Different Masses, Falling Rate
We are taught in school a classic example of dropping 2x
objects with different weights from a tall height and other things
equal, including wind-resistance, they both fall at the same rate.
What if you had 2 thin containers, filled with a different
substance, one helium, the other regular air or lead pebbles or
something heavier, would that not be an example where you have two
different objects with the same wind-resistance ( if the containers
are the same shape and made of the same materials on their own ),
but different weight and if dropped would not fall at the same rate?
Because the one with lighter-than-air gas filled inside of it would
float if it was enough, or descend very slowly. Wiki calls the
experiment the Equivalence Principle and states "objects with
different masses or composition", which sounds right, and the list
of experiments done in history have some dramatic ones like a
feather and a hammer being dropped at the same time on the moon, so
I cant think of any reason not to count the theoretical version with
2 containers above, is there any?
If EVERYTHING but weight is the same, including ALL effects of the air,
then the two containers will fall together. An object "lighter than
air" rises in air for the same reason that some objects float in water.
Air resistance slows down an object as it moves through air: the object
has to push the air molecules out of the way. Buoyancy pushes upward on
an object in air: air molecules below the object crash into the object
a little harder than do air molecules above the object. If the object's
weight is small enough and volume is large enough, the upward buoyancy
will be stronger than the downward weight. The object will float
Without air, both air resistance AND buoyancy disappear. On the moon, a
bottle of helium will fall just as fast as a bottle of steel marbles.
Although advanced quantum theory tells us that there are really very few
forces in the universe, these few forces show up in very many different
ways. This is why we experience have so many different forces to work
with. Many of them do not have simple formulas. As we cannot calculate
them all, we try to do experiments where these forces are small enough
to ignore. When measuring gravitational acceleration, we use dense
objects that are not shaped like parachutes. This will make buoyancy
and air resistance very small.
Dr. Ken Mellendorf
Illinois Central College
I will call this principle the Equivalency Principle too,
just because it is a good label and we need a label for what we are talking about.
The Equivalency Principle is only about gravity and mass.
It is not meant to apply with air drag present.
The accurate way to get rid of air drag is to do your drop-test in a vacuum.
You wanted to make the two air-drags irrelevant by making them the same.
Your two same-shaped containers will have the same drag if they are going the same speed,
but it turns out they will not be going the same speed.
When falling downwards in air, there is a drag-force in the backwards/upwards direction.
This extra force accelerates the object upwards from where it would have been if falling in a vacuum.
A given force will accelerate the lighter object more than the heavier object.
Thus the lighter object will be higher than the heavier one at a given instant,
and going slower,
and then it will hit the ground at a later time.
Air drag changes the problem a lot.
Have you heard of terminal velocity?
In a vacuum, a falling object keeps accelerating, going faster and faster, until it hits the ground.
It can hit the ground very fast, and starting higher always means hitting faster than before.
In air, a falling object accelerates only until the increasing force due to air-drag
is equal and opposite the force of the mass times the gravity field.
After falling a little while, you do not accelerate any more.
You just push through heavy wind while going down at a constant speed.
And then you hit the ground, but not as fast as it would have been without air.
For a human body in a spread-eagle position, it only takes about 500 feet to reach terminal velocity.
After falling 500 feet, you will not speed up any more by falling further.
Jumping from 10,000 feet or 1,000: you would hit the ground at the same speed from either height.
That is a very different situation than the Equivalency Principle was meant to
Different objects do have different terminal velocities depending on their mass and frontal area.
(The ratio of mass / frontal area is called the Ballistic Coefficient; look it up...)
I hope you get to study physics someday.
Then you can figure these things out by designing the right formulas for the forces and speeds,
starting from a diagram of the situation.
You might find that using the math sometimes makes things feel clearer.
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Update: June 2012