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The Bulgarian, Ivan Charakov, is shown moments before his "ascent" stage of a back squat. The back squat consists of taking the load from the rack, descent to squatted position then ascent to full upright. A typical "ascent" required two seconds with the elevation of the bar increasing about one meter. Once, Ivan (in the 90kg class) did three repetitions of this lift with the bar set at 330kg.
Analysis to proceed past our event scenario "single-completed ascent" requires selection of a system. A number are apparent; none are "wrong." The system might be the weight - (W), Ivan - (I), or Ivan and the weight, (I+W) taken together.
An event and system defined, the next considerations are system properties/charateristics: mass, force, momentum, work, and energy aspects.The "ascent" stage.
Analysis: 2nd Law integrated over time.
The schematic (right) shows the weight (W) in its initial position and (ghosted) final position.
|(1) This is Newton's 2nd Law written to express momentum, explicitly.|
The weight is constant. The term left-of-equality reduces as show below. Also two forces are relevant; the force of gravity toward Earth and the force exerted by Ivan.Free-Body-Diagram:
The usual form, f = m A, makes more sense written as,|
d(mV)/dt = ΣF with acceleration expressed as dV/dt.
Ivan supports the barbell. The event might be called, permanence or static equilibrium. Suppose Ivan holds the weight for 5 seconds. Let's look at 3 seconds of time within that 5 second duration. Steps to proceed are. Specify the gravity force as mass times Earth-surface acceleration directed, (-K). Next separate variables, apply integration operator with limits to obtain:
The term above left integrates promptly to equal zero. The result, Eqn-4 below seems strange at first.
|(4)What is the meaning of this?|
What can be the meaning of the above equation? Well, a theorem of calculus states, "if an integral equals zero, then its integrand is everywhere zero" below left.
Our calculation using the 2nd Law with lift as event shows the same conclusions as "support as event". Newton's 2'nd Law, we learn, perceives no differentiation in the obviously different events, "shouldering" and "lifting." By retro-inspection, observe that the equations (Eqn-1 to 5) for just holding the weight are the same as for the weight being lifted. Yet the events are different. More than Newton's 2'nd Law is needed. For this event, the 2'nd Law perceives no difference of the "weight lifted" and the "weight shouldered."
is different from the squat.
Work, a new idea is the answer.