# Find mass by linear density?

• Jul 13th 2010, 11:19 AM
Alpina540
Find mass by linear density? ......SOLVED........
A thin wire is bent into the shape of a semicircle x^2+y^2=4 x>0

If the linear density is 3, find the mass of the wire.

Anyone have a clue how to tackle this problem?

Thanks for your help(Happy)

18pi
6pi^2
3pi
6pi
2pi
• Jul 13th 2010, 11:30 AM
Ackbeet
If the linear density $\lambda$ is constant, then you can just use the formula $M=\lambda L$, where $M$ is the mass, and $L$ is the length of the wire. Where would you go from there?
• Jul 13th 2010, 11:35 AM
Alpina540
Well it looks like now I need to find the length of the curve of wire.
• Jul 13th 2010, 11:42 AM
Ackbeet
Correct. And how could you find the length of a semicircle?
• Jul 13th 2010, 11:43 AM
Alpina540
So I just graphed it and cheated a bit and just ruffed out the length of the curve by the Pythagorean theorem and I got the curve to be ~ 6 so 3*6= 18

So the answer is 6pi?

• Jul 13th 2010, 11:45 AM
Ackbeet
You can get the exact answer (which is not $18\pi$, by the way). What's the length of a wire that's in the shape of a circle?
• Jul 13th 2010, 11:56 AM
Alpina540
ok ok you win, lol (duh about the 18pi! thats what happens when 20 vector calc problems are running through your head.)

(180/360)*((2(pi)*2)=6.28

6.28*3=18.84
6*pi=18.84

Thanks for your help, I really appreciate it!

-Anson
• Jul 13th 2010, 12:37 PM
Ackbeet
You're very welcome.
• Jul 13th 2010, 12:39 PM
HallsofIvy
By the way, "pie" is what you eat. "pi" is the standard transliteration of $\pi$.
• Jul 13th 2010, 12:43 PM
Alpina540
lol........ I knew that I just didn't think about it as I never write pi out in words.