# Mass along a wire?

• Mar 11th 2013, 08:15 AM
kidi3
Mass along a wire?
I have no idea how i should solve this problem..

http://snag.gy/L6hWl.jpg

• Mar 11th 2013, 09:13 AM
Shakarri
Re: Mass along a wire?
From the definition of dr
$dr= dxi+ dyj+ dzk$

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

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

You can find the values of $\frac{dx}{dt},\frac{dy}{dt} and \frac{dz}{dt}$ 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
• Mar 11th 2013, 10:21 AM
kidi3
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)?
• Mar 11th 2013, 11:05 AM
peysy
Re: Mass along a wire?
m=int(density*sqrt((x'(t))^2+(y'(t))^2+(z'(t))^2)d t
• Mar 11th 2013, 11:09 AM
Shakarri
Re: Mass along a wire?
Quote:

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
• Mar 11th 2013, 11:12 AM
HallsofIvy
Re: Mass along a wire?
Quote:

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

Quote:

This is the length of the wire not the mass
No, with that "density" function in there, it is the mass.
• Mar 11th 2013, 11:14 AM
peysy
Re: Mass along a wire?
density=(1+t) g/u =)
• Mar 11th 2013, 12:19 PM
Shakarri
Re: Mass along a wire?
Quote:

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.