vintwc
Mar7-10, 01:15 PM
1. The problem statement, all variables and given/known data
Let Ω be a tank whose shape is that of the lower hemisphere of radius R. The tank with a muddy suspension whose density ρ is ρ(x,y,z):=e^-h(x,y,z), where h(x,y,z) is the height of (x,y,z) above the lowest point of the tank. Find the center of mass in the tank
2. Relevant equations
3. The attempt at a solution
First of all, how does one determine the height, h(x,y,z)? I guess it would be R but I am not able to give a reasoning to my guess. I would appreciate if someone could give me a graphical illustration on how to find the limits of integration for this problem as well (ignore this if it will cause too much hassle). Thanks
Let Ω be a tank whose shape is that of the lower hemisphere of radius R. The tank with a muddy suspension whose density ρ is ρ(x,y,z):=e^-h(x,y,z), where h(x,y,z) is the height of (x,y,z) above the lowest point of the tank. Find the center of mass in the tank
2. Relevant equations
3. The attempt at a solution
First of all, how does one determine the height, h(x,y,z)? I guess it would be R but I am not able to give a reasoning to my guess. I would appreciate if someone could give me a graphical illustration on how to find the limits of integration for this problem as well (ignore this if it will cause too much hassle). Thanks