Classical Dynamics of Particles and Systems · Problem 9-56

Motion in a Noninertial Reference Frame — Marion & Thornton

Physics — Mechanics · variable-mass

Problem

A water droplet falling in the atmosphere is spherical. Assume that as the droplet passes through a cloud, it acquires mass at a rate equal to

kA

where

k

is a constant

(>0)

and

A

is its cross-sectional area. Consider a droplet of initial radius

r_0

that enters a cloud with a velocity

v_0

. Assume no resistive force and show (a) that the radius increases linearly with the time, and (b) that if

r_0

is negligibly small then the speed increases linearly with the time within the cloud.