Physics

Physics

Problem

Which of the following equations correctly gives the restoring force exerted by an ideal spring that has been displaced by Δx\Delta x from its equilibrium position along a straight line? a) F⃗s=−12k Δx⃗\vec{F}_s=-\dfrac{1}{2}k\,\Delta\vec{x} b) F⃗s=k Δx⃗\vec{F}_s=k\,\Delta\vec{x} c) F⃗s=−k Δx⃗\vec{F}_s=-k\,\Delta\vec{x} d) F⃗s=−2k Δx⃗\vec{F}_s=-2k\,\Delta\vec{x}
Intuitive explanation

Hooke's Law describes how springs resist displacement—the farther you stretch or compress it, the harder it pushes back. The key insight is that the restoring force is always proportional to displacement and always points toward equilibrium, which is why a negative sign appears in the equation. You're looking for the relationship that captures both the magnitude (proportional to Δx\Delta x) and the direction (opposite to displacement).

Intuitive explanation

Hooke's Law describes how springs resist displacement—the farther you stretch or compress it, the harder it pushes back. The key insight is that the restoring force is always proportional to displacement and always points toward equilibrium, which is why a negative sign appears in the equation. You're looking for the relationship that captures both the magnitude (proportional to Δx\Delta x) and the direction (opposite to displacement).

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