Calculate Young`s modulus Essay
Calculate Young`s modulus
Thus of course meaning that factors that need to be kept constant must be identified and kept that way. In this scenario I will be isolating Force as my variable. Force is directly related to the load on the wire; only multiplied by the gravitational pull (approx. 9. 81) as the load is measured in Kg as it is a mass. From the equation we can see that a change in Force will indeed affect the extension of the wire, at this stage it is apparent to say that; Theoretically the larger the force the greater the extension according to the equation above, as it is the value that is being divided.
Following this it is also imperative that both the Cross sectional area of the wire is indeed accurately measured, as well as remaining constant through out the experiment, as a change in this value would indeed effect the value for Tensile stress, and in turn the extension. The length of the wire must also remain consistent through out the experiment. This is because each unit of wire will stretch or elongate by a proportional amount to the load being applied to it. Thus changing the length of will increase or decrease the amount of units of wire that can be stretched, causing different readings to be measured.
The wire will indeed elongate and extend no matter what the length, but for these experimental purposes it is best to be long as explained above to stand a greater chance of measuring it properly.
The important thing is to set the length of wire you wish to work with and do not change it. B) Implementing Results, observations and description. Cross sectional diameter of wire Measurement number and degrees of rotation 1/mm 2/mm 3/mm 1/ Average Calculation of Average wire diameter=Thus the average cross sectional area of the wire is Force = mass 9. 81 ms Table of readings Final length, attempt;
Mass/g Mass/Kg Force/N Orig. L/M 1/M 2/M 3/M Mean Extensionnfortunately errors can easily occur in this experiment, the first way of minimizing the percentage error in the experiment is to identify the sources that could cause such a problem; these being. When measuring the extension there are 3 main sources of uncertainty.
Meter rule Parallax error Zero error I plan to minimize these by; Careful choice of meter rule, as man are bent and warped Fixing a head and eye position against something so that the parallax error is minimized as I will be looking at the ruler from exactly the same angle. Record results from 0. 0 M If there is a zero error, take it away from the results. When measuring the weight of the mass the following sources could effect the results; Zero error on the scales Not allowing for the weight of the cradle
Simply using the weight that is imprinted on the mass instead of weighting it. I will minimize these sources by selecting my masses carefully and weighing each one separately to find its exact weight, as well as double checking a pair of scales against each other by putting the same weight on both scales to see if there is a zero error. The final measurement source of error is the measurement of the diameter of the wire. This is typically a source of inaccuracy because the wire does vary in cross sectional area, because of the way it was made.
This can be accommodated for by measuring the wire extremely accurately with the micrometer, and measuring the wire in three different areas of the length and taking two readings at each of the three points along the wire, twisting it 90 degrees at each point to allow for ovals etc. The average can then be taken and used in the calculations to give a better representation of the wire being used Diagram of ideal and misshapen wire. Observations for experiment conducted on the 14th of December 2002 * At approximately 0930 the equipment was set up and the working area was in suitable condition to go ahead with the experiment as planned.
I had two main concerns whilst conducting the experiments, these were of measuring natures, the first of these being that, when measuring the wire with the micrometer it proved initially extremely hard to turn the wire 90 degrees, I quickly remedied this by sticking a label on the wire so that it was clear what angle the wire had to be turned. The second was that of concerning minimization of the parallax error, this proved to be quite challenging, so we decided to look at the ruler twice each a couple of seconds apart and in what i8 thought was the same position to see if it was a fair test.
This way through up different results so we deemed it necessary to have someone stand over the wire and not move until the experiment was finished to minimize this risk. Another observation I made was that I didn’t think we were measuring the extension accurately enough I felt that measuring it to 1mm was far to inaccurate as the extension as will be seen by the graphs was minimal, I will mention this point heavily in the Evaluating. The equipment was packed away and the experiment was completed within the hour. I observed a changing in mass or load on the wire and no change in any of the identified variables.
C Analyzing Evidence and Drawing Conclusions. Force/N Area/M Sress/Nm (Pa) Length/M Extension/M Strain Youngs modulus 1 The stress was simple to calculate as it simply meant dividing the force by the area, as so; The strain is a simple ratio it involves dividing theextension by the length; Thus the young’s modulus can be found for every plotted point separately on the graph; this is done by dividing the stress by the strain.
As I predicted earlier the material obeys hookes law and froms a straight line through the origin until the elastic limit is reached. As well as we can calculate the extension from the gradient of the graph because its equal to L / EA. When a material obeys Hooke’s law, then its force, extension graph is a straight line through the origin (see graph). This is only the case up to the proportional limit. The graph being a graph of force against extension, the area is the energy stored in the wire. As the equation of the graph is F=kx, the equation of the area is .
From the graph we can say that as the load increases on the wire the extension also increases proportionally, up to a certain point known as the elastic limit, this is because it is obeying kooks law as described above, and for this material whilst under low load the strain is proportional to the stress.. Show preview only The above preview is unformatted text This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.
University/College: University of Arkansas System
Type of paper: Thesis/Dissertation Chapter
Date: 13 October 2017