Electricity and Magnetism - Sample Essay
To plan an experiment to measure the extension in a piece of copper wire, taking accuracy to be of the utmost importance. The aim is to determine the Young’s Modulus of the copper wire. Introduction: I am required to investigate how the extension e of a length of copper wire changes as the stretching force F is increased. In doing this, making sure I play careful attention to safety. Accuracy is the main issue in this experiment, so it has to be taken into account, in the equipment used, this means that the percentage error has to be at its lowest possible value.
There many things that I can look at which are related to this investigation, such as the Young’s modulus of a wire: Stiffness is a measure of the resistance to deformation such as stretching or bending. The Young modulus is a measure of the resistance to simple stretching or compression. It is the ratio of the applied force per unit area (stress) to the fractional elastic deformation (strain). Its SI units are MN/m2 (meganewtons per sq m) or, equivalently, MPa (megapascals). The properties of materials can be looked at also: Elasticity.
This is the ability of a material to return to its original shape and size after distorting forces (i. e. tension, where this investigation is concerned) have been removed. Materials, which have this ability, are elastic: those, which do, not, are plastic. Elasticity is a result of intermolecular forces- if an object is stretched or compressed, its molecules move further apart or closer together respectively. This results in a force of attraction (in the first case) or repulsion (in the second), so the molecules return to their average separation when the distorting force is removed.
This always happens while the strength of the force is below a certain level (different for each material), but all elastic materials finally become elastic if it exceeds this level (elastic limit and yield point). Hooke’s law. States that, when a distorting force is applied to an object, the strain is proportional to the stress. As the strength of the force increases, though, the limit of proportionality is reached, after which Hooke’s law is no longer true. Piece of wire under extension Strain is stated as change in length per unit length. Strain = e l Where e = change in length; l = original length.
Stress is stated as force applied per unit area. Stress = F A Where F = force applied; A = cross-sectional area. Elastic limit. The point, just after the limit of proportionality, beyond which an object ceases to be elastic, in the sense that it does not return to its original shape and size when the distorting force is removed. It does return to a similar shape and will continue to return to this new form if forces are applied, i. e. it stays elastic in this sense. The yield stress of a material is the value of the stress at its elastic limit. Yield point.
The point, just after the elastic limit, at which a distorting force causes a major change in a material. In a ductile material, like copper, the internal structure changes- bonds between molecular layers break and layers flow over each other. This change is called plastic deformation. (The material becomes plastic). It continues, as the force increases, and the material will eventually break. Below is a stress/strain graph for a ductile material, like copper. The tension force acts on the wire when it is under stress and strain, it is equal and opposite which, when applied to the ends of an object, such as a wire, increase the length.
The intermolecular force resists them. From my research, I found that the Young’s Modulus of copper is 11. 0 x 1010 Nm-2, from The Usborne Dictionary of Science. Prediction: Having overlooked my background knowledge and the research done, I can predict, that Hooke’s law will be true from the start of the experiment to the limit of proportionality shown in fig. 1. Therefore, I feel that the copper wire will follow the same trend line as in fig. 1. I think that when the weights applied, (hence stretching force) is increased the extension increases proportionally. However, this is true up to the point at which the wire reaches its elastic limit.
As well as this, the wires cross-sectional area will decrease as the length of the wire increases because of the tension, stress and the strain, which act on the wire. Fair test: However, the accuracy of the experiment depends on the thickness of the wire used initially and the temperature of the wire/ room. The thicker the wire, the more force needed to extend the wire, and vice versa. The temperature affects the state of the wire, if the wire is warm it will extend further, hence the longer length, but a cold wire, will no make much of an extension and is likely to snap quicker than a warm wire.