- Mathematically expressed as Force α extension.
Spring constant- Since Force α extension then Force / Extension = constant (k).
- The constant of proportionality (k) is called the spring constant.
F / e = k or Force (N) = k e.
- The spring constant is a measure of the stiffness of a spring. The greater the constant the stiffer the spring.
- The spring constant varies with the following;-
- Material – identical springs mad of different materials will have different constants i.e. steel and copper.
- Diameter – the stiffness decreases with the increase in diameter.
- Thickness of the wire – a spring made of a thicker wire is stiffer than the one made of thin wire of the same material.
- Length of spring – a short spring is stiffer than a longer one.
- Number of turns per unit length – a spring with higher number of turns per unit length is less stiff than the one with fewer turns per unit length.
1. If the springs shown below are similar and the constant of proportionality (k) is 100 Nm-1, determine total extension in each arrangement.
k = 100 Nm-1
extension = force / k = 10 ÷ 100 = 0.1 m = 10 cm. Extension of the lower spring = 10 cm, extension of the two parallel springs = 5 cm.
Total extension = 10 + 5 = 15 cm. Extension of the two lower springs = 5 cm
Middle spring extend by = 10 cm
Upper two springs extend by = 5 cm
Total extension = 5 + 10 + 5 = 20 cm.
The spring balance
- It is made up of a spring mounted in a metal or plastic casing.
- The spring is fitted with a pointer which moves along a calibrated scale divided into ten equal parts.