1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Differential equations hw problem

  1. Jan 21, 2010 #1
    the rate of growth of the mass M of a spherical rain drop falling through a particular cloud is given by dM/dt = Cr^3 where M = (rho)(4/3)(pi)r^3 and C is a constant

    a) eliminate M from the above equation so that the size of the drop is expressed solely in terms of the radius r.

    b) separate the variables and integrate to find an expression for r(t), given an intial radius r0 at time t=0



    my attempt at part a consisted of me switching the Mass equations to Volume equations, yielding V = (4/3)(pi)r^3
    and getting r = (3V/4(pi))^1/3

    i dont think this is right. i havent had any differential equations course as of yet
     
  2. jcsd
  3. Jan 21, 2010 #2
    You have M in terms of r. Knowing that r changes in time (dr/dt != 0), what would be dM/dt in terms of r and dr/dt?
     
  4. Jan 21, 2010 #3
    idk, thats why i posted the question
     
  5. Jan 21, 2010 #4

    Mark44

    Staff: Mentor

    Use the chain rule. You have M = f(r) and f = g(t), so dM/dt = (?)(?)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook