Checking a spring’s force–extension data

Part (a) marking points

Final answer: 40 N m⁻¹. Numerical checks assess the final value only; they do not check working or the number of digits typed.

1. Use F/x = 2.0/0.050. (1 method mark)
2. Obtain 40 N m⁻¹. (1 accuracy mark)

No earlier numerical result is required. Award method credit for valid working and accuracy credit for the stated answer. Accept a defensible equivalent method; wrong physics cannot earn dependent accuracy credit.

Common errors: This reverses F/x.

Part (b) marking points

Final answer: 0.050 J. Numerical checks assess the final value only; they do not check working or the number of digits typed.

1. Use ½kx² or triangular area under force–extension. (1 method mark)
2. Obtain 0.050 J. (1 accuracy mark)

Use the spring constant from part (a) in ½kx². Alternatively use the triangular force–extension area directly.

Common errors: The force increases from zero. Use a triangular area or the factor ½.

Part (c) marking points

1. At 1.2 N, extension 0.042 m is inconsistent with the trend (about 0.030 m expected). (1 independent mark)
2. Repeat that load/reading and check measurement or transcription before deciding whether to exclude it. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Part (d) marking points

1. Remove the load and measure residual extension. (1 independent mark)
2. A non-zero permanent extension after unloading indicates that the elastic limit was exceeded. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Common errors: A curved loading graph alone proves plastic deformation: non-Hookean behaviour and permanent deformation are different tests.