In this small group activity, students calculate a (linear) function to represent the charge density on a one-dimensional rod from a description of the charge density in words.
Consider a rod of length \(L\) lying on the \(z\)-axis. Find an algebraic expression for the mass density of the rod if the mass density at \(z=0\) is \(\lambda_0\) and at \(z=L\) is \(7\lambda_0\) and you know that the mass density increases linearly.
This activity is surprisingly difficult for some students. This activity is partly an opportunity to introduce language for functional dependence and partly an exercise in modeling physical behavior with a function with parameters that must be determined. Once students get the idea, it's pretty straightforward, but it helps solidify the concept if the exercise recurs a few times as part of future in-class activities and homework.