Strain ε ௦ ௦ ࢤ బ where ઢ l change in

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Strain ( ε )= ஼௛௔௡௚௘௜௡ௗ௜௠௘௡௦௜௢௡ ை௥௜௚௜௡௔௟ௗ௜௠௘௡௦௜௢௡ = ࢤࡸ Where L = change in length ܮ = Original length Example Calculate the tensile strain in a member of a strut 2m long, which extends by 0.03cm when under a load. Solution Strain ( ε ) = ࢤࡸ L = 0.03cm ܮ = 2m x 100 200cm ε = ࢤࡸ = ଴.଴ଷ௖௠ ଶ଴଴௖௠ = 1.5x10 4
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Prepared By: ChilesheMwenyaMporokoso Page 63 THERMAL STRAIN Change in temperature in a material gives rise to a thermal strain. The extension in a bar of length L is given by; L = α ܮ θ Where = α = Coefficient of linear expansion ܮ = original length θ = change in temperature ε = ࢤࡸ = ஑௅ ୼஘ = α θ ε = α θ HOOKE’S LAW Many objects such as a coiled spring or a metal rod exhibit a property called elasticity. When stretched or compressed by an applied force, they tend to return to their original length when a force is removed provided the elastic limit is not exceeded. Beyond the elastic limit, they material loses its elasticity. HOOKE’S LAW states that when an object is distorted, the amount of distortion is linearly proportional to the distortion provided the elastic limit is not exceeded. From hooke’s law Stress Strain Stress = E x Strain
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Prepared By: ChilesheMwenyaMporokoso Page 64 E = ௌ்ோாௌௌ ௌ்ோ஺ூே Where E = Young’s Modulus Example A 2.6kg mass is attached to the end of a vertical wire of length 2m and diameter 2mm. If the wire extended by 0.08mm, Calculate ; Solution F = W = mg = 2.6x9.81 = 2.506N ܮ = 2m = 2000mm L = 0.08mm r = = 1mm = 1mmx ଵ௠ ଵ଴଴଴௠௠ = 1.0 x 10 3 A = π r 2 = π (1.0 x 10 3 ) 2 = 3.142 x 10 6 m 2 (a) σ = ி = ଶ.ହ଴଺ ଷ.ଵସଶ௫ ଵ଴ షల = 8.11x10 6 N/m 2 (b) ε = ࢤࡸ = ଴.଴଼௠௠ ଶ଴଴଴௠௠ = 4.0 x 10 5 (c)E = = ଼.ଵଵ ௫ ଵ଴ ସ.଴ ௫ ଵ଴ షఱ = 2.027 x 10 11 N/m 2 ULTIMATE TENSILE STRESS ( U.T.S) This is the ratio if the maximum load to the original cross sectional area ( U.T.S) = ெ௔௫௜௠௨௠ ௟௢௔ௗ ௢௥௜௚௜௡௔௟ ௖௥௢௦௦ି௦௘௖௧௜௡௔௟ ௔௥௘௔
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Prepared By: ChilesheMwenyaMporokoso Page 65 FACTOR OF SAFETY This is the ratio of the ultimate tensile stress to the working stress Example An aluminium wire with an initial length L= 25m and diameter d = 2m is used to lift a 10kg load. Determine (i)The length of the wire (ii)working stress in the wire (iii)Strain in the wire (iv)The factor of safety (v)The maximum load that the wire can support [Young’s modulus for aluminium ε = 7.0 x 10 10 N/m 2 , ultimate tensile strength (U.T.S) for aluminium is 1.4 x 10 8 Pa]. UNIT 2.0: HEAT AND TEMPERATURE Heat is a form of energy which is transmitted between two bodies at different temperatures. Temperature is the degree of hotness and coldness of an object. INSTRUMENTS USED FOR MEASURING TEMPERATURE A thermometer is a device used for measuring temperature The principle of operation of the thermometer is based on some of effects such as; i. Expansion ii. Increase in pressure iii. Electrical changes i. The following are some of the common types of thermometers. LIQUID IN GLASS THERMOMETER
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Prepared By: ChilesheMwenyaMporokoso Page 66 ii. These depend on the expansion of the liquid (mercury or alcohol) used.
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