# modeling with first order equations

• Apr 5th 2011, 02:18 PM
Taurus3
modeling with first order equations
a body falling in a relatively dense fluid, oil for example, is acted on by three forces: a resistive force R, a buoyant force B, and its weight due to gravity. The buoyant force is equal to the weight of the fluid displaced by the object. For a slowly moving spherical body of a radius a, the resistive force is given by Stoke's law, R=6pi*μ*a*absolute value of v, where v is the velocity of the body, and μ is the coefficient of viscosity of the surrounding fluid.
1. Find the limiting velocity of a solid sphere of radius a and density p falling freely in a medium of density p' and coefficient of viscosity μ.

2. Millikan studied the motion of tiny droplets of oil falling in an electric field. A field of strength E exerts a force Ee on a droplet with charge e. Assume that E has been adjusted so the droplet is held stationary(v=0) and that w and B are as given above. Find and expression for e. Millikan repeated this experiment many times, and was able to deduce the charge of an electron.
• Apr 5th 2011, 03:34 PM
TheEmptySet
Quote:

Originally Posted by Taurus3
a body falling in a relatively dense fluid, oil for example, is acted on by three forces: a resistive force R, a buoyant force B, and its weight due to gravity. The buoyant force is equal to the weight of the fluid displaced by the object. For a slowly moving spherical body of a radius a, the resistive force is given by Stoke's law, R=6pi*μ*a*absolute value of v, where v is the velocity of the body, and μ is the coefficient of viscosity of the surrounding fluid.
1. Find the limiting velocity of a solid sphere of radius a and density p falling freely in a medium of density p' and coefficient of viscosity μ.

2. Millikan studied the motion of tiny droplets of oil falling in an electric field. A field of strength E exerts a force Ee on a droplet with charge e. Assume that E has been adjusted so the droplet is held stationary(v=0) and that w and B are as given above. Find and expression for e. Millikan repeated this experiment many times, and was able to deduce the charge of an electron.

Here is an outline
First remember that

$\displaystyle \displaystyle F=ma=m\frac{dx^2}{dt^2}$

Now make a force diagram

$\displaystyle \displaystyle m\frac{dx^2}{dt^2}=...$

put your forces on the right hand side.

Last when an object reaches terminal velocity it is no longer accelerating therefore

$\displaystyle \displaystyle \frac{d^2x}{dt^2}=0$

sub this in then solve for $\displaystyle |v|$