elastic force

Meaning: Elastic force is the restoring force exerted by a deformed elastic object, such as an ideal spring, when it is stretched or compressed from its equilibrium length. It comes from the object's bonds resisting the change in shape. For small deformations within the elastic limit, its magnitude is proportional to the displacement and its direction is opposite the displacement, so it pushes or pulls the object back toward equilibrium.

Equation: F = −kx, where F is the elastic force (N), k is the spring constant (N/m), and x is the displacement from equilibrium (m). The stored elastic potential energy is U = ½kx², where U is in joules (J).

On the MCAT: Expect a mass on a spring, hanging or on a frictionless surface. For a hanging mass at rest, set kx = mg and solve for x or k. Predict that doubling the stretch doubles the force and quadruples the stored energy. A force-versus-displacement graph is a straight line whose slope has magnitude k, and the area under it equals the work done. Elastic force also drives simple harmonic motion, where T = 2π√(m/k) and the period does not depend on amplitude.

Common confusion: The minus sign does not mean the force has a negative size. It means the force points opposite the displacement. Also, x is measured from the equilibrium length, not from the spring's full length. The force changes as x changes, so constant-acceleration kinematics does not apply to a mass on a spring.