Hooke's Law and Spring Stiffness

Steps:

• Recall Hooke's Law: The restoring force F in a spring is proportional to its extension x, so F = kx.
• Rearrange the formula to solve for k: k = F / x.
• Recognize that k measures the spring's stiffness as the force required per unit extension.
• Compare to options: D matches force divided by extension.

Why D is correct:

• Hooke's Law defines the spring constant k as force per unit extension (k = F/x), quantifying how stiff the spring is.

Why the others are wrong:

• A: This is the inverse (x/F), called compliance, not stiffness.
• B: Force times extension (Fx) equals kx², related to potential energy but not k.
• C: Identical to B, so also incorrect for the same reason.

Final answer: D