(Solved): f) Figure Q2(b) shows the cross sectional area of the cantilever in a plane orthogonal to the long ...

f) Figure Q2(b) shows the cross sectional area of the cantilever in a plane orthogonal to the long axis of the cantilever. The origin of the co-ordinate axis is located at the centroid of the cross section (a depth $t/2$ from the top surface and distance $w/2$ from the left most side of the cantilever, as shown in the figure. Figure Q2(b): Cross sectional geometry of the cantilever If bending of the cantilever occurs about the $z$-axis, calculate the second moment of area around this axis in terms of the cantilever thickness, $t$, and the width, $w$. (4) g) If the cell exerts a force of $1.2\mathrm{nN}\left(1.2\times 10^{-9}\mathrm{N}\right)$ on the tip of the cantilever, a distance $l$ from the anchor point, calculate the curvature $(1/r)$ of the AFM if the cantilever is made of crystalline silicon with a Young's modulus of $E=1.69\times 10^{11}\mathrm{Pa}$. In order calculate this, you will need to use your answer to question $2(f)$ and the pure bending equation that relates the bending curvature of the rod to the applied moment and material properties of the cantilever. (3)