WJEC Physics for AS: Study and Rev Guide

Elastic hysteresis = when a material such as rubber is put under stress and then relaxed, the stress–strain graphs for increasing and decreasing stress do not coincide but form a loop. Key Term 1.5.7 The stress–strain properties of rubber The stress–strain and load–extension graphs have the following features: ▪ ▪ Non-linear: steep → less steep → very steep; Hooke’s law is approximately obeyed only for very low stresses. ▪ ▪ Large strains: up to ~ 5 (or 500%) depending on the type of rubber. ▪ ▪ The stress needed to stretch is low, i.e. the Young modulus is very low. ▪ ▪ Loading and unloading curves different: called elastic hysteresis . Because the area under a load–extension curve is the work done, the work done by the rubber band in contracting is less than the work done on the rubber band in stretching. The area between the graphs represents the energy dissipated in moving once around the hysteresis loop. It manifests itself as random vibrational energy of the rubber molecules. Why does rubber behave like this? 1. The C–C bonds in the long chains can rotate; 2. Successive C–C bonds are at an angle ( ~ 110 ° ) to each other. A rubber molecule in the unstressed state is naturally tangled up: it is very unlikely to form in a linear state [see Fig. 1.5.19 – remember it is 3D]. Applying a small longitudinal force rotates the bonds and straightens out the molecules: no bonds are stretched; large extensions are produced. The force works against the thermal motions of the molecules which tend to pull the ends in. When the force is relaxed, the natural vibration of the molecules tangles up the long chains again. Because of the work done, the molecules end up vibrating more, i.e. energy is dissipated. The energy losses in hysteresis can be useful , e.g. in shock absorbers. It can be a nuisance , e.g. the rolling resistance in car tyres. It can be reduced by introducing cross-linkages between molecules (or different parts of the same molecule) in the process called vulcanisation . 1.5.8 Specified practical work (a) Determination of the Young modulus for the material of a wire Fig. 1.5.18 Stress–strain curve for rubber Fig. 1.5.19 Rotating bonds in rubber molecules stress strain C C C F F wooden blocks clamp scale paper rider load length , l Fig.1.5.20 Young modulus for a wire 59 1.5 Solids under stress