Thread: Mass along a wire?

1. Mass along a wire?

I have no idea how i should solve this problem..

http://snag.gy/L6hWl.jpg

2. Re: Mass along a wire?

From the definition of dr
$\displaystyle dr= dxi+ dyj+ dzk$

Take the magnitude of dr
$\displaystyle |dr|^2= (dx)^2+ (dy)^2+ (dz)^2$

$\displaystyle (\frac{|dr|}{dt})^2= (\frac{dx}{dt})^2+ (\frac{dy}{dt})^2+ (\frac{dz}{dt})^2$

You can find the values of $\displaystyle \frac{dx}{dt},\frac{dy}{dt} and \frac{dz}{dt}$ in terms of t easily. Then get |dr| on its own and integrate it between t=0 and t=1

Edit. Didnt see that the density wasn't constant.
After you get an expression for dr in the form |dr|=g(t)dt since the density is 1+t find the integral of (1+t)g(t)dt between 0 and 1

3. Re: Mass along a wire?

After you get an expression for dr in the form |dr|=g(t)dt?..

what do you mean by numeric form of it, and g(T)?

4. Re: Mass along a wire?

m=int(density*sqrt((x'(t))^2+(y'(t))^2+(z'(t))^2)d t

5. Re: Mass along a wire?

Originally Posted by peysy
m=int(density*sqrt((x'(t))^2+(y'(t))^2+(z'(t))^2)d t
This is the length of the wire not the mass

6. Re: Mass along a wire?

Originally Posted by peysy
m=int(density*sqrt((x'(t))^2+(y'(t))^2+(z'(t))^2)d t
This is the length of the wire not the mass
No, with that "density" function in there, it is the mass.

7. Re: Mass along a wire?

density=(1+t) g/u =)

8. Re: Mass along a wire?

Originally Posted by HallsofIvy
No, with that "density" function in there, it is the mass.
I realise that. I included the density function in the integration in my first reply, I was preventing op from getting muddled between the two answers.