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

[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?

 

[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.

 

[LCKurtz]

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?

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.