6.2 Hooke's Law
If a force F is applied on a spring to stretch or compress it, the extension or compression x has been found to be directly proportional to the applied force within the elastic limit. Thus:
F ∝ x
F = kx
k = F/x ............ (6.1)
where k is the constant of proportionality and is known as the spring constant. In fact, it is a measure of the stiffness of the spring. The greater the value of the spring constant, the greater is the stiffness or strength of the spring. Its unit is N m⁻¹.
A graph of force against extension is a straight line passing through the origin. If the applied force or load exceeds the elastic limit of the spring, it is permanently deformed and its graph will no longer remain linear. The gradient or slope of the force-extension graph is a measure of the spring constant k.
Hooke's law also holds when a force is applied to a straight thin wire or a rubber band within its elastic limit.
lightbulbActivity 6.1 Suspend a helical spring from a stand. Adjust a pointer so that it can move freely along a scale. Place a slotted weight in the hanger and note the position of the pointer. Repeat this step five times, each time increasing the load by equal amounts. Draw a graph between force F along the y-axis and extension x along the x-axis. Find the slope of the straight line. What does it represent?