Find the total mass m and the center of mass of the solid with mass density σ(x, y, z) = kxy3(9 − z) g/cm3, where k = 5 ✕ 106, that occupies the region bounded by the planes x = 0, y = 0, z = 0, z = 1, and x + y = 1.

Zirconium has an hcp crystal structure and a density of 6.51 g/cm3. (a) what is the volume of its unit cell in m3? (b) if the c/a ratio is 1.593, compute the values of c and a.

Determine the change in width a, height b, thickness t when a plate is subjected to the uniform distributed load and is made of material having modulus of elasticity e=230 gpa and poisson's ratio ν=1/3. given : a=400 mm and b= 300 mm also the uniformly distributed load in downward y direction of plate is 2 mn/m and in the positive x direction is 3 mn/m and t=20 mm

Asap and show ! a 14 kg rock starting from rest free falls through a distance of 5.0 m with no air resistance. find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earths velocity. earth mass is 6.0 * 10^24 kg. show your work assuming the rock earth system is closed.