(Solved): 2. (15 pts) Here are two identical timber planks. They have actual dimensions of \( 3^{\prime \prime ...

2. (15 pts) Here are two identical timber planks. They have actual dimensions of \( 3^{\prime \prime} \times 12^{\prime \prime} \). Set across a muddy stream, as shown, one is easy to walk on but bends too much while the other is hard to walk on, but is rigid. The ease with which a beam bends is directly related to its moment of inertia. The strong direction is "about the \( x \)-axis" and the weak direction is "about the \( y \)-axis." Compare both moments of inertia, \( I_{x} \) and \( I_{y^{\prime}} \) for this cross section.