal |x|. This demonstrates the force's dependence on position, not velocity or history. Choice B incorrectly suggests direction stays the same, overlooking the oppositional nature. A key strategy is to evaluate force at each position independently using F = -kx, comparing direction and magnitude for changes.

This question assesses understanding of Hooke's law and the direction of the restoring force in ideal springs. The restoring force exerted by a spring always acts to return the system to its equilibrium position, opposing the displacement from equilibrium. For a spring stretched to a positive displacement, such as x = +0.10 m, the force pulls the block back toward x = 0, which is to the left or negative x-direction. The magnitude of this force is proportional to the displacement, following F = -kx, where the negative sign indicates the oppositional direction. A common distractor is choice D, which incorrectly suggests the force aligns with the block's velocity rather than opposing the displacement. To analyze similar problems, always determine the direction of the restoring force by checking if the spring is stretched or compressed and remember it points toward equilibrium.

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.