a wood circular cylinder having a specific

Question

A wood circular cylinder, having a specific gravity, S, of 0.54, floats in water as shown in Figure P4.

 

Figure

For a floating body, the weight of the floating body equals the weight of fluid displaced, thus

                                            where

            S = the specific gravity of the wood.

            γ_w= the specific weight of water.

            R = the radius of the cylinder.

            L = the cylinder length.

            V = the volume of water displaced

             

The integral was obtained from integral tables. Substituting the limits of integration gives:

Substituting Equation c) into Equation (a) and rearranging terms and dividing by R² gives:

 

(d)

Create a MATLAB program that will use MATLAB's fzero function to determine d for the following parameters: R = 0.5 m and   in steps      of 0.1. Create a table consisting of S and d.