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# 3-02 - 3-2a If the straight wire illustrated in Figure 3.2a...

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3-2a. If the straight wire illustrated in Figure 3.2a has a uniform mass per unit length equal to ξ , the total mass of the wire is given by o o mass L = ξ If the mass per unit length is given by () x ξ ,the total mass is determined by the following line integral : 0 () xL x mass x dx = = For the following conditions 2 1 o 2 3 o 0.0065 kg/m, 0.0017 kg/m , 1.4 m xx L L ξ= ξ + α α= = determine the total mass of the wire. Figure 3.2a . Wire having a uniform or non-uniform mass density 3-2a. The mass contained in the wire can be expressed as 2 00 ( /2 ) o mass x dx x L dx == = ξ + α ∫∫ (1) and evaluation of the integral leads to 333 324 1 o LLL L mass L L  3 2 o α =ξ + α +   (2) Making use of the data that are given provides (3) 23 (0.0065 kg/m ) (1.4m) (0.0017 kg/m ) (1.4m) /12 mass =+ 3 and the mass is calculated to be 0.0095 kg mass = (4) 3.2b. If the flat plate illustrated in Figure 3.2b has a uniform mass per unit area equal to ψ , the total mass of the plate is given by o oo mass A L L 1 2 = ψ= ψ

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If the mass per unit area is given by (, )
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3-02 - 3-2a If the straight wire illustrated in Figure 3.2a...

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