In this experiment, you will compare the stiffness of two springs labelled A and B. You hangs each spring in turn from a clamp and measures the extension wh...

(a) The extension values for both springs are recorded: [1]

(b) Graph of extension (y-axis) against mass (x-axis) for both springs: [4]

Spring A data points are plotted as filled circles and spring B as open squares. Both lines pass through the origin, confirming proportional behaviour (Hooke's law). Line B has a steeper gradient, showing greater extension per unit mass.

(c) Spring A is stiffer. [2] For the same load, spring A extends less than spring B. For example, at 250 g, A extends 40 mm while B extends 75 mm. A stiffer spring resists deformation more strongly, producing a smaller extension for the same applied force. On the graph, the stiffer spring has the shallower gradient.

(d) From the graph at a mass of 125 g, the extension of spring B is approximately 37 mm. [1] (Accept 36 to 39 mm.) This is found by locating 125 g on the x-axis, reading up to line B, and across to the y-axis.

(e) The ratio of the extension of B to the extension of A for the same load: [1]

\[ \text{Ratio} = \frac{75}{40} = 1.875 \approx 1.9 \]

This ratio is constant for all loads (e.g. at 100 g: \( \frac{30}{16} = 1.875 \)), confirming both springs obey Hooke's law and the ratio of their spring constants is fixed.

(f) Remove all masses from the spring and measure its length again. [1] Compare this unloaded length with the original length recorded at the start. If they are the same, the spring has returned to its original length and has not been permanently deformed, meaning it remained within its elastic limit throughout the experiment.