Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration Engineering Problem

  1. Nov 3, 2011 #1
    1. The problem statement, all variables and given/known data

    A cylinder of length 5 and diameter 2 units is constructed such that the density of the material comprising it varies as the distance from the base. If K is a proportionality constant such that the density is given by K * distance from base, use an integral to show that the
    mass of the cylinder is given by : M =25Kpi/2

    2. Relevant equations

    Area of Circle : A = pi* r^2

    3. The attempt at a solution

    Fairly stuck with this question. Im not even sure where to begin with this. Im certain it isnt a very difficult problem but Im just not sure where to begin with it. Its going to consist of a definite integral somewhere along the line.
    I understand that questions don't get answered without some sort of an attempt but im stumped at where to begin with this.
  2. jcsd
  3. Nov 3, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    Try slicing up the cylinder in little pieces of width dz.
    If you take such a slice, at height z to dz, you can assume that its density is constant for sufficiently small values of dz. What is the mass then?

    When you add this up for all slices, that will give you the definite integral you are looking for.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook