View Single Post
Old 07-31-2019, 10:55 AM
RAMSET RAMSET is offline
Gold Member
Join Date: Mar 2009
Location: NYC and Conn USA
Posts: 1,420
a reply ...and a build is moving forward.

“Unless I am missing a nuance, the litre (a measurement of volume) defined the Kg. A litre does not vary according to altitude or proximity to a planet. “

A litre is a measure of volume and does not vary, correct. The litre defined the Kg, correct. Was this litre's weight measured with the buoyancy force of air acting on it at 1g of acceleration, or without the buoyancy force of air acting on it, is the question. In the absence of air's buoyancy force a litre would not weigh 1 Kg if it was originally defined immersed in air.

“The apparent weight can also differ from weight when an object is "partially or completely immersed in a fluid", where there is an "upthrust" from the fluid that is working against the force of gravity.[2] “

“To discuss weight, one is always considering it relative to its surroundings. The weight of 1kg in space maybe 9.8N (for sake of discussion) but in orbit the same Kg weighs 0N because it is in a permanent state 'of falling' and is therefore absent the effect of gravity. “

This statement is incorrect. w=mg therefore an astronaut weighs the same as the same as he would on Earth because his mass and his acceleration have remained the same. What the astronaut experiences as the feeling of weightlessness is the absence of stress forces acting in opposition from a normal plane. What you can say is that the 1Kg has a weight of 9.8N but exerts a force of 0N on it's surroundings.

Weightlessness in Newtonian mechanics

In Newtonian mechanics the term "weight" is given two distinct interpretations by engineers.

Weight1: Under this interpretation, the "weight" of a body is the gravitational force exerted on the body and this is the notion of weight that prevails in engineering. Near the surface of the earth, a body whose mass is 1 kg has a weight of approximately 9.81 N, independent of its state of motion, free fall, or not. Weightlessness in this sense can be achieved by removing the body far away from the source of gravity. It can also be attained by placing the body at a neutral point between two gravitating masses.

Weight2: Weight can also be interpreted as that quantity which is measured when one uses scales. What is being measured there is the force exerted by the body on the scales. In a standard weighing operation, the body being weighed is in a state of equilibrium as a result of a force exerted on it by the weighing machine cancelling the gravitational field. By Newton's 3rd law, there is an equal and opposite force exerted by the body on the machine. This force is called weight2. The force is not gravitational. Typically, it is a contact force and not uniform across the mass of the body. If the body is placed on the scales in a lift (an elevator) in free fall in pure uniform gravity, the scale would read zero, and the body said to be weightless i.e. its weight2 = 0. This describes the condition in which the body is stress free and undeformed. This is the weightlessness in free fall in a uniform gravitational field. (The situation is more complicated when the gravitational field is not uniform, or, when a body is subject to multiple forces which may, for instance, cancel each other and produce a state of stress albeit weight2 being zero. See below.)

To sum up, we have two notions of weight of which weight1 is dominant. Yet 'weightlessness' is typically exemplified not by absence of weight1 but by the absence of stress associated with weight2. This is the intended sense of weightlessness in what follows below.

A body is stress free, exerts zero weight2, when the only force acting on it is weight1 as when in free fall in a uniform gravitational field. Without subscripts, one ends up with the odd-sounding conclusion that a body is weightless when the only force acting on it is its weight.

The apocryphal apple that fell on Newton's head can be used to illustrate the issues involved. An apple weighs approximately 1 newton. This is the weight1 of the apple and is considered to be a constant even while it is falling. During that fall, its weight2 however is zero: ignoring air resistance, the apple is stress free. When it hits Newton, the sensation felt by Newton would depend upon the height from which the apple falls and weight2 of the apple at the moment of impact may be many times greater than 1 N. It was great enough—in the story—to make the great man invent the theory of gravity. It is this weight2 which distorts the apple. On its way down, the apple in its free fall does not suffer any distortion as the gravitational field is uniform.

A complicated subject indeed...

Force, Mass & Acceleration: Newton's Second Law of Motion

Acceleration and velocity

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

The bold letters F and a in the equation indicate that force and acceleration are vector quantities, which means they have both magnitude and direction. The force can be a single force or it can be the combination of more than one force. In this case, we would write the equation as ∑F = ma

The large Σ (the Greek letter sigma) represents the vector sum of all the forces, or the net force, acting on a body.

It is rather difficult to imagine applying a constant force to a body for an indefinite length of time. In most cases, forces can only be applied for a limited time, producing what is called impulse. For a massive body moving in an inertial reference frame without any other forces such as friction acting on it, a certain impulse will cause a certain change in its velocity. The body might speed up, slow down or change direction, after which, the body will continue moving at a new constant velocity (unless, of course, the impulse causes the body to stop).

There is one situation, however, in which we do encounter a constant force — the force due to gravitational acceleration, which causes massive bodies to exert a downward force on the Earth. In this case, the constant acceleration due to gravity is written as g, and Newton's Second Law becomes F = mg. Notice that in this case, F and g are not conventionally written as vectors, because they are always pointing in the same direction, down.
The product of mass times gravitational acceleration, mg, is known as weight, which is just another kind of force. Without gravity, a massive body has no weight, and without a massive body, gravity cannot produce a force. In order to overcome gravity and lift a massive body, you must produce an upward force ma that is greater than the downward gravitational force mg.

The key part here to note is the last sentence...

An upward force ma that is greater than the downward gravitational force mg will lift a massive body, as demonstrated in the real world by the Mythbusters team:

Mythbusters - Ping pong salvage

In conclusion it is possible to switch a massive bodies apparent weight by manipulating the buoyancy force acting upon it. The ratio between water and air density is:

1000/1.225 = 816.3265306122449
Reply With Quote