Solid State Physics

Objects do fall at the same rate, regardless of mass, in a vacuum. In air, wind resistance affects the NET of the forces accelerating the object. The heavier object WILL fall faster in air because the wind resistance, although the same between the two objects, represents a larger percentage of the forces acting on the lighter object. The heavier object will fall faster.

That is incorrect.

Weight has nothing to do with how fast things fall, only wind resistance. Take two 16 ounce soda bottles, open one drink eight ounces. The unopened bottle is twice as heavy as the opened bottle. Close the bottle you just drank half of and drop them at the same time from a tall building, they will hit the ground at the same time. That is because gravity is a constant and the velocity of any falling object is 9.8 meters per second/per second.

Acceleration is the same for all objects at 9.8m/sec/sec.

Acceleration due to gravity near the earth's surface is the same for all objects regardless of their mass.

I took a 20lb (9.07kg) heavy exercise ball (aka medicine ball or strength training ball), and a soccer ball (which weighs 16 ounces aka 1 pound or 0.45kg). I dropped them both simultaneously, they both hit the ground at the same time, even though the medicine ball weighed 20 times as much as the soccer ball. I am not sure what you would like explained. as I can tell you that your example of 1% full and 100% full is false. 1/4, 1/2 full or completely full, it makes no difference. Your experiment must have been flawed, as it is impossible for them to fall at different rates. Here's the science behind it.

Every planetary body (including the Earth) is surrounded by its own gravitational field, which exerts an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.

The strength of the gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted g, is expressed below as the standard average. According to the Bureau International de Poids et Mesures, International Systems of Units (SI), the Earth's standard acceleration due to gravity is:

g = 9.80665 m/s2 = 32.1740 ft/s2).

This means that, ignoring air resistance, an object falling freely near the Earth's surface increases its velocity by 9.80665 m/s (32.1740 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.80665 m/s (32.1740 ft/s) after one second, approximately 19.62 m/s (64.4 ft/s) after two seconds, and so on, adding 9.80665 m/s (32.1740 ft/s) to each resulting velocity.

Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time. So two objects with the same aerodynamic values (aka air resitance) will hit the ground at the same time. That includes our coke bottles and the soccer ball and exercise ball.

A set ofdynamical equations describe the resultant trajectories when objects move owing to a constant gravitational force under normal Earth-bound conditions. For example, Newton's law of universal gravitation simplifies to F = mg, where m is the mass of the body.

Near the surface of the Earth, use g = 9.8 m/s² (meters per second squared; which might be thought of as "meters per second, per second", or 32 ft/s² as "feet per second per second"), approximately. For other planets, multiply g by the appropriate scaling factor. It is essential to use a coherent set of units for g, d, t and v. Assuming SI units, g is measured in meters per second squared, so dmust be measured in meters, t in seconds and v in meters per second.

In all cases, the body is assumed to start from rest. Generally, in Earth's atmosphere, this means all results below will be quite inaccurate after only 5 seconds of fall (at which time an object's velocity will be a little less than the vacuum value of 49 m/s (9.8 m/s² × 5 s), due to air resistance). When a body is travelling through any atmosphere other than a perfect vacuum it will encounter a drag force induced by air resistance, this drag force increases with velocity. The object will reach a state where the drag force equals the gravitational force at this point the acceleration of the object becomes 0, the object now falls at a constant velocity. This state is called the terminal velocity.

The drag force is dependant on the density of the atmosphere, the coefficient of drag for the object, the velocity of the object (instantaneous) and the area presented to the airflow.

This equation occurs in many applications of basic physics.

Distance travelled by an object falling for time : Time taken for an object to fall distance : Instantaneous velocity of a falling object after elapsed time : Instantaneous velocity of a falling object that has travelled distance : Average velocity of an object that has been falling for time (averaged over time): Average velocity of a falling object that has travelled distance (averaged over time): Instantaneous velocity of a falling object that has travelled distance on a planet with mass , with the combined radius of the planet and altitude of the falling object being , this equation is used for larger radii where is smaller than standard at the surface of Earth, but assumes a small distance of fall, so the change in is small and relatively constant:

Instantaneous velocity of a falling object that has travelled distance on a planet with mass and radius (used for large fall distances where can change significantly):

Example: the first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 12 = 4.9 meters. After two seconds it will have fallen 1/2 × 9.8 × 22 = 19.6 meters; and so on.

We can see how the second to last, and the last equation change as the distance increases. If an object were to fall 10,000 meters to Earth, the results of both equations differ by only 0.08%. However, if the distance increases to that of geocynchronous orbit, which is 42,164 km, the difference changes to being almost 64%. At high values, the results of the second to last equation become grossly inaccurate.

For astronomical bodies other than Earth, and for short distances of fall at other than "ground" level, gin the above equations may be replaced by G(M+m)/r² where G is the gravitational constant, M is the mass of the astronomical body, m is the mass of the falling body, and r is the radius from the falling object to the center of the body.

Removing the simplifying assumption of uniform gravitational acceleration provides more accurate results. We find from the formula for radial eliptic trajectories:

The time t taken for an object to fall from a height r to a height x, measured from the centers of the two bodies, is given by:

where is the sum of the standard gravitational parameters of the two bodies. This equation should be used whenever there is a significant difference in the gravitational acceleration during the fall.

Galileo Galilei (1564 -- 1642) was an Italian physicist , astronomer, astrologer, and philosopher closely associated with the scientific revolution. One of his most famous experiments was his demonstration from the Leaning Tower of Pisa.

In the late 16th century, it was generally believed heavier objects would fall faster than lighter objects; Galileo thought differently. He hypothesized that two objects would fall at the same rate regardless of their mass. Legend has it that in 1590 he climbed the Leaning Tower of Pisa and dropped several large objects from the top. The objects did reach the ground at very similar times and Galileo concluded if you removed air resistance, they would reach the ground at exactly the same time.

Gravity is the force of attraction between any tow objects. All objects have it and it's proportional to the mass of the objects and inversely proportional to the square of the distance between them.

Strictly speaking, gravity only exists between two objects with mass, but since every (known) object has at least a relativistic mass, it works out to more or less the same thing.

On the other hand, looking at the bigger picture . . . No mass ? No problem !

You may substitute the mass of each object into the customary formula . . .

F = G M1 M2 / R2

and the result of the formula is the correct force, whether or not both objects have mass.

It is literally the inability to be penetrated (pierced, soaked through), to a greater or lesser extent. Nothing is completely impenetrable.

It is used metaphorically to indicate something not understandable, or incomprehensible -- not because it does not make sense but because it is presented or explained in an unenlightening, obtuse, or unclear manner (to use another idiom, it is "too dense").

Example: Quantum mechanics textbooks are renowned for their impenetrability.

An aperature OS size a illluminated by a parallel beam sends diffracted light into a angle of approximately ~y/a. This is the angular size of the bright central maximum. In trevelling a distance z, the diffracted beam therefore acquires a width zy/a due to diffraction. this gives distance beyond which divergence of the beam of width a becomes significant. Therefore, z ~ a2/y we define a quantity ZF called the Fresenls distance by the following equation ZF= a2/y

For distance greater than ZF the spreading due to diffraction over that due to ray optics. The above equation shows that ray optics is valid in the limit of wavelength tending to zero.