A spring produces the following (extension in cm, force in N) readings: (0, 0), (1, 0.25), (2, 0.5), (3, 0.75), (5, 1). (a) Determine its spring constant from the straight section, in N/m. (b) Identify the first listed reading that departs from direct proportionality. (c) Explain why loading data alone cannot prove permanent deformation and give an additional measurement.

Question

Accepted Answer

25 N/m; the 5 cm reading departs; unload and check the original zero-load length. Hooke's law states that force is proportional to extension within the proportional region. The points from zero to 3 cm lie on a straight line through the origin, so their gradient gives the spring constant. Convert 3 cm to 0.030 m before calculating k = F/x = 0.75/0.030 = 25 N/m. Using centimetres without conversion would produce N/cm instead. At 5 cm the proportional model predicts 1.25 N, but the recorded force is 1 N. Thus this point departs from the straight-line relation; the exact limit lies somewhere between the last proportional point and this point. Nonlinear loading does not by itself establish a permanent change in length. Remove the loads and measure the zero-load length again: a residual extension would show permanent deformation. Read the scale at eye level and do not overload a real spring.

Spring loading data 2

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Spring loading readings

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Spring loading readings — supplied values
Extension / cm	Force / N
0	0
1	0.25
2	0.5
3	0.75
5	1