Avessel at rest at the origin of an xy coordinate system explodes into three pieces. just after the explosion, one piece, of mass m, moves with velocity (-31 m/s) i and a second piece, also of mass m, moves with velocity (-31 m/s) j. the third piece has mass 3m. just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the +x axis) of the velocity of the third piece?

Orange juice has a lower or higher viscosity than chocolate syrup

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?

The average density of the planet uranus is 1.27 103 kg/m3. the ratio of the mass of neptune to that of uranus is 1.19. the ratio of the radius of neptune to that of uranus is 0.969. find the average density of neptune.