The human body is a collection of solid objects arranged in treelike configuration. Each object or tree of objects is composed of large number of particles with small mass and small volume (Fig. 3.1). Newton's laws presented in the previous chapter hold for each of these particles. According to the second law:
where Fi denotes the net force exerted on particle i by particles external to the system B of particles under consideration. The gravitational force is an example of an external force. It is acted on particle i by earth, which is outside the collection of particles under study. The internal force fij is exerted by particle j in the system of particles B on particle i in B. The symbol m1 is the mass of particle i, and ai is its acceleration. Note that, in accordance with Newton's third law, the force of reaction is equal to the negative of the force of action; that is:
Because a particle cannot exert a force on itself, fii is always equal to zero.
The motion of each particle i in B is described by Eqn. 3.1. Let us sum the left- and the right-hand side of Eqn. 3.1 from i = 1 to i = n where i takes the integer values and n is the number of particles in B:
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The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.