Force & Mass

Discussion

different forces on same object (result?)
different objects with same forces (result?)
different objects with same acceleration (how?)

Lex. I.		Law I.
Corpus omne perſeverare in ſtatu ſuo quieſcendi vel movendi uniformiter in directum, niſi quatennus illud a viribus impreſſi cogitur ſtatum suum mutare.		Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Projectilia perſeverant in motibus ſuis, niſi quatenus a reſiſtentia aëris retardantur, & vi gravitatis impelluntur deorſum. Trochus, cujus partes cohærendo perpetuo retrahunt ſeſe a motibus rectilineis, non ceſſat rotari, niſi quatenus ab aëre retardantur. Majora autem planetarum & cometarum corpora motus ſuos & progreſſivos & circulares in ſpatiis minus reſiſtentibus factos conſervant diutius.		Projectiles continue in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are continually drawn aside from rectilinear motions, does not cease its rotations, otherwise than it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in freer spaces, persevere in their motions both progressive and circular for a much longer time.

Newton also defined what he called "the quantity of matter" "the quantity of motion". We now call them "mass" and "momentum", respectively.

Definitio. I.		Definition I.
Quantitas materiæ est mensura ejusdem orta ex illius densitate et magnitudine conjunctim.		The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.
Aer densitate duplicata, in spatio etiam duplicato, sit quadruplus; in triplicato sextuplus. Idem intelige de nive & pulveribus per compressionem vel liquesactionem condensatis. Et par eft ratio corporum omnium, quæ per caufas quascunque diversimode condensantur. Medii interea, si quod fuerit, interstitia partium libere pervadentis, hic nullam rationem habeo. Hanc autem quantitatem sub nomine corporis vel masse in sequentibus passim intelligo. Innotescit ea per corporis cujusque pondus: Nam ponderi proportionalem esse reperi per experimenta pendulorum accuratissime instituta, uti posthac docebitur.		Thus air of double density, in a double space, is quadruple in quantity; in a triple space, sextuple in quantity. The same thing is to be understood of snow, and fine dust or powders, that are condensed by compression or liquefaction; and of all bodies that are by any caused whatever differently condensed. I have no regard in this place to a medium, if any such there is, that freely pervades the interstices between the parts of bodies. It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body; for it is proportional to the weight, as I have found by experiments on pendulums, very accurately made, which shall be shewn hereafter.
Definitio. II.		Definition II.
Quantitas motus est mensura ejusdem orta ex velocitate et quantite materiæ conjunctim.		The quantity of motion is the measure of the same, arising from the velocity and the quantity of matter conjunctly.
Motus totius est summa motuum in partibus singulis; ideoque in corpore duplo majore, æ quali cum velocitate, duplus est, & dupla cum velocitate quadruplus.		The motion of the whole is the sum of the motions of all the parts; and therefore in a body double in quantity, with equal velocity, the motion is double; with twice the velocity it is quadruple.

(Newton, interpreted by Elert) Newton's second law of motion states that …

• acceleration is directly proportional to net force when mass is constant, and
• acceleration is inversely proportional to mass when net force is constant, and consequently
• net force is directly proportional to mass when acceleration is constant.

Newton's second law of motion is more compactly written as an equation that combines these relationships

∑ F = m a

Acceleration is directly proportional to net force and inversely proportional to mass.

Net force equals mass times acceleration. (note: acceleration means change in speed or direction.)

So what is mass?

1. pick an object to be the standard unit mass
2. push mass with reproducible force (or use the principle of action-reaction)
3. measure its acceleration
4. push an unknown mass with the same force
5. measure new acceleration
6. mass is inversely proportional to acceleration

Mass …

• Mass is a measure of resistance to acceleration.
  (More generally, mass is a measure of resistance to change.)
• Mass is a scalar quantity associated with matter.
• When a system is composed of several objects it is the total mass that matters.
• The SI unit of mass is the kilogram [kg].

So what's a force?

Force …

• A force is an interaction that causes acceleration.
  (More generally, a force is an interaction that causes a change.)
• Force is a vector quantity associated with an interaction.
• When several forces act on a system it is the net, external force that matters.
• The SI unit of force is the newton [N = kg m/s²].

When more than one force acts on an object it is the net force that is important. Since force is a vector quantity, use geometry instead of arithmetic when combining forces.

For a force to accelerate an object it must come from outside it. External force. Can't pull yourself up by your own bootstraps. Anyone who says you can is engaging in hyperbole.

Rule of thumb: one newton is approximately equal to a quarter pound

The concept of inertia comes in many forms.

The Physics Hypertextbook © 1998–2013 Glenn Elert

No condition is permanent.