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_A_ mass is an unspecified quantity; _the_ mass is a specific quantity

_A_ mass is an unspecified quantity; _the_ mass is a specific quantity - Physics Forum

_A_ mass is an unspecified quantity; _the_ mass is a specific quantity - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

_A_ mass is an unspecified quantity; _the_ mass is a specific quantity

Is this a subtle difference or what? When speaking of quantities
matter:

_A_ mass is an unspecified quantity; _the_ mass is a specific quantity;
called inertia.

Newton defined mass as the quantity of matter in a body; as the product
of its bulk and density conjointly. To find the specific quantity of
matter in a body requires both its bulk and density.

A specific quantity of matter is called inertia, and is the ratio of
the force exerted on and/or by a body, divided by the acceleration
caused. To find the specific quantity of matter in a body requires both
its weight and the acceleration at which it will free fall: or the
force and acceleration caused.

_A_ mass is an unspecified quantity; _the_ mass is a specific quantity

Don is still confused by his own non-sequiturs:

But Force (and therefore, weight, too) is _per_definition_ derived from
the cahnge of momentum over time:

F=dp/dt

For small velocities (v<<c), mass can be considered to be a constant,
therefore:

F=m*dv/dt

For continuous acceleration, this can be reduced to:

F=m*a

This definition holds true for both SI and imperial system, so if you
insist on force/weight being a fundamental value, not a derived one,
you'd have to invent a new definition on force (which I already
proposed, but you choose to ignore).

This new definition would also make it possible to omit any artifacts,
that seem to incumber you.

_A_ mass is an unspecified quantity; _the_ mass is a specificquantity

Don1 wrote:
:

Shead is confusing mass and inertia.

Inertia [Only registered users see links. ]
The resistance to change in state of motion which all matter exhibits.
It's a concept, Shead, not a number with units, not a ratio.

Newton's First Law [Only registered users see links. ]

Also called the "law of inertia," Newton's first law states that a
body at rest remains at rest and a body in motion continues to move
at a constant velocity unless acted upon by an external force.

Newton's Second Law is about "inertial mass" [Only registered users see links. ]

A force F acting on a body gives it an acceleration a which is in
the direction of the force and has magnitude inversely proportional
to the mass m of the body: F = ma

Inertia is an intrinsic property of mass. Most of what follows is
quoted from [Only registered users see links. ]

Gravitational Mass F = GmM/r^2
Inertial Mass F = ma
Acceleration a = dv/dt

1) Inertial mass. This is mainly defined by Newton's law,
the all-too-famous F = ma, which states that when a force
F is applied to an object, it will accelerate
proportionally, and that constant of proportion is the
mass of that object. In very concrete terms, to determine
the inertial mass, you apply a force of F Newtons to an
object, measure the acceleration in m/s^2, and F/a will
give you the inertial mass m in kilograms.

2) Gravitational mass. This is defined by the force of
gravitation, which states that there is a gravitational
force between any pair of objects, which is given by

F = G m1 m2/r^2

where G is the universal gravitational constant, m1 and m2
are the masses of the two objects, and r is the distance
between them. This, in effect defines the gravitational
mass of an object.

As it turns out, these two masses are equal to each other
as far as we can measure. Also, the equivalence of these
two masses is why all objects fall at the same rate on
earth.

The only difference that we can find between inertial and
gravitational mass that we can find is the method.

Gravitational mass is measured by comparing the force of
gravity of an unknown mass to the force of gravity of a
known mass. This is typically done with some sort of
balance scale. The beauty of this method is that no matter
where, or what planet, you are, the masses will always
balance out because the gravitational acceleration on each
object will be the same. This does break down near
supermassive objects such as black holes and neutron stars
due to the high gradient of the gravitational field around
such objects.

Inertial mass is found by applying a known force to an
unknown mass, measuring the acceleration, and applying
Newton's Second Law, m = F/a. This gives as accurate a
value for mass as the accuracy of your measurements. When
the astronauts need to be weighed in outer space, they
actually find their inertial mass in a special chair.

The interesting thing is that, physically, no difference
has been found between gravitational and inertial mass.
Many experiments have been performed to check the values
and the experiments always agree to within the margin of
error for the experiment. Einstein used the fact that
gravitational and inertial mass were equal to begin his
Theory of General Relativity in which he postulated that
gravitational mass was the same as inertial mass and that
the acceleration of gravity is a result of a "valley" or
slope in the space-time continuum that masses "fell down"
much as pennies spiral around a hole in the common
donation toy at your favorite chain store.

Useful references for Shead [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ]