Prove that if the block is released from rest at point B of a smooth path of arbitrary shape, the speed it attains when it reaches point A is equal to the speed it attains when it falls freely through a distancev = /2gh. B h A

Who do you think is more Important, Design or Analysis of a structure? Explain. Explain Equilibrium conditions in details.

(Civil Engineering Mathematics) * Surface Integrals Try to detail how it can be applied in life

Learning Goal: An object's moment of inertia is calculated analytically via integration, which involves dividing the object's area into the elemental strips that are parallel to the axes and then performing the integration of the strip's moment of inertia. In practice, engineers often encounter structural members that have areas composed of the common geometric shapes, such as rectangles, triangles, and circles, whose areas, centroidal locations, and moments of inertia about their centroidal axes are either known or can be calculated easily. Determining the moment of inertia of a composite area with respect to any axis is based on the following definitions: I₂ = fy² dA Iy = √x² dA For a composite area consisting of a finite number of components, the integration is replaced by summation and the general equation simplifies to 771 m A composite area consisting of the rectangle, semicircle, and a triangular cutout is shown (Figure 1). Calculate the moment of inertia of the triangle with…