• Support PF! Buy your school textbooks, materials and every day products Here!

Centre of mass

  • Thread starter vintwc
  • Start date
  • #1
24
0

Homework Statement


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


Homework Equations





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
 

Answers and Replies

  • #2
1,953
248
If z is the vertical coordinate, and z =0 at the bottom of the tank, then h(x,y,z) = z
 
  • #3
24
0
I got a feeling its z+R. Could anyone let me know what are the phi limits of integration?
 

Related Threads on Centre of mass

  • Last Post
Replies
5
Views
762
Replies
7
Views
10K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
726
Replies
2
Views
976
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
9
Views
646
Top