# Relationship of distance and acceleration due to gravity

### Free Fall – The Physics Hypertextbook

Near the earths surface, acceleration due to gravity is m/s2. Understanding the relationship between velocity, acceleration and distance traveled allows us. In this science fair project on the relationship between distance and time, kids explore the Is your reaction time faster than acceleration due to gravity?. Distance, Velocity, Momentum, Force, Pressure, Work and Energy. Distance, Speed the acceleration due to gravity at the surface of the earth. force exerted by.

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.

### Acceleration Due to Gravity Formula

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. 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?

## Acceleration Due to Gravity Formula

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. Together, they should have twice their original acceleration. But how do they know to do this? How do inanimate objects know that they are connected?

Let's extend the problem.

## Gravitational Acceleration

Isn't every heavy object merely an assembly of lighter parts stuck together? How can a collection of light parts, each moving with a small acceleration, suddenly accelerate rapidly once joined? We've argued Aristotle into a corner. The acceleration due to gravity is independent of mass. Galileo made plenty of measurements related to the acceleration due to gravity but never once calculated its value or if he did, I have never seen it reported anywhere.

Instead he stated his findings as a set of proportions and geometric relationships — lots of them. His description of constant speed required one definition, four axioms, and six theorems. All of these relationships can now be written as the single equation in modern notation. Contrary to the common wisdom, mathematics makes life easier. Although mass has no effect on the acceleration due to gravity, there are other factors that do.

Everyone reading this should be familiar with the images of the astronauts hopping about on the moon and should know that the gravity there is weaker than it is on the Earth — about one sixth as strong or approximately 1. That is why the astronauts were able to hop around on the surface easily despite the weight of their space suits.

Astronauts cruising through the top of Jupiter's thick atmosphere would find themselves struggling to stand up inside their space ship. The acceleration due to gravity varies with location. Furthermore, even on the Earth, this value varies with latitude and altitude to be discussed in later chapters.

The acceleration due to gravity is greater at the poles than at the equator and greater at sea level than atop Mount Everest. There are also local variations that depend upon geology. The value of 9. The acceleration due to gravity is effectively 9. How crazy are you for accuracy? For most applications, the value of 9. During a multiple choice exam where calculators aren't allowed, this is often the way to go. If you need greater accuracy, consult a comprehensive reference work to find the accepted value for your latitude and altitude.

If that's not good enough, then obtain the required instruments and measure the local value to as many significant digits as you can. You may learn something interesting about your location. I once met a geologist whose job it was to measure g across a portion of West Africa. When I asked him who he worked for and why he was doing this, he basically refused to answer other than to say that one could infer the interior structure of the Earth from a gravimetric map prepared from his findings.

Knowing this, one might then be able to identify structures where valuable minerals or petroleum might be found. Like all professions, those in the gravity measuring business gravimetry have their own special jargon.

Note that the unit is written in lowercase as a word but is capitalized as a symbol. Split that into a thousand parts and you get a milligal [mGal]. Measurements with this precision can be used to study changes in the Earth's crust, sea levels, ocean currents, polar ice, and groundwater.

Push it a little bit further and it should be possible to detect changes in earth's atmosphere. Gravity is a heavy subject that will be discussed in more detail later in this book. Gee, Wally As was discussed earlier, don't confuse the phenomena of acceleration due to gravity with the unit of the same name. While the quantity g has a value that depends on location and is approximately 9.

The unit uses the roman or upright g while the natural phenomena uses the italic or oblique g. Don't confuse g with g. Time will be on the x-axis, distance traveled in meters will be on the y-axis. Use the following equation to calculate the time it takes for the meter stick to fall. How close is your calculated time to your stopwatch value? Where d is the distance the object traveled, in meters g is the gravitational acceleration on Earth, equal to 9.

Calculate the acceleration at any point on the graph. How close is it to the gravitational acceleration of Earth? Repeat the experiment with a dollar bill. Use the above equation to calculate how long it will take for the length of the dollar to pass through your fingers.

Can you catch it? Results Graphing results will show that distance traveled is in proportional to the square of the time spent falling.

Your calculated acceleration should be close to 9. Human reaction time is approximately 0. The graph you create will show that the longer the meter stick falls, the faster it ends up moving. This explains the curve in the graph: When objects are in true free fall, they will eventually reach their terminal velocity when the downward force from gravity and the upward force from air resistance are equal.