Aparticle of mass m moves along the r-axis under the influence of a time- dependent force given by fr, t) = -kret/7, where k and 7 are positive constants. (a) compute the lagrangian function. [7 points) (b) find the lagrangian equation of motion explicitly. (7 points) (c) compute the hamiltonian function in terms of the generalized coordinate and generalized momentum. (show clearly how you got this.) (7 points] (d) determine hamilton's equations of motion explicitly for this particular problem (not just general formulae). [7 points) (e) does the hamiltonian equal the total energy of the mass? explain. [6 points) (f) is the total energy of the mass conserved?

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.

An automobile steering wheel is shown. what is the ideal mechanical advantage? if the ama is 8, what is the efficiency of the steering wheel?

The rocket is fired vertically and tracked by the radar station shown. when θ reaches 66°, other corresponding measurements give the values r = 32700 ft, r¨ = 85 ft/sec2, and θ˙ = 0.019 rad/sec. calculate the magnitudes of the velocity and acceleration of the rocket at this position.