calculate mass of the wire

**mohammadmurtaza** · December 6th 2009, 05:37 PM

Hello

If anyone is able to help me with this problem, I would greatly appreciate it. Since this is also an even numbered question, im not able to look up the answer. Special thanks to Scott who helped me with the Stoke's Theorem problem.

Question:

A wire is formed to the shape of the curve r(t) = 2 t i + 4/3 t^(3/2) j + 1/2 t^(2) k , for 0<= t <= 1. The density of the wire at the point (x,y,z) is given by p (x,y,z) = 4 x z + 9 y^(2) grams per linear unit. Calculate the mass of the wire.

**Chris L T521** · December 6th 2009, 05:52 PM

Originally Posted by mohammadmurtaza

Hello

If anyone is able to help me with this problem, I would greatly appreciate it. Since this is also an even numbered question, im not able to look up the answer. Special thanks to Scott who helped me with the Stoke's Theorem problem.

Question:

A wire is formed to the shape of the curve r(t) = 2 t i + 4/3 t^(3/2) j + 1/2 t^(2) k , for 0<= t <= 1. The density of the wire at the point (x,y,z) is given by p (x,y,z) = 4 x z + 9 y^(2) grams per linear unit. Calculate the mass of the wire.

You're given the parameterization of the curve: $x=2t$ , $y=\tfrac{4}{3}t^{3/2}$ and $z=\tfrac{1}{2}t^2$ . Note that $\left|\left|r^{\prime}(t)\right|\right|=\sqrt{4+4t +t^2}=t+2$

Thus, the density function becomes $\rho(t)=4(2t)\left(\tfrac{1}{2}t^{2}\right)+9\left (\tfrac{4}{3}t^{3/2}\right)^2=4t^3+16t^3=20t^3$ .

Thus, the mass of the wire is defined by $\int_0^120t^3(t+2)\,dt$ .

I'm sure you can take it from here.

**mohammadmurtaza** · December 6th 2009, 05:54 PM

Thanks Chris you ROCK!!!!!!!!! My attempt was waaaaaayyyyy off

**mohammadmurtaza** · December 6th 2009, 09:39 PM

Originally Posted by Chris L T521

You're given the parameterization of the curve: $x=2t$ , $y=\tfrac{4}{3}t^{3/2}$ and $z=\tfrac{1}{2}t^2$ . Note that $\left|\left|r^{\prime}(t)\right|\right|=\sqrt{4+4t +t^2}=t+2$

Thus, the density function becomes $\rho(t)=4(2t)\left(\tfrac{1}{2}t^{2}\right)+9\left (\tfrac{4}{3}t^{3/2}\right)^2=4t^3+16t^3=20t^3$ .

Thus, the mass of the wire is defined by $\int_0^120t^3(t+2)\,dt$ .

I'm sure you can take it from here.

Hi Chris,

I just wanna make sure I did it correctly, perhaps you can verify I have the correct answer. I got 14 linear units as the answer.

Thread: calculate mass of the wire

LinkBack

Thread Tools

Display

calculate mass of the wire

Thanks Chris :)

verify answer

Similar Math Help Forum Discussions

Particle of mass, calculate change in K.E.?

A coil of wire has 400 metres of wire. Suppose there are 20 nicks.

Solving for Mass, Given Mass as Constant + Infinite # of Discrete Unknown variables)

please help with using double integrals to solve for mass and center of mass

find mass of wire

Search Tags