Homework Help: Calculus 3 question- don't even know how to approach this problem

1. Feb 24, 2010

krtica

Find the mass of one turn of wire in the form of a helix with a linear density e^(-z) in lbs/ft.

Would I write as <e^(-z)*cost,e^(-z)*sint, t>? Maybe?

2. May 20, 2011

jonthebaptist

The first thing to check for is units. The problem with your proposed solution is that the x and y components have units of weight, while the z component has units of length.

What is given is the density (ratio weight per length), so to get weight just multiply the density by the length. The arclength of a curve is given as the integral of the modulus of the derivative of the curve. So just put the density inside the integral and solve.

3. May 20, 2011

LCKurtz

First, you should note that the problem is not well posed. It makes a difference which turn of the wire since the density is not constant. You want to calculate

$$\int_C \delta(x,y,z)\ ds$$

with appropriate units.