Physics

Physics

Problem

Which of the following equations gives the restoring force exerted by an ideal spring on an attached object that is displaced a distance Δx\Delta x from equilibrium along a straight line? a) Fs=−12k ΔxF_s=-\dfrac{1}{2}k\,\Delta x b) Fs=k ΔxF_s=k\,\Delta x c) Fs=−k ΔxF_s=-k\,\Delta x d) Fs=−k ∣Δx∣F_s=-k\,|\Delta x|
Intuitive explanation

Hooke's Law describes how springs resist displacement: the restoring force is always proportional to how far you've pulled or pushed the spring away from its resting position, and it always points back toward equilibrium. The key insight is that the force opposes the displacement, so if you displace the spring in one direction, the force pushes back in the opposite direction—this opposite-sign relationship is what makes it "restoring."

Intuitive explanation

Hooke's Law describes how springs resist displacement: the restoring force is always proportional to how far you've pulled or pushed the spring away from its resting position, and it always points back toward equilibrium. The key insight is that the force opposes the displacement, so if you displace the spring in one direction, the force pushes back in the opposite direction—this opposite-sign relationship is what makes it "restoring."

Browse the problem library