(1) Derive the equations for relative deflections of the cantilever due to the gravity- and surface tension-induced forces. Draw both graphs by using the following parameters

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For gravity: p=7800kg/m', g=9.8m/sec, E=200GPA, t/l=0.1 For surface tension: t/l=0.1, y=0.073N/m (note that the cross section of the cantilever in surface tension is a square having a length t. Thus the equation needs to be revised for this problem.) wx² \(6L° – 4Lx+ x²) У(х) %— 24 EI У = pgt (for gravity), I=- w = 2y (for surface tension; t is neglected for 12 where surface tension) Y max Relative deflection: ( (2) Find the length at the crossing points of two graphs. You can either solve the equations or use numerical methods. For gravity: p=7800kg/m', g=9.8m/sec, E=200GPA, t/l=0.1 For surface tension: t/l=0.1, y=0.073N/m (note that the cross section of the cantilever in surface tension is a square having a length t. Thus the equation needs to be revised for this problem.) wx² \(6L° – 4Lx+ x²) У(х) %— 24 EI У = pgt (for gravity), I=- w = 2y (for surface tension; t is neglected for 12 where surface tension) Y max Relative deflection: ( (2) Find the length at the crossing points of two graphs. You can either solve the equations or use numerical methods.