Prom Wear 2010 Manila

inertial mass and gravitational mass

The concept of mass is one of the concepts of physics more "complicated" to be defined.
mass, like every physical quantity must be measurable. Then need to define the laws expressed in mathematical formulas that invoke it.

There are therefore two types of mass

1) the inertial mass , one that appears in the formula 2 'principle of dynamics:

F = ma

2) the gravitational mass , one that appears in the formula of the law of gravitation:

F = Gm 1 m 2 / R.

These are two different types of mass, as defined in the phenomena of a different nature and therefore different mathematical formulas. But then we see to give a more precise definition of the two types of mass.

1) The inertial mass indicates the "resistance" that a body opposed to a change in its state of motion .

In fact, if we apply the same force to two different bodies, we get different accelerations.
If, for example, a force of 100 N to a body of 10,000 kg inertial mass we get an acceleration equal to:

a = F / m = 100/10000 = 0, 01 m / s ^ 2

If we apply the same force to a body's inertial mass 5 kg, we get the acceleration:

a = F / m = 100 / 5 = 20 m / s ^ 2.

A higher body mass inertia opposes a greater "resistance" to change its state of motion that, with the same force, you get a lower acceleration. A body mass inertia opposes child less "resistance" to change its state of motion that, with the same force, you get a greater acceleration.

We can then define the inertial mass as the ratio:

m = F / a.

To calculate the inertial mass of a body then simply divide the force acting on it by the acceleration it undergoes. At equal strength, lower inertia mass means faster acceleration, greater inertial mass means less acceleration (acceleration and inertial mass are inversely proportional).

2) The gravitational mass indicates the "capacity" that the bodies of attract gravitationally.

The gravitational force that occurs between two bodies is directly proportional to the masses
bodies and inversely proportional to the square of their distance (calculated with respect to their centers of mass).

What is the relationship between the two types of mass?

Experience has shown that inertial mass and gravitational mass are linked with each other (
for this reason that justifies the use of the term "mass").

In fact, thanks to sophisticated experiments, occurs inertial mass and gravitational mass
coincide (with great precision), this fact is not obvious, so as to represent a new
law of nature, which he called Einstein equivalence principle . The equivalence between the two types of mass is the basic logic underlying the theory of general relativity .