Thread: Find mass by linear density?

1. 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?

18pi
6pi^2
3pi
6pi
2pi

2. If the linear density $\displaystyle \lambda$ is constant, then you can just use the formula $\displaystyle M=\lambda L$, where $\displaystyle M$ is the mass, and $\displaystyle L$ is the length of the wire. Where would you go from there?

3. Well it looks like now I need to find the length of the curve of wire.

4. Correct. And how could you find the length of a semicircle?

5. 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

6. You can get the exact answer (which is not $\displaystyle 18\pi$, by the way). What's the length of a wire that's in the shape of a circle?

7. 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

8. You're very welcome.

9. By the way, "pie" is what you eat. "pi" is the standard transliteration of $\displaystyle \pi$.

10. lol........ I knew that I just didn't think about it as I never write pi out in words.