Apparent Weight

The apparent weight of an object corresponds to the weight indicated by a Peson (or any other instrument appropriate to the measurement of a force), when this weight is not identical to the “real” weight of the object, definite either as the gravitational force purely exerted on the object, or generally as the force due to the Pesanteur.

For example, if one weighed an object under water, the Poussée of Archimedes would make appear the lighter object and the measured weight would be lower than the actual weight. Obviously, in the daily life, when an object is weighed, the push of Archimedes exerted by the ambient air is for whatever purpose it may serve negligible.

Here another example. Balances an object by suspending it with a dynamometer. It will be subjected to two forces: its weight, directed to the bottom, and forces it exerted by the dynamometer, directed upwards. When the object does not accelerate, the two forces have the same size and the dynamometer indicates the actual weight of the object. However, if one takes the measure to a Ascenseur while this one is put moving to the top, the force exerted by the dynamometer will be higher than the weight (at least with the eyes of a motionless observer located outside the elevator), in accordance with the second law of the movement of Newton:

F - P = my ,

where F is the force exerted by the dynamometer, P the weight of the object and has the Accélération of the elevator (and of the dynamometer).

Since weight indicated by dynamometer corresponds to intensity F of force that exerts on him object to weigh (this force being the reaction with the force which the dynamometer exerts on the object), this “apparent” weight is higher than the actual weight ( F > P , because has > 0).

(For an observer located in the elevator, the object to be weighed appears obviously motionless. In this case, to explain that the force exerted by the dynamometer is higher than the actual weight of the object, one must utilize a inertia directed downwards.)

Thus, in a general way, the measuring instruments like the Peson (or dynamometer) indicate the apparent weight of the objects, which usually corresponds to the force of gravity, but never corresponds perfectly to the purely gravitational force, would be this only because the Ground itself is not a reference frame rigorously galiléen.

Lastly, like last example, let us mention the state of Impesanteur tested by the Spationaute S. Ainsi, in the International space station, their weight apparent is completely null, although their actual weight, to 386 km of altitude, is only approximately 11% weaker than on Earth.

Numerical example:

Which is the apparent weight of a person of 70 kg in an elevator which decelerates to 2 m/s ² while going up?

That is to say G = 9,8 m/s² the acceleration of gravity. The actual weight of the person, equal to Mg , is worth (70 kg) (9,8 m/s²) = 686 NR.

The person is subjected to two forces: on the one hand its actual weight P , directed downwards, and on the other hand the force normal NR , directed upwards, exerted on it by the floor of the elevator (or the Pèse-personne on which it is held). When the elevator slows down, its acceleration is directed in the direction opposed at the speed, i.e. in fact downwards.

By directing the Axis reference upwards, one will thus write, in accordance with the second law of Newton:

NR - P = m (- A)

NR - Mg = - my

NR = Mg - my

NR = m ( G - has )

NR = (70 kg) m/s²) - (2 m/s²) = 546 NR

One obtains an apparent weight of 546 NR, lower than the actual weight.

See too

External bonds

http://sc.physiques.free.fr/htmlfiles/cours/foy/poids.htm (in an elevator)

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