Hello, greetings, this is my first post and I want to briefly explain the error that is committed when the value of gravity is used as 10 m /s ̂2.
There are some absurd justifications for the use of this value in the basic texts of the baccalaureate physics, which are presented below:
- The value of 10, allows rapid multiplications, which saves us time in the resolution of problems, which are already extensive (reference: William Suarez, Eli Brett).
- When preparing videos of problem solving, the objective is to teach the subjects in less time, because many people do not like to watch extensive videos, for which, it is preferred not to use decimals.
- However, and for those who wish, they can develop the problems with the value of 9.8 m /s ̂2 and evaluate their results. It should be an approximate result, but never get a totally different result than what is seen in the problems.
As you see, there are different kinds of suggestions to solve problems, which are based in saving time and writing, in addition to the use of the calculator. In the experiences that have arisen, students find that in most cases they do not know how to use the calculator, to obtain a result of the solution of a formula or a problem in general, that is why mistakes are made at any time to give a result.
Let's see the definition of gravity
According to Galileo's hypothesis, in one place on Earth, and in the absence of air resistance, all bodies fall with the same uniform acceleration. This acceleration is called gravity on the earth and its approximate value is 9.80 m /s ̂ 2, whose direction is towards the center of the earth (Figure 1).
Actually the g depends on the altitude and geographical position of the earth and there are several gravimetric models to determine its value (see table).
Table. Representation of the values of gravity in different places on earth. Source: Giancoli Douglas
We also say that the minimum value of gravity is located on the equatorial line and in the highest parts of the planet, for example on Mount Everest you can estimate a gravity value of 9,771m / s ̂2, using equation (1) . That is to say that the weight of a body is much smaller in the equator and in high places, than in other geographical positions of the planet
Figure 1 Comparison of severity with height. Source:
Imagenlink
The earth is considered as an ellipsoid of revolution with ellipticity. Ellipity is the difference between the equatorial radius and the polar radius, divided by the equatorial radius, that is, 1/297. That is why this surface of revolution is assumed as a gradient of gravitational potential, where the force of gravity is by definition perpendicular to the surface at all points. In this way, gravity can be defined with respect to latitude and sea level as.ecuación:
Equation that was adopted in 1967, by the International Union of Geodesy and Geophysics and whose absolute value is given as 981.274m / s ̂2 (Gal), measured by KUHNEN AND FURTWANGLER in Potsdam in 1906 (reference: Parasnis D.S). Where φ = is the geographical latitude and Gal is the unit of acceleration that is used in geophysics and its name is in honor of Galileo. In addition, in the year 1980 it is recommended to use the following more precise equation to find the value of the gravity ecuación:
Suggested by the International Geodesy Association
Imagen link
Because gravity is different on earth
The value of the g can vary locally in the terrestrial surface because it presents irregularities and rocks of different densities. One of the consequences of this variation is produced in the polar ice caps, where the ice sheet that covered this area has disappeared 10 thousand years ago and is currently following that process due to global warming. Such irregularities are known as gravitational anomalies and are of the order of a part by 10 ̂6 or 10 ̂7. These very small values are measured with a gravimeter, which current times detect more than one part by 10 ̂8. Geophysicists use these measurements as parts of their research to investigate the earth's crust, and its goal is the search for groundwater, mining and oil. It is important to note that mineral exploration is an important parameter for the variation of gravity and its value may be slightly higher in mineral deposits than in underlying zones. While in underground salt domes the values of gravity tend to decrease and there is often oil (reference: Giancoli Douglas).
Conclusions
The conclusion that has been reached is that the value of gravity varies slightly in the earth and depends on the height and geographical position on the ground, so it can be noticed that there is no value of 10 m/s ̂2 anywhere on the earth surface. It is significant to teach the concept of the value of gravity in high school and to focus on the importance it has in physics and in geophysical exploration.
References
Breet. Eli, Suarez. William (2012). Física. Cuarto año. Editorial Distribuidora Escolar. Corporación Marca S.A. Caracas-Venezuela
Giancoli Douglas (1997). Physics: Principles with Applications Fourth 4th Edition. Prentice Hall
Hernández Víctor. (2016). Física 4. Editorial Ingenio. Genio Matic. Edición Secundaria. Lima-Perú.
Parasnis D.S. (1970). Principios de Geofísica Aplicada. Editorial Paraninfo. Madrid