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Question: you were asked to design a canoe paddle used to...

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You were asked to design a canoe paddle used to help propel the boat across the water. The paddle consists of three main parts: handle, shaft, and blade (Figure 4). For simplicity, consider only the shaft as a beam. The paddle should be as light as possible, but must also be stif (a) (i) Write down the objective, function, constraints, and free variable. (ii) Derive the performance index. (ii) Use the result in (ii) and material properties given in Table 4 to select the subset of three candidate materials using the appropriate materials selection chart. (iv) Using the cost of materials given in Table 4, how would the selection be affected? (13 marks) Shaft Handle Blade Figure 4 Table 4 Materials Steel Aluminium Titanium Elastic Modulus (Gpa) Density (Mg/m) 7.8 2.7 4.5 4.0 3.2 1.3 Cost (S/kg) 0.5 2.5 10 1.5 27 1.0 0.8 0.45 200 210 70 115 390 450 AI SiC Polystyrene Glass Wood Carbin Fibre 70 12 200 1.5 Composite
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