Consider a particle-on-a-sphere with a spherical harmonic wave function ψt, mt(θ,φ). a. Suppose that l= 2 and ml= 2. Compute the following observables (numerically):

i. magnitude of the angular momentum vector of the particle |L|.
ii. projection of the angular momentum vector of the particle on the z-axis Lz.

b. Now suppose the particle is in the state withl= 1 and ml= 1. What are the values of the observables |L| and Lz(as multiples of~)? Sketch the angular momentum vector of the particle in thex-zplane, labeling its length |L| and z-component. What is the angle that the angular momentum vector makes with the zaxis?

Ashielded metal arc-welding operation is accomplished in a work cell by a fitter and a welder. the fitter takes 5.5 min to load components into the welding fixture at the beginning of the work cycle, and 1.5 min to unload the completed weldment at the end of the cycle. the total ength of the weld seams 1200 mm, and the travel speed used by the welder averages 300 mm/min. every 600 mm of seam length, the welding stick must be changed, which takes 0.8 min. while the fitter is working, the welder is idle (resting): and while the welder is working the fitter is idle. (a) determine the average arc-on time as a fraction of the work cycle time. (b) how much improvement in arc-on time would result if the welder used flux-cored arc welding (manually operated), given that the spool of weld wire must be changed every 10 weldments, and it takes the welder 5.0 min to accomplish the change? (c) what are the production rates for these two cases (weldments completed per hour)? attach your work and solutions.