Investigating the Relationship Between Force and
Extension (Hooke’s Law)
Objective:
To investigate how the extension of a spring changes as the applied force increases, and to verify
Hooke’s Law.
Background Theory:
Hooke’s Law states that: “The extension of an elastic object (like a spring) is directly proportional to
the force applied, provided the limit of proportionality is not exceeded.”
Mathematically: F = k × e, where F is the applied force (N), k is the spring constant (N/m), and e is
the extension (m).
A graph of force versus extension should be a straight line through the origin, with gradient equal to
the spring constant.
Apparatus:
• Retort stand and clamp
• Spring
• Metre rule or ruler (with millimetre scale)
• Set of weights (e.g., 0.5 N, 1 N, 1.5 N, etc.)
• Weight hanger
• Pointer (e.g., paper marker on spring)
Method:
1 Set up the spring vertically on the retort stand with a pointer attached.
2 Record the initial position of the pointer (unstretched length).
3 Hang a known weight on the spring and record the new position of the pointer.
4 Calculate the extension as the difference between the new and initial lengths.
5 Repeat with increasing weights (e.g., every 0.5 N up to 3 N).
6 Record all results in a table.
7 Plot a graph of force (y-axis) against extension (x-axis).
8 Determine the spring constant (k) from the gradient of the graph.
Example Data Table:
Load (N) Extension (cm)
0.5 1.2
1.0 2.4
1.5 3.5
2.0 4.7
2.5 5.8
3.0 6.9
Graph Work and Sample Calculation:
Plot force (N) on the y-axis and extension (cm or m) on the x-axis. Draw the best-fit line. Gradient =
∆F / ∆e = spring constant (k).
Example: If Force = 2.0 N and Extension = 4.7 cm = 0.047 m, then k = 2.0 / 0.047 = 42.6 N/m.
Sources of Error:
• Parallax error when reading the scale.
• Zero error in ruler alignment.
• Spring may vibrate when weights are added.
• Spring exceeding elastic limit (non-linear behavior).
Improvements:
• Use a pointer and vertical ruler to reduce reading error.
• Wait for oscillations to stop before taking measurements.
• Repeat readings and calculate an average.
• Do not exceed the spring’s elastic limit.
