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semi infinite sheet watch

1. Asked to find mass of semi infinite sheet with mass per unit area

psi = ke^-(x^2 + y^2)/a^2 for x is greater than or equal to 0 and psi = 0 for x is less than 0.

is the mass infinite?

because when i transform to polar coords and find area via double integral, it comes out as e^ infinity about half way through the problem
2. edit: i dont think it should be infinite, but i cant see where ive gone wrong..

ive found the integral from -pi/2 to pi/2 then integral 0 to infinity of kre^-r^2/a^2 dr dtheta..
3. (Original post by King of TSR)
edit: i dont think it should be infinite, but i cant see where ive gone wrong..

ive found the integral from -pi/2 to pi/2 then integral 0 to infinity of kre^-r^2/a^2 dr dtheta..
The integral your doing is the righ one. You've made a mistake integrating. As you get exp^infinity I assume you made the substitution
u=-r^2 and then didn't change the limits.
The integral your doing is the righ one. You've made a mistake integrating. As you get exp^infinity I assume you made the substitution
u=-r^2 and then didn't change the limits.

indeed i did.

many thanks!! great help.

didnt think anyone would understand the question haha
5. Now asked to find COM..

I can see that by symmetry y bar = 0

x bar = double integral -pi/2 to pi/2 and then 0 to infinity of kr^2e^-r^2/a^2 costheta dr dtheta

this time, i don't know how to do the integral...can't do it by parts..

I'm given the integral between 0 and infinity of e^-bu^2 du, but don't see how this helps..
6. think i may have got it actually..

is it ka^3/2 root pi?
7. (Original post by King of TSR)
Asked to find mass of semi infinite sheet with mass per unit area

psi = ke^-(x^2 + y^2)/a^2 for x is greater than or equal to 0 and psi = 0 for x is less than 0.

is the mass infinite?

because when i transform to polar coords and find area via double integral, it comes out as e^ infinity about half way through the problem
Need to find the moment of I of this about x axis but can't do the integral..
any tips?
8. I have to do the very same problem. I got a^2*pi/2 for the mass and a/sqrt(pi) for x(com), but now I'm stuck on the last part. Could you please state your results?

Btw which college are you from?

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