Prove that the total mechanical energy in gravitational field is always conserved​

Me to solve all the questions on the sheet attached

Classify the following soils according to the uscs classification system. provide appropriate uscs designations. a) this sample of well-graded gravel with sand was obtained from a large earthen dam in vancouver, canada. the sample has 73% fine to coarse sub-angular gravel, 25% fine to coarse sub-angular sand and 2% fines. the maximum size of the particles is 75 mm. the coefficient of curvature is 2.7, while the uniformity coefficient is 12.4. b) this dark brown and wet soil with a “strong organic odor” has 100% passing the no. 200 sieve. the liquid limit of the material is 32% when not dried and is 21% when oven-dried. the plastic index is 21% when not dried. c) this sand has 61% predominantly fine sand, 23% silty fines, and 16% fine sub-rounded gravel size. the maximum size is 20 mm. the liquid limit is 33% and the plastic limit is 27%. d) this soil has 74% fine to coarse sub-angular reddish sand and 26% organic and silty dark brown fines. the liquid limit is 37% when not dried and is 26% when oven dried. the plastic index is 6% when not dried.

Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?