# Snowball Rolling down a hill problem.

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• Sep 18th 2010, 06:28 PM
canadia
Snowball Rolling down a hill problem.
Hi all,

I've just started taking differential equations and I've gotten a little bit stuck on this problem.

A snowball rolling down a hill gains mass, m , at a rate proportional to its surface area.Assume the density of the snowball is constant such that mass is proportial to volume. Find a DE for the change in mass over time. And also given is that the rhs should depend only on m and constants

So here's what I think,

Surface= $4Pi^2$
Volume= $4/3Pi^3$

dm/dt=m0 + k*4pi^2

Maybe something like the rate of change of the mass depends on the initial mass + the change proportinal to its surface area?
• Sep 18th 2010, 11:33 PM
CaptainBlack
Quote:

Originally Posted by canadia
Hi all,

I've just started taking differential equations and I've gotten a little bit stuck on this problem.

A snowball rolling down a hill gains mass, m , at a rate proportional to its surface area.Assume the density of the snowball is constant such that mass is proportial to volume. Find a DE for the change in mass over time. And also given is that the rhs should depend only on m and constants

So here's what I think,

Surface= $4Pi^2$
Volume= $4/3Pi^3$

dm/dt=m0 + k*4pi^2

Maybe something like the rate of change of the mass depends on the initial mass + the change proportinal to its surface area?

First the mass is proportional to volume, and surface area proportional to volume to two thirds, and so surface area is proportional the power 2/3 of mass.

Now we have:

$\dfrac{dm}{dt}=km^{2/3}$

CB
• Sep 19th 2010, 10:44 AM
canadia
Thanks CaptainBlack