# Relationship between mass and acceleration of gravity

### Acceleration Due to Gravity Formula

Mass does not affect the acceleration due to gravity in any measurable way. . All of these relationships can now be written as the single equation in modern. While the mass is normally considered to be an unchanging property of an on the object and may be defined as the mass times the acceleration of gravity. Since this acceleration due to the Force of Gravity, it is called Acceleration due to If you recall that F = ma (Force = mass times acceleration) then this answer is The understanding of reality need you to understand the relation of equation.

For these reasons, all of the eight statements are false; there is an erroneous part to each statement due to the confusion of weight, mass, and force of gravity.

But if the elephant weighs more and experiences a greater downwards pull of gravity compared to the feather, why then does it hit the ground at the same time as the feather? To answer this question, we must recall Newton's second law - the law of acceleration.

Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. When figuring the acceleration of object, there are two factors to consider - force and mass. Applied to the elephant-feather scenario, we can say that the elephant experiences a much greater force which tends to produce large accelerations.

Yet, the mass of an object resists acceleration. Thus, the greater mass of the elephant which tends to produce small accelerations offsets the influence of the greater force. Even though a baby elephant may experience times the force of a feather, it has times the mass. The greater mass of the elephant requires the greater force just to maintain the same acceleration as the feather.

A simple rule to bear in mind is that all objects regardless of their mass experience the same acceleration when in a state of free fall. When the only force is gravity, the acceleration is the same value for all objects. On Earth, this acceleration value is 9. This is such an important value in physics that it is given a special name - the acceleration of gravity - and a special symbol - g.

But what about air resistance? Newton also critiqued and expanded on the work of Rene Descartes, who also published a set of laws of nature intwo years after Newton was born. Descartes' laws are very similar to Newton's first law of motion.

Acceleration and velocity Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

The bold letters F and a in the equation indicate that force and acceleration are vector quantities, which means they have both magnitude and direction. The force can be a single force or it can be the combination of more than one force. It is rather difficult to imagine applying a constant force to a body for an indefinite length of time.

### Force, Mass & Acceleration: Newton's Second Law of Motion

In most cases, forces can only be applied for a limited time, producing what is called impulse. Decreasing speed is also considered acceleration. But acceleration is more than just changing speed. Pick up your battered object and launch it one last time. This time throw it horizontally and notice how its horizontal velocity gradually becomes more and more vertical. Since acceleration is the rate of change of velocity with time and velocity is a vector quantity, this change in direction is also considered acceleration.

In each of these examples the acceleration was the result of gravity. 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.

## Newton's Laws and Weight, Mass & Gravity

If we could somehow reduce this drag we'd have a real experiment. 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. 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.