Here we have a clip from the excellent movie adaptation of Tom Stoppard's play Rosencrantz and Guildenstern are Dead. In addition to engaging and nuanced performances by Gary Oldman, Tim Roth, Richard Dreyfus, and Iain Glen, the script is full of thought-provoking metaphysical introspection, and some delightful physics introspection as well. It's well worth renting.
A classic conceptual difficulty for first-year physics students -- and the public in general -- is the idea that all objects (in the absence of significant air resistance) accelerate toward the ground at the same rate. This is not intuitively obvious; in fact, for over 1,000 years, between the time of Aristotle and Galileo, the general consensus was that heavier things fall faster. Much of the confusion was, and is, the result of the masking effect of air resistance.
In the film scene, Rosencrantz (Gary Oldman) is fascinated when he watches an object constructed of feathers fall as fast as a heavy ball. He expects the feathers to take longer because he is used to seeing the effect of air resistance on light objects. But when he tries to demonstrate his initial counterintuitive result to Guildenstern (Tim Roth) using only a single feather, the feather does fall more slowly. Why? Because in the first case the feathers are fixed to a denser (although still light) base so that they are streamlined and relatively unaffected by air friction. With the single feather, the effect of air resistance is large because the feather is both light and has a lot of surface area exposed as it falls. Get rid of the air, and the feather falls as fast as the ball, as David Scott demonstrated in a famous experiment performed on the moon when he dropped a hammer and a feather off the steps of the lunar module.
But constant acceleration due to gravity is not necessarily conceptually obvious to physicists either! Here's why. Although we normally think of mass as, well, simply mass, we can actually separately define two distinct types of mass, which we call inertial mass and gravitational mass. Inertial mass is defined by the resistance of an object to a change in motion. For example, an object with more inertial mass will experience a smaller acceleration for a given amount of force compared to an object with less inertial mass. This property is encapsulated in Newton's Second Law, F = ma, where the mass refers to an object's resistance to acceleration.
On the other hand, we know that objects attract each other via the force of gravity. The more gravitational mass that the objects have, the greater that force. According to Newton's Universal Law of Gravitation, the force of gravity between two objects is given by F = Gm1m2/r2, where G is a universal constant of nature, the ms are the gravitational masses of each object and r is the distance between the centers of the objects. Now, according to physicists, there is theoretically no requirement that gravitational mass should have the same value as inertial mass -- but it does! This is why all objects accelerate at the same rate. To see why this is true, let's look at the acceleration of a ball of mass m near the surface of the Earth, which has mass M. We get: F = GMm/r2 = ma
The m on the left is the gravitational mass of the ball, while the m on the right is its inertial mass. Since the two are equal, they cancel on both sides of the equation and we get a = GM/r2 for any mass of object. This acceleration due to gravity depends only on the gravitational constant, the mass of the Earth, and the distance to the center. On another planet this value of acceleration would be different than on Earth but it would still be equal for every object when on that planet.
Esoteric? Maybe. But not if you're a physicist, and, I suspect, not if you're Rosencrantz or Tom Stoppard!
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.
Heavier objects should fall faster than lighter objects through the air due to both air resistence and atomic interaction between the air molecules and the molecules of the object. An object with more mass has more potential energy and will be effected by the gravitational pull of the air molecules less than if a lighter object were to fall since there is less atomic interaction by the lighter object. A heavier object would displace more air than a lighter object and the only way it could stay in the air is if it is traveling fast enough to repel against the air molecules it travels over. That is one reason why a 747 which is ten times heavier than a bus can fly while a bus normally stays on the ground. The surface area of the plane is greater thus displacing the molecules of the plane better as it travels through the air and displaces the air molecules.
In a vacuum, with no air resistence, objects should also fall faster the heavier thay are due to gravity. It's just that the difference in speed is nearly undetectable. An object should fall faster on earth in a vacuum than on the moon since the interactive gravity of the moon and the objects is less. With dark energy possibly existing in a vacuum out in space, there could be some atomic interaction between the objects and the energy in the vacuum.
A way to overcome gravity might be by using repulsive energy fields around the objects that are falling. If an object with a circulating electromagnetic displacement field is generated that is equal to or greater than the repulsive mass of the air and electromagnetic fields of the earth or body that the object is passing over, the object should be levitated at least or traveling through the air in the same fashion a UFO travels. If gravity can become repulsive in nature, a circulating repulsion field that is generated by an object will allow the object to repel gravity.
One of the easiest ways to repel off of gravity in order to travel out into space is to use a tubular electromagnetic field that is projected into space. An object placed inside the field that would generate a repulsive electromagnetic field similar to a linear induction field should be able to fly out into space and bring down the cost of placing objects into orbit and even on the moon to pennies on the dollar. If air can be ionized and made to produce a linear induction effect, an object with a repulsive field circulating around it should fly at whatever speed the field is circulating and travel in the direction the field is flowing. That is why I believe flying cars and other similar vehicles should be possible in the future. A double field motive system which uses a circulating repulsion field and an internal levitation field that repels against the motive field should allow a vehicle to glide nearly effortlessly above the ground and through the air. So when you see flying cars in movies or on TV, it could be that a double field motive system will make it possible.
What you have come out with is complete drivel! The author has just demonstrated through the equations of motion, that the only thing that determines the acceleration of an object in a vacuum is the gravitational field exerted by the body upon the object is dropped! Yet you still insist that the mass of the object dropped has anything to do with it!
"Gravity is the universal cryptic language of spacetime; a major player in unified field theory, and perhaps much more than we think. The scientific equation may also be read as:
F = G P1 + P2 (P = Person)
Person ( P1 ) and Person ( P2 ) with similar thought patterns or vibrations produces results of gravitational force ( F ) on the subjects, directed toward each other by nature. In other words, vibrational matches gravitationally attract; this is "The Secret" Law of Attraction in action; the formula used to represent G THEORY."
EXCERPT from: Solar Plexus: The Secret Gravitational System - ISBN: 1456300474
G THEORY: "Unification of the Science of Gravity with God and 'The Secret' Law of Attraction"
Courtesy of Whiffs of Bliss