welcome to the world of physics
MR v. ABRAHAM
YEAR 12 CIE AS EXAMS
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YEAR 11 REVISION PAST PAPERS YEAR 10 OPTICS UNIT TEST WAVES ON SUNDAY YEAR 9 PHYSICS 3 UNIT TEST PHYSICS ON SUNDAY YOUNG MODULUS Introduction When a stretching force (tensile force) is applied to an object, it will extend. We can draw its force  extension graph to show how it will extend. Note: that this graph is true only for the object for which it was experimentally obtained. We cannot use it to deduce the behaviour of another object even if it is made of the same material. This is because extension of an object is not only dependent on the material but also on other factors like dimensions of the object (e.g. length, thickness etc.) It is therefore more useful to find out about the characteristic extension property of the material itself. This can be done if we draw a graph in which deformation is independent of dimensions of the object under test. This kind of graph is called stress strain curve. Stress Stress is defined as the force per unit area of a material. i.e. Stress = force / cross sectional area: where, σ = stress, F = force applied, and A= cross sectional area of the object. Units of s : Nm2 or Pa. Strain Strain is defined as extension per unit length. Strain = extension / original length where, ε = strain, lo = the original length e = extension = (llo), and l = stretched length Strain has no units because it is a ratio of lengths. We can use the above definitions of stress and strain for forces causing tension or compression. If we apply tensile force we have tensile stress and tensile strain If we apply compressive force we have compressive stress and compressive strain. A useful tip: In calculations stress expressed in Pa is usually a very large number and strain is usually a very small number. If it comes out much different then, you've done it wrong! Young Modulus Instead of drawing a force  extension graph, if you plot stress against strain for an object showing (linear) elastic behaviour, you get a straight line. This is because stress is proportional to strain. The gradient of the straightline graph is the Young's modulus, E E is constant and does not change for a given material. It in fact represents 'stiffness' property of the material. Values of the young modulus of different materials are often listed in the form of a table in reference books so scientists and engineers can look them up. Units of the Young modulus E: Nm2 or Pa. Note: The value of E in Pa can turn out to be a very large number. Therefore some times the value of E may be given MNm2. If you plot a stress against strain of a material with the (linear) elastic behaviour, you get a straight line. i.e. stress is proportional to strain. The gradient of the above straight line is the Young's modulus, E and E is constant and does not change for a given material, no matter what the size of the sample we test. It can be considered as a property of the material. The value of E reflects the stiffness of the material. Stiffer materials have higher values of E. Young's modulus values of different materials are often listed in the form of a table in reference books so scientists and engineers can look them up. Units of the Young modulus E: Nm2 or Pa. Note: The value of E in Pa can turn out to be a very large number. It is for this reason that, some times the value of E may be given MNm2. Note: Because 'stress' and 'strain' are (uniquely) related to force and extension, it is not surprising that the two graphs, stress v/s strain and force v extension, have similar shapes and characteristics. Experimental Determination of stressstrain graph and E We can experimentally determine the value of E by choosing a specimen of the material in a convenient shape and form. For example, it is easier to deal with a specimen in the form of a long, thin wire for determining the value of Young's modulus of a metal. In principle we can apply different forces to a wire by hanging different weights on it and measure the extension of the wire for the magnitudes of the force applied to draw a stress strain graph. We have already noted that strain is a small number so it needs to be measured more accurately. We can do this by using : Searle's apparatus This is a schematic diagram of the apparatus. We actually use two wires of equal lengths attached to a rigid support. Although the support is rigid it to can 'give' slightly under the forces applied. This can affect results. By using two wires, spurious strain can be eliminated from the measurements. One wire acts as a control wire. We can accurately measure extension of the other (test) wire. Both control and test wires are attached to the other ends by a horizontal bar supporting a spirit level. The bar is hinged to the control wire so that when the test wire is extended due to the addition of weights on the side of the test wire, the spirit level is tilted by a small amount. We can remove any tilt of the spirit level and restore it to the horizontal position by turning the screw of a micrometer, which is positioned on the test wire side and making the bar mounted spirit level travel in the desired direction. Caution: It is possible that a wire under tension can snap suddenly and damage eyes. Wear safety glasses. It is also possible that weights attached to the wires could fall down and land on your feet or other part of the body. Experimental determination consists of the following steps: Step 1: Attach equal weights both wires to make them equally taut. Step 2: Measure the initial length of the wire several times to obtain the average value of lo Step 3: Measure the diameter of the wire at several points along the wire and the average value of the diameter (d) and then calculate the circular crosssectional area From the formula: A = (πd2) Step 4:Adjust the spirit level so that it is in the horizontal position by turning the micrometer. Record the micrometer reading to use it as the reference reading. Step 5:Load the test wire with a further weight. Wait while the wire is being stretched to the equilibrium position and the spirit level is maximally tilted. Step 6: Adjust the micrometer screw to restore the spirit level into the horizontal position. Step 7: Subtract the first micrometer reading from the second micrometer reading to obtain the extension (e) of the test wire. Step 8: Calculate stress and strain from the formulae and Step 9: Repeat steps 4,5,6 to obtain more values of stresses and strains Step 10: Plot the above values on stress strain graph; it should be a straight line. Determine the value of the gradient E. Worked example A wire of length 2m and diameter 0.4mm is hung from the ceiling. Find the extension caused in the wire when a weight of 100N is hung on it. Young Modulus (E) for the wire is 2.0 x 1011 Pa. Answer: e ~ 8 mm. Stress  strain graph beyond elastic behaviour In this 'Learnit' so far, we have drawn stressstrain graphs for the elastic behaviour of a material. In the elastic region the stressstrain graph is a straight line. We can, however draw a stress strain graph beyond the elastic region. The graph, then becomes nonlinear because Hooke's law is not obeyed and stress is not proportional to strain. My name is Vellareth Abraham. I have a Master’s degree in Physics and Chemistry and also hold a Bachelor of Education degree. After I graduated, I started my teaching career in South Africa, and taught Physics for eleven years in a Secondary School. During this time I was appointed as chief examiner for Physics IGCSE exams. I then wanted to further enhance my teaching career and decided to move to the UK and worked as a Key Stage 3 and 4 Physics teacher for ten years. For the last five years, I have been teaching Physics in Qatar to IGCSE and A level students. During these five years, I got the opportunity to work as Assistant Principal, Academic coordinator, Resource coordinator and as Head of department.

