Hooke's Law
Section: Deformation of Solids | Syllabus: Cambridge AS Level Physics (9702)
Hooke's Law
In 1678, Robert Hooke found that the extension (x) of a spring is proportional to the load (force) applied (F), provided the limit of proportionality is not exceeded.
Force (N) = spring constant (N m^-1) × extension (m)F = kx
The spring constant (k) is a measure of stiffness. A larger k means the spring is stiffer (harder to stretch).
Figure 6.2: Investigating Extension
((a) Apparatus setup with clamp, spring, weights, and pointer/rule. (b) Force-extension graph showing a straight line through origin up to the limit of proportionality.)
Experimental TipUse a pointer attached to the bottom of the spring and read the scale with your eye aligned with the pointer to avoid parallax error.
Note: When plotting, Extension is often on the x-axis. The gradient of the straight section equals the spring constant k (if F is on y-axis).
Worked Example: Newton MeterQuestion: A newton meter measures loads up to 50.0 N. The extension at maximum load is 61 mm. Calculate the spring constant.
Answer1. Convert to SI units: x = 0.061 m.
2. Use k = F/x: k = 50.0 / 0.061 = 820 N m^-1.
Experimental Skills 6.1: Combinations of Springs
Springs can be combined in series or parallel.
Figures 6.5 & 6.6: Spring Combinations
(Show (a) Two springs in Parallel with a light rigid bar, and (b) Two springs in Series.)
- Parallel: The load is distributed (shared). Effective k increases (k_total = k_1 + k_2). Harder to stretch.
- Series: Each spring experiences the full load. Total extension is sum of individual extensions. Effective k decreases (1/k_total = 1/k_1 + 1/k_2). Easier to stretch.
Interactive revision notes, videos and practice questions load below.