A student investigates how four springs (A, B, C, D) stretch under applied forces by hanging masses and measuring extension with a ruler.
Spring A — Force (N): 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 | Extension (cm): 0.0, 2.5, 5.0, 7.5, 10.0, 12.5
Spring B — Force (N): 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 | Extension (cm): 0.0, 1.0, 4.0, 9.0, 16.0, 25.0
Spring C — Force (N): 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 | Extension (cm): 0.0, 3.0, 6.0, 9.0, 12.0, 15.0
Spring D — Force (N): 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 | Extension (cm): 0.0, 1.5, 3.0, ?, 6.0, 7.5
aConstruct a graph of extension (cm) against force (N) for springs A, B, and C on the same axes. [3]
bIdentify which springs obey Hooke's law (F=kx) and explain, using your graph, why Spring B does not. [2] cCalculate the spring constant k (in N/cm) for Spring C. Show your working. [2] dDeduce the missing extension for Spring D at 3.0 N. Justify whether Spring D obeys Hooke's law, using both the completed data set and your findings from parts (b) and (c). [2]