When in use, a fishing rod can be approximated to act as a cantilevered beam. Assume that the force (P) is applied to the end of the beam by a fish while the fisherman rigidly holds the other end of the beam. The deformation (Delta) of the rod is given by the following equation: (Delta = PL^3/3EI)
Assume that the length of the rod is fixed (ie., can not be changed) and the cross section of the rod is square. The dimensions of the cross section can be varied to answer the questions below, but the section must remain square. You should assume the materials behave as a linearly elastic material.
a) Develop an equation that determines the mass of the finishing rods in terms of the materials properties (e.g. elastic modulus and dimension), section geometry (e.g. cross sectional length and length), and the design inputs (e.g. load and deformation)
b) Using the data below, determine which of the materials should be used if we want to make the lightest rod (assume all the rods have the same siffness)
c)Using the data below, determine which of the materials should be used if we want to make the most economic rod (assume all the rods have the same stiffness)
Candidate Material / E (Gpa) / Density (kg/m^3) / Price ($/tonne)
Stainless steel / 200 / 7800 / 3700
Aluminum alloy / 69 / 2700 / 3000
Fiberglass / 35 / 1800 / 3300
Carbon fiber rienforced polymer / 270 / 1500 / 270000
*1 tonne = 1000 kg