1 · IGCSE Physics
Hooke's law and the limit of proportionality
Hang 100 g masses on a spring or a rubber band and watch each force–extension point appear on the graph. Find the spring constant from the gradient and see what happens beyond the limit of proportionality.
Load:
F = k x (only up to P)
W = m g, g = 9.8 N kg⁻¹
k = gradient = ΔF ÷ Δx
extension x = length − original length
W = m g, g = 9.8 N kg⁻¹
k = gradient = ΔF ÷ Δx
extension x = length − original length
Try this
- With the steel spring, add masses one at a time up to 500 g. Check that the points lie on a straight line through the origin and that the gradient matches the k slider.
- Keep adding masses past P, then remove them all. Read the permanent extension: the spring no longer returns to its original length.
- Switch to the rubber band and load it to 1.0 kg. Describe how the gradient changes as it stretches, and explain why no single k can be quoted.
Common error: reading the gradient from a graph with extension in cm and quoting it in N m⁻¹ — convert to metres first (a gradient of 0.600 N cm⁻¹ is 60.0 N m⁻¹).