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Unformatted text preview: Work So far, the problems that we have studied have had either a constant force, or one that is time dependent. In these cases we have been able to solve for the velocity, and from that the position as a function of time. However, in many of the problems that we face, we only know the force as a function of position. In these cases, our "standard" methods do not work well and new methods are needed. The most important method is the use of work and energy conservation. We can define energy as a measurement of the capacity of an object to do work, where work is a measurement of the amount of force applied through a distance. Mathematically, this can be written as = 2 1 x x x d F W (10.1) where x is the vector tangent to the path that the object traverses. Conservation Principles One of the most important concepts that is connected to energy is that of conservation of energy . Conservation of energy is one of the major conservation laws in physics. What do we mean by a conservation law? Whenever we attempt to describe a physical system, we create a mathematical model of it. This model uses various parameters to describe the state of the system at any given time. Most of these parameters can vary when the system undergoes a transformation or an interaction, but some of the parameters remain constant. These parameters are referred to as having been conserved by the transformation or interaction. There are three major conservation principles in physics today: conservation of energy-momentum , conservation of angular momentum , and conservation of charge . Conservation of energy-momentum leads to our familiar principles of conservation of energy, conservation of linear...
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