The vpython command norm returns the unit vector of a vector. remember that a unit vector has a length of one and points in the direction of the original vector. for exampe, if l = vector(0,3,0) then norm(l) = < 0,1,0> and, if l = vector(0,3,0) then norm(-l) = < 0,-1,0> additionally, if l = vector(0,3,0) then norm(5l) = < 0,1,0> and, for example, if m = vector(1,1,0) then norm(m) = < 0.707,0.707,0> . another example, if n = vector(2,3,0) then norm(m) = < 0.5547,0.83205,0> an for another example, if p = vector(1,2,3) then norm(p) = < 0.267261,0.534522,0.801784> if q = vector(3,4,0) then norm(q) =

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.

An ideal otto cycle with air as the working fluid has a compression ratio of 8. the minimum and maximum temperatures in the cycle are 300 k and 1340 k. use constant specific heats at room temperature to determine (a) the amount of heat transferred to the air during the heat- addition kj/kg, (b) the thermal efficiency, and (c) the thermal efficiency of a carnot cycle ope limits. process, in rating between the same temperature

You are making beer. the first step is filling the glass carboy with the liquid wort. the internal diameter of the carboy is 15 in., and you wish to fill it up to a depth of 2 ft. if your wort is drawn from the kettle using a siphon process that flows at 3 gpm, how long will it take to fill?