VIDEO: Formula for acceleration

Gravitational acceleration and gravity - you should know that

• The earth attracts bodies. Reason is a general principle of physics, after which masses attract each other (see below).
• If a body falls down due to this attraction, this movement is called "free fall" in physics. The body is then accelerated.
• This so-called. Gravitational acceleration is a quantity that varies within small limits on the (flattened) earth; an average value is g = 9.81 m / s².
• The mutual mass attraction, which also applies to the course of the planets around the sun and in principle everywhere, already preoccupied the physicist Isaac Newton.
• He found a formula with which the force between two masses can be calculated, the law of gravitation.


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• It reads F = γ _* m₁* m₂/ r², where γ = 6.67 _* 10^-11 m³ / kg * s² the so-called. The gravitational constant is a natural constant that Cavendish was able to measure with his gravitational balance. The two masses of the bodies involved are m
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  ₁ and m₂ and r is the distance between the two centers of mass.
• In principle, this formula can be used to calculate all forces between masses, including those between two breakfast rolls, even if these are of course vanishingly small.

Formula for the acceleration of gravity - this is how it works

In general, the value for the acceleration due to gravity g is determined experimentally, for example through experiments on free fall. Galileo carried out similar experiments. However, the acceleration due to gravity can also be calculated:

1. If a test specimen of mass m falls on the earth, it experiences on the one hand a gravitational force F, which the earth (it has mass M) exerts on it. This force can be calculated using Newton's formula.
2. On the other hand, it is accelerated by gravity; this is calculated (also according to Newton) as G = m _* G.
3. These two forces must be equal in the case of the earth.
4. So F = G and in formulas: γ _* m _* M / r² = m * g.
5. You can use this equation to calculate the acceleration due to gravity g: First, you reduce the mass m of your imaginary test specimen and you get: g = γ _* M / r².
6. For the calculation you need the gravitational constant γ, the earth's mass M = 6 _* 10²⁴ kg (rounded up slightly) and the radius of the earth r = 6371 km (mean value, rounded up slightly) = 6.371 _* 10⁶ m.
7. You insert the values ​​into the formula for the acceleration due to gravity and you get g = 9.86 m / s², a value that certainly applies to some places around the world and is quite acceptable in the context of the slightly rounded initial values is.