WJEC Physics for AS: Study and Rev Guide

Pointer The analysis of the data is as follows: E = Δ l , , so F = Fl 0 A Δ l EA l 0 where A = π . d 2 4 So the gradient, m , of the graph is given by m = . ∴ E = EA l 0 l 0 m A A long piece of wire is used, with l typically about 2 m. The blocks are to prevent damage to the wire. The original length l 0 is measured using a metre rule (giving an uncertainty of ~ 0.1 %). The extension is measured using the paper rider (or a paint blob) and the mm scale – this is the least precise part of the experiment. For accurate work a travelling microscope can be used. The tension is determined from the mass of the load – typically increased in 0.1 kg steps – and use of W = mg . After the maximum load is reached, the load is decreased and the mean of the D l values for each of the two values of load is calculated. The diameter of the wire is determined using a micrometer / digital calliper (giving an uncertainty of 0.01 mm, i.e 3% for a 0.3 mm diameter wire). A graph is plotted of F against D l . The value of the Young modulus is calculated from the gradient as shown in the Pointer. Sample data: Copper wire; l 0 = 2.105 ± 0.001 m; d = 0.38 ± 0.01 mm; gradient = 6200 ± 300 N m –1 . Calculation: Gradient m = , so E = = = 115 2 π 0.38 × 10 –3 2 2.105 m × 6200 N m –1 l 0 EA A l 0 m GPa Uncertainty : % uncertainties: d – 2.6%; gradient – 4.8%; l 0 – 0.05% [ignore]. So total uncertainty = 2.6% + 4.8% = 7.4%. 7.4% of 115 = 8.5 So E = 115 ± 9 GPa (b) Investigation of the force–extension relationship for rubber This experiment is carried out as for the spring in Section 1.5.1. The extensions are measured for increasing loads until the rubber band shows very little additional extension. The load is then gradually decreased and the extensions measured. A load–extension graph of the same shape as the graph in Fig. 1.5.2 is obtained, clearly showing elastic hysteresis. Fig. 1.5.21 Force–extension for rubber 60 AS Physics: Study and Revision Guide