Question

F =ma докажите что g не зависит от m

Answer 1

Возьмем закон Всемирного тяготения. На тело, находящееся вблизи поверхности Земли, действует сила
$F=G \frac{mM}{ R^{2} }$
m - масса тела, М - масса Земли
С другой стороны, по 2-му закону Ньютона
$F=ma$
Следовательно
$ma=G \frac{mM}{ R^{2} } \\ a=G \frac{M}{ R^{2} }$
Из этого выражения видно, что ускорение не зависит от массы тела.
Т.к. величины G, M, R не меняются, то и величина ускорения а есть тоже величина постоянная. Именно её мы и обозначаем g.
g не зависит от m.
Что и требовалось доказать.

Answer 2

The Relationship between Force, Mass, and Acceleration

The equation F = ma, also known as Newton's second law of motion, describes the relationship between force (F), mass (m), and acceleration (a). According to this law, the force acting on an object is equal to the mass of the object multiplied by its acceleration.

To prove that the acceleration due to gravity (g) does not depend on the mass of an object, we can examine the equation F = ma in the context of gravitational force.

When an object is near the surface of the Earth, it experiences a force due to gravity, which can be calculated using the equation F = mg, where m is the mass of the object and g is the acceleration due to gravity.

If we substitute this equation into Newton's second law, we get:

mg = ma

By canceling out the mass (m) on both sides of the equation, we are left with:

g = a

This equation shows that the acceleration due to gravity (g) is independent of the mass (m) of the object. In other words, all objects near the surface of the Earth experience the same acceleration due to gravity, regardless of their mass.

This conclusion is supported by experimental evidence and observations. For example, when objects of different masses are dropped from the same height, they fall with the same acceleration. This is known as the equivalence principle, which states that the gravitational mass and inertial mass of an object are equivalent.

Therefore, we can confidently say that the acceleration due to gravity (g) does not depend on the mass (m) of an object.

[[1]](https://www.uscis.gov/sites/default/files/document/guides/M-618_r.pdf)