Hooke's+Law

Elastic devices, such as springs, exert forces when stretched/compressed

The a spring is neither stretched/compressed, it is said to be at equilibrium, and its position, x, is equal to 0

The force exerted by a spring is equal in magnitude, but opposite in direction to the force applied to the spring (causing a stretch/compression in the spring) – **Newton’s 3rd Law**

o If a spring is stretched in the +x direction, then the force exerted by the spring is in the –x direction o If a spring is compressed in the –x direction, then the force exerted by the spring is in the +x direction

Newton’s 3rd law only holds true once the spring arrives at a new equilibrium position (i.e. the spring returns to rest as a force is applied)

“Experiments with springs show that the magnitude of the force exerted by the spring is directly proportional to the distance the spring has moved from equilibrium” (p. 204 of textbook)

The latter relationship is known as Hooke’s Law (named after Robert Hooke)

Algebraically, we write this relationship as: F = k · x, where

o F is the force exerted by the spring [N], o x is the position of the spring **relative to equilibrium** [m] o k is a proportionality constant known as the **force constant** of the spring (or elastic device) [N/m]

In the case of Newton’s 3rd law, if an applied force stretches a spring in the +x direction, then the applied force applied **to** the spring would take the form F = +kx, while the force exerted **by** the spring would have the form F = -kx (equal in magnitude, but opposite in direction)

If a spring is compressed in the –x direction, the applied force would be F = -kx and the force exerted by the spring would be F = +kx

Hooke’s law applies to any elastic device (other examples include bungee cords).

Any elastic device that obeys Hooke’s law is said to be **ideal.** Elastic devices that do not obey Hooke’s law are considered **real**.