Question

Been a long while since I've done this, could use some help haha. Find the mass of a wire..
@ganeshie8
@Kainui
@zepdrix

Answer 1

From what I recall since mass is density*volume the integral should be \[m = \int\limits \rho ds \]

Answer 2

\[ds = \sqrt{\left( \frac{ dx }{ dt } \right)^2+\left( \frac{ dy }{ dt } \right)^2+\left( \frac{ dz }{ dt } \right)^2}dt\]

Answer 3

\[ds = 3\sqrt{1+4t^2+4t^4}dt\] mhm this is what I get for ds heh

Answer 4

Ah that works out \[ds = 3 \sqrt{(2t^2+1)^2}\]

Answer 5

Then our parameterization is just x = 3t so we have

\[\rho = 1+t \implies m = 3\int\limits\limits_{0}^{1}(1+t)(2t^2+1)dt \] I think this is it?

Answer 6

I got m=8 if anyone cares lol, but I just want to know if the set up is correct haha.

Answer 7

yes, that is what I got. Hopefully, that means great minds think alike.

Answer 8

Yeah I just worked it out and that's what I got, did the same steps as you too for the most part.

Answer 9

Haha thanks fellas!