IGCSE 0625 / Section 1.5 / Core

A spring keeps its promise, up to a point.

Hang a load on a spring and it stretches. Double the load and it stretches twice as far, a tidy straight-line relationship, but only up to a point. Past the limit of proportionality, the spring stops playing fair.

The Key Idea

Up to the limit of proportionality, the extension of a spring is directly proportional to the load: F = kx, where k is the spring constant in N/m. Beyond that limit, extension is no longer proportional to load and the graph curves.

SECTION 01

Straight line, then a curve.

Toggle between a stiff spring and a soft spring. Notice how the stiffer spring has a steeper gradient and can take a much larger load before it passes its limit of proportionality. The softer spring stretches easily but gives up and curves much sooner.

SECTION 02

Reading the graph.

Straight-line region: extension is proportional to load; the gradient gives the spring constant k.
The limit of proportionality: the point where the line stops being straight; beyond it, F = kx no longer holds.
Spring constant: k = F ÷ x in the straight-line region, measured in N/m (or N/cm).
Extension: the increase in length, the stretched length minus the original length.

Use the syllabus term

The point where the straight line ends is the limit of proportionality. Avoid writing "elastic limit", which is a different point on the graph and is not the term the syllabus wants here. When a load-extension graph stops being a straight line, the quantity you name is the limit of proportionality.

Worked Example

A spring extends by 0.080 m when a load of 4.0 N is hung on it, within the proportional region. Find the spring constant, and the load needed for an extension of 0.12 m.

Step 1 : Spring constant k = F ÷ x = 4.0 ÷ 0.080 = 50 N/m

Step 2 : Load for 0.12 m F = k x = 50 × 0.12 = 6.0 N

Step 3 : Note the assumption This is valid only while the spring stays below its limit of proportionality.

Practice this topic

Six original Cambridge-style questions.

Hooke's law and F = kx, finding the spring constant, the load-extension graph, and naming the limit of proportionality correctly. Attempt each, then reveal the worked solution.