Gravity is a universal phenomenon, without which not a single cosmic process can do. In our life, we feel the effect of gravity when we try to jump or jump from an object, or when we throw and catch different things. An important characteristic of gravity is gravity, which imparts some acceleration to all bodies. The acceleration of gravity on our Earth is discussed in detail in the article below.
Isaac Newton and his law
As mentioned in the introduction, a person feels the acceleration of gravity (the acceleration of the fall of bodies in an airless space) when performing almost all everyday activities. Nevertheless, a mathematical description of the phenomenon of gravity appeared relatively recently. It owes its appearance to the great English mathematician and physicist Sir Isaac Newton.
In the 80s of the XVII century, carefully studying a huge layer of experimental data on the motion of cosmic bodies, as well as analyzing Kepler’s laws from a mathematical point of view, Newton derived a mathematical formulation of the law of gravitation in the Universe. The scientist showed that any two bodies that have masses m 1 and m 2 , and which are at a distance r from each other, are attracted with a force F. The latter is calculated by the formula:
F = G * m 1 * m 2 / r 2 .
Here G = 6.67 * 10 -11 N * m 2 / kg 2 . The value of G is called the universal constant of gravity. Its value is equal to the force with which two bodies with masses of 1 kg each are attracted, being at a distance of 1 meter from each other. The value of this constant was experimentally measured by Cavendish at the end of XVIII using torsion weights. Knowing the value of G allowed us to calculate the mass of our planet.
Gravity, gravity and acceleration of gravity
To understand where gravity acceleration comes from, we use Newton's law of gravity:
F = G * m * M / R 2 .
Here M is the mass of the globe, R is its average radius. These values are currently known with great accuracy. Substitute them in the written equality, we get:
F = 6.67 * 10 -11 * 5.972 * 10 24/6371000 2 * m = 9.81 * m.
What does the resulting expression mean? It says that the force with which the globe attracts bodies depends solely on the mass of these bodies (directly proportional to the mass m).
Let us write out the resulting expression again:
F = m * g, where g = 9.81.
If you carefully look at the formula for the force F, you can see that it exactly corresponds to the mathematical formulation of Newton’s second law. This fact suggests that each body is informed by gravity acceleration (acceleration g), which is called the acceleration of gravity. Near the surface of the planet, it is 9.81 m / s 2 .
The meaning of the term "acceleration of gravity"
It is useful to clarify the term "free fall acceleration." The word "free" means the absence of any external force, except for gravity, which would interfere with the movement of the body. On Earth, such a force is the friction of air. The latter explains why heavy bodies fall faster than light ones (air friction is much less than gravity for heavy bodies and comparable to that for lungs).
As for the word “fall” in the term under consideration, we note that the acceleration of gravity by gravity is generated not only for falling, but also for rising bodies. The difference between these directions of motion lies only in the fact that when the body falls, the acceleration g is directed along the velocity vector, and when it rises, it is directed against it.
Galileo's experiments on measuring g
Newton discovered his law at the end of the 17th century, however, the significance of the acceleration of gravity on Earth was known at least 100 years before this discovery, thanks to the experiments of Galileo Galilei.
The famous Italian scientist of modern times conducted a series of experiments in which he dropped bodies of various masses from the top of the tower in the city of Pisa. Given the air resistance, Galileo came to the conclusion that gravity acceleration (acceleration g) tells all bodies the same when they fall.
The experiments mentioned were extremely simple. A body was thrown from a known height, and with the help of a stopwatch the time was measured when it reached the surface of the earth. Galileo used the following kinematic expression for uniformly accelerated motion to determine g:
h = g * t 2/2 =>
g = 2 * h / t 2 .
The g values obtained in these experiments are close to the current value of 9.81 m / s 2 .
Modern instruments for measuring Earth gravity
A science that studies and measures the acceleration of gravity (the acceleration of a free fall) is called gravimetry. The corresponding device is called a gravimeter. Modern gravimeters are divided into two types:
Absolute instruments operate on the principle of the described Galileo experiments. Modern absolute gravimeters are quite accurate and have compact dimensions. The first absolute gravimeter is the Galilean pendulum. Knowing the period of oscillation of the pendulum allows us to calculate the value of g.
Relative gravimeters make it possible to measure local oscillations of Earth's gravity. Before use, these instruments are calibrated with respect to some known value of g in a particular area. The simplest relative gravimeter is a spring with a weight suspended from it.
When in school physics problems they ask "determine the acceleration of gravity," this question is not only of theoretical but also of important practical interest. Thus, knowledge of fluctuations in g allows one to determine the deposits of various minerals and groundwater in a particular area.