The work done by a force on a body during a time interval t2 — t1 is equal to the integral of the power exerted by the force on the body over the same time interval:
in which W1-2 denotes the work done by the force on the body during the time interval t2 - t1. In this equation, the vector v represents the velocity of the point of application of force F. The position vector connecting the origin O of the inertial reference frame E to the point of application of the force F is termed r and is represented in terms of its projections to the axes of the coordinate system as follows:
In the following, we present expressions for the work done by various types of forces that are commonly associated with human movement and motion.
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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.