# Discuss the relationship between speed and acceleration due to gravity

### Gravitational Acceleration | Science Primer

It is equal to the ratio of change in velocity with respect to time between the given Let's discuss about the calculation of acceleration due to gravitational force. The Physics of the Universe - Special and General Relativity - Gravity and Acceleration. Motion at constant speed is clearly a very special case, and in practice, . Special Theory of Relativity for a more detailed discussion of time dilation). About the Concept Builders · Relationships and Graphs · Kinematics · Newton's Laws · Vectors and Projectiles · Momentum and . 1-D Kinematics - Lesson 5 - Free Fall and the Acceleration of Gravity What is the, acceleration of gravity on It is the ratio of velocity change to time between any two points in an object's path.

Your object was accelerating because gravity was pulling it down. Even the object tossed straight up is falling — and it begins falling the minute it leaves your hand. If it wasn't, it would have continued moving away from you in a straight line. This is the acceleration due to gravity. What are the factors that affect this acceleration due to gravity? If you were to ask this of a typical person, they would most likely say "weight" by which the actually mean "mass" more on this later.

That is, heavy objects fall fast and light objects fall slow. Although this may seem true on first inspection, it doesn't answer my original question. The two quantities are independent of one another. Light objects accelerate more slowly than heavy objects only when forces other than gravity are also at work.

When this happens, an object may be falling, but it is not in free fall. Free fall occurs whenever an object is acted upon by gravity alone. Obtain a piece of paper and a pencil.

Hold them at the same height above a level surface and drop them simultaneously. The acceleration of the pencil is noticeably greater than the acceleration of the piece of paper, which flutters and drifts about on its way down. Something else is getting in the way here — and that thing is air resistance also known as aerodynamic drag. If we could somehow reduce this drag we'd have a real experiment.

ACCELERATION DUE TO GRAVITY

Repeat the experiment, but before you begin, wad the piece of paper up into the tightest ball possible. Now when the paper and pencil are released, it should be obvious that their accelerations are identical or at least more similar than before.

We're getting closer to the essence of this problem. If only somehow we could eliminate air resistance altogether. The only way to do that is to drop the objects in a vacuum. It is possible to do this in the classroom with a vacuum pump and a sealed column of air.

Under such conditions, a coin and a feather can be shown to accelerate at the same rate. In the olden days in Great Britain, a guinea coin was used and so this demonstration is sometimes still called the "guinea and feather". A more dramatic demonstration was done on the surface of the moon — which is as close to a true vacuum as humans are likely to experience any time soon.

## Acceleration Due to Gravity

In accordance with the theory I am about to present, the two objects landed on the lunar surface simultaneously or nearly so. Only an object in free fall will experience a pure acceleration due to gravity.

It was an immensely popular work among academicians and over the centuries it had acquired a certain devotion verging on the religious.

It wasn't until the Italian scientist Galileo Galilei — came along that anyone put Aristotle's theories to the test. Unlike everyone else up to that point, Galileo actually tried to verify his own theories through experimentation and careful observation. He then combined the results of these experiments with mathematical analysis in a method that was totally new at the time, but is now generally recognized as the way science gets done. For the invention of this method, Galileo is generally regarded as the world's first scientist.

In a tale that may be apocryphal, Galileo or an assistant, more likely dropped two objects of unequal mass from the Leaning Tower of Pisa. Quite contrary to the teachings of Aristotle, the two objects struck the ground simultaneously or nearly so.

Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse stopwatches and photogates having not yet been invented.

This he repeated "a full hundred times" until he had achieved "an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat.

Professors at the time were appalled by Galileo's comparatively vulgar methods even going so far as to refuse to acknowledge that which anyone could see with their own eyes. In a move that any thinking person would now find ridiculous, Galileo's method of controlled observation was considered inferior to pure reason.

### Free Fall – The Physics Hypertextbook

I could say the sky was green and as long as I presented a better argument than anyone else, it would be accepted as fact contrary to the observation of nearly every sighted person on the planet. Galileo called his method "new" and wrote a book called Discourses on Two New Sciences wherein he used the combination of experimental observation and mathematical reasoning to explain such things as one dimensional motion with constant acceleration, the acceleration due to gravity, the behavior of projectiles, the speed of light, the nature of infinity, the physics of music, and the strength of materials.

His conclusions on the acceleration due to gravity were that… the variation of speed in air between balls of gold, lead, copper, porphyry, and other heavy materials is so slight that in a fall of cubits a ball of gold would surely not outstrip one of copper by as much as four fingers. Having observed this I came to the conclusion that in a medium totally devoid of resistance all bodies would fall with the same speed.

For I think no one believes that swimming or flying can be accomplished in a manner simpler or easier than that instinctively employed by fishes and birds.

## Gravity and Acceleration

When, therefore, I observe a stone initially at rest falling from an elevated position and continually acquiring new increments of speed, why should I not believe that such increases take place in a manner which is exceedingly simple and rather obvious to everybody? I greatly doubt that Aristotle ever tested by experiment. Galileo Galilei, Despite that last quote, Galileo was not immune to using reason as a means to validate his hypothesis. In essence, his argument ran as follows.

Imagine two rocks, one large and one small. Since they are of unequal mass they will accelerate at different rates — the large rock will accelerate faster than the small rock. Now place the small rock on top of the large rock. According to Aristotle, the large rock will rush away from the small rock. What if we reverse the order and place the small rock below the large rock?

It seems we should reason that two objects together should have a lower acceleration. The small rock would get in the way and slow the large rock down. But two objects together are heavier than either by itself and so we should also reason that they will have a greater acceleration. This is a contradiction. Here's another thought problem. Take two objects of equal mass. According to Aristotle, they should accelerate at the same rate. Now tie them together with a light piece of string.

### Acceleration of Gravity

Together, they should have twice their original acceleration. His resulting General Theory of Relativityover ten years in the making it was published inhas been called the greatest contribution to science by a single human mind.

Newton's Law of Universal Gravitation Source: Gravity is the organizing force for the cosmos, crucial in allowing structure to unfold from an almost featureless Big Bang origin. Although it is a very weak force feebler than the other fundamental forces which govern the sub-atomic world by a factor of or 1,,,,,,it is a cumulative and consistent force which acts on everything and can act over large distances.

So, even though gravity can be effectively ignored by chemists studying how groups of atoms bond together, for bodies more massive than the planet Jupiter the effects of gravity overwhelm the other forces, and it is largely responsible for building the large-scale structures in the universe.

Even before Newton, the great 17th Century Italian physicist Galileo Galilei had shown that all bodies fall at the same rate, any perceived differences in practice being caused by differences in air resistance and drag. Newton, however, had assumed that the force of gravity acts instantaneously, and Einstein had already shown that nothing can travel at infinite speed, not even gravitybeing limited by the de facto universal speed limit of the speed of light.

Furthermore, Newton had assumed that the force of gravity was purely generated by masswhereas Einstein had shown that all forms of energy had effective mass and must therefore also be sources of gravity.

The principle of equivalence says that gravity is not a force at all, but is in fact the same thing as acceleration Source: Time Travel Research Center: He realized that if he were to fall freely in a gravitational field such as a skydiver before opening his parachute, or a person in an elevator when its cable breakshe would be unable to feel his own weight, a rather remarkable insight inmany years before the idea of freefall of astronauts in space became commonplace.

A simple thought experiment serves to clarify this: