Given the vector current density J = (10rho2z)arho − (4rho cos2φ)aφ mA/m2 :

a. Find the current density at P (rho = 2, φ = 60◦ , z = 3);
b. Determine the total current flowing outward through the circular band rho = 4, π < φ < 2π ,
3 < z < 8.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Shafts are machine elements that are used to a) carry axial loads b) direct shear loads c) transmit power d) rotate at constant speed e) none of the above circular and square shafts subjected to the same torque under the same circum behave a) the same way b) almost the same way

Avolume of 2.65 m3 of air in a rigid, insulated container fitted with a paddle wheel is initially at 264 k, 5.6 bar. the air receives 432 kj by work from the paddle wheel. assuming the ideal gas model with cv = 0.71 kj/kg • k, determine for the air the amount of entropy produced, in kj/k