Hooke's Law states that the force needed to extend or compress a spring by a given distance is proportional to which quantity?

Hooke's Law states that the force needed to extend or compress a spring by a given distance is proportional to which quantity?

• A. The acceleration
• B. The displacement
• C. The mass
• D. The velocity

Answer: (B)

A spring’s restoring force increases directly with how far you move it from its rest length. In Hooke’s law, this is expressed as F = -k x, where x is the displacement from equilibrium and k is the spring constant. The negative sign simply means the force acts to pull the spring back toward the equilibrium position. So doubling the stretch doubles the force (within the elastic, linear range). Acceleration comes from the resulting force via F = m a, so mass determines how rapidly the motion responds to that force, not how the force scales with displacement. Velocity, being how fast the displacement is changing, doesn’t set the force in Hooke’s law. The proportionality to displacement holds only for ideal springs in the linear region, beyond which the relation can become nonlinear.

A spring’s restoring force increases directly with how far you move it from its rest length. In Hooke’s law, this is expressed as F = -k x, where x is the displacement from equilibrium and k is the spring constant. The negative sign simply means the force acts to pull the spring back toward the equilibrium position. So doubling the stretch doubles the force (within the elastic, linear range).

Acceleration comes from the resulting force via F = m a, so mass determines how rapidly the motion responds to that force, not how the force scales with displacement. Velocity, being how fast the displacement is changing, doesn’t set the force in Hooke’s law. The proportionality to displacement holds only for ideal springs in the linear region, beyond which the relation can become nonlinear.