Consider a steady, two-dimensional, incompressible flow of a newtonian fluid in which the velocity field is known: u=-2xy, v=y 2 - x 2 , w=0. (a) does this flow satisfy conservation of mass? (b) find the pressure field, p(x, y) if the pressure at the point (x=0, y=0) is equal to pa.

How would you place two electrons on a sphere of radius r so that the electrostatic potential energy is minimized. how would you place three electrons to solve the same problem.

5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?

Aball has an initial velocity of 3 m/s. if there is no friction, what is the highest it could roll?