The taughtness of the wire - Sample Essay
The aim of this experiment is to investigate how the extension of a length of wire is affected by the force. I will then find stress and strain after finding these variables, for which I can finally complete my objective which is to find the young’s modulus for the material, in this case copper wire. Hypothesis I predict that when a wire is subjected to a stretching force, in this case wire being pulled by the force of weight, then the wire likely to be stretched. This does depend on the material as the more flexible the material is the more possibility there is of stretching.
I think that the copper wire will have a young’s modulus of about 130 GPa, as the secondary source has worked this out The stretching force which extends material by equal steps is called Hooke’s law. Equation: Stretching force, F = spring constant, k * extension, ? x (N) (N 1/m) (m) So the lower the gradient the more flexible the spring will be, vice verser. This formula can be used to calculate the spring constant, which means that we can work out the force needed to extend the copper wire by 1 metre.
So we can predict the amount of extension of the copper wire when adding Newton’s. ?x = stretched length – original length k, can also be referred to as stiffness The point before X is the limit of proportionality (F ? x) it is where the strain is proportional to stress. Point X is called the elastic limit, the point at which elasticity ceases and after the material becomes plastic. So smaller the elastic limit the material returns to its original phase, after the elastic limit there is slight extension to the material and after the elastic limit the material now becomes plastic.
The copper wire I will test will be tested so the wire breaks, in my preliminary experiment, I will then be able to decide my range to test the wire. Hooke’s law is important because the young’s modulus works if the extension in material is in equal steps so if this was not the case then the extension could be in any size steps, though if not in equal steps the graph will not show a good proportionality, which affects the experiment as it must be constant, it could give one low and then high so points on a graph would not match up.
I predict that the copper wire will follow a course similar to the graph that I have drawn below; I predict that the stress and strain will be proportional at the start reaching the elastic limit then a dip in stress as strain goes on where there is the yield point (where the weakest part of the wire begins to neck). The strain being much more than the stress, both carry on reaching the tensile strength. Finally after some time the wire will stretch and snap at the ultimate tensile strength. The elastic potential energy
This is also important to the investigation because one of the variables in this rule is the extension, ? x, so the formula: Elastic potential energy = 1/2 stretching force extension (J) (N) (m) Rearranging: 2Ep / F = ? x This means we can work out the extension another way and see how much energy there is in the copper wire. Apparatus G-clamp: to hold down the wire on the wooden block 2 metre rulers in mm: to measure the wire length and the changes Level horizontal table: so it doesn’t affect the experiment by adding more force to the load Sellotape: make a pointer to see the change in wire size.
Smooth pulley with clamp: so no friction can affect the force, F = i?? R Load of masses: at least 1kg of mass to test the wire Copper wire: I will be testing the stretching and so finally the young’s modulus on it Micrometer: to accurately measure the diameter of the wire to 0. 001mm Vernier caliper: to accurately measure the tiny extensions in the length of wire to 0. 1mm Tri-square: measure the downward movement at a 90i?? angle Goggles: to protect the eyes from the wire Gloves: to protect our hands as the thin wire can cut through skin.
Wooden block: to be horizontal with the pulley, so the angle cannot affect the experiment Stress, strain & young’s modulus Stress: the load acting on an object per unit cross-sectional area. This is measured in Pascal’s, and can be though of as pressure acting on an object. This is not the case, this is because stress occurs inside a solid and pressure occurs on a surface. Stress, ? = force, F (N) Cross-sectional area, A (m^2) For e. g. the copper wire, the thinnest part of it would be more likely to stretch, so the thinner the wire the greater the tensile strength.