Student handout: Modeling Nonuniform Density

AIMS Maxwell 2021
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.
What students learn
  • how to distinguish the two different uses of the word “linear” in a linear charge density that varies linearly;
  • some of the words for describing functional variation: linear, quadratic, exponential, falls off like ..., proportional to the square, etc.
  • how to “name the thing you don't know” with an algebraic symbol so that it can appear in an equation.

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.

Author Information
Corinne Manogue
Learning Outcomes