- #1
squelch
Gold Member
- 57
- 1
This is from a physics course, but felt more appropriate to post here.
I just want some sanity checking on my procedure, since I'm not this far in my calculus course yet but am having to work through it anyway for physics.
I have no idea how to approach part c, not even an inkling of where to begin. If all you give me are Google search terms, then I'll be happy.
A cylinder of radius R and length L is given.
a) Use the shell method to write the infinitesimal volume DV
b) Integrate dv to obtain the volume of the cylinder.
c) The density of the cylinder is given by [itex]\rho = {\rho _0}(1 - \frac{r}{R})[/itex] where [itex]{\rho _0}[/itex] is constant.
NA.
a) A cylinder can be divided into infinitesimal shells of height L and width dr. Therefore, the infinitesimal volume is given by:
[tex]dv = 2\pi LRdr[/tex]
b) This infinitesimal volume can then be integrated as:
[tex]V = \int_0^R {2\pi LRdr = 2\pi LR\int_0^R {dr = 2\pi LR(\left. r \right|_0^R) = 2\pi L{R^2}} } [/tex]
c) No idea.
I just want some sanity checking on my procedure, since I'm not this far in my calculus course yet but am having to work through it anyway for physics.
I have no idea how to approach part c, not even an inkling of where to begin. If all you give me are Google search terms, then I'll be happy.
Homework Statement
A cylinder of radius R and length L is given.
a) Use the shell method to write the infinitesimal volume DV
b) Integrate dv to obtain the volume of the cylinder.
c) The density of the cylinder is given by [itex]\rho = {\rho _0}(1 - \frac{r}{R})[/itex] where [itex]{\rho _0}[/itex] is constant.
Homework Equations
NA.
The Attempt at a Solution
a) A cylinder can be divided into infinitesimal shells of height L and width dr. Therefore, the infinitesimal volume is given by:
[tex]dv = 2\pi LRdr[/tex]
b) This infinitesimal volume can then be integrated as:
[tex]V = \int_0^R {2\pi LRdr = 2\pi LR\int_0^R {dr = 2\pi LR(\left. r \right|_0^R) = 2\pi L{R^2}} } [/tex]
c) No idea.