Energy
In this chapter, we introduce the concept of energy and energy conservation through two examples: A vertical bowshot and an atom moving along a surface. Based on the examples, we introduce the concept of potential energy for a position-dependent force to
- PDF / 1,249,585 Bytes
- 48 Pages / 439.37 x 666.142 pts Page_size
- 80 Downloads / 128 Views
Energy
You have now learned to use the work-energy theorem as an alternative formulation of Newton’s second law—as a “calculation” tool to determine the motion of an object. Using Newton’s second law, we find the motion of an object described as the position as a function of time. The work-energy theorem allows us to find the velocity as a function of position without determining the whole motion, and we have learned that this may be useful, in particular when we are unable to find an exact solution to the equations of motion. While this was a practical application of the work-energy theorem, the real strength of the work-energy theorem is a conceptual change: We go from discussing motion and processes in terms of forces to instead discuss them in terms of energy and energy conservation. Conservation laws: One of the most important consequences of Newton’s second law and its alternative formulation through the work-energy theorem is the concept of a conservation law: That there are quantities in a system that are conserved throughout a process. We observe the system and record a particular quantity. Then we let the system develop in time, and we measure the same quantity again. If the quantity is conserved, it means that the quantity is unchanged, no matter what happens inside the system. The two most important conservation laws you will learn are the conservation of (mechanical) energy and the conservation of momentum. The conservation laws in mechanics are consequences of Newton’s laws of motion, but the conservation law for energy is much more general than that—it is one of the most general laws we know in nature. Throughout your studies of physics you will gradually learn to make energy considerations and energy conservation an integral part of your thought process, starting from this chapter. In practice the conservation laws represent clever ways to solve physics problems. In many cases we cannot solve the equations of motion we get from Newton’s second law directly, but in some cases we can solve the equations we get when we integrate Newton’s second law. The conservation law for momentum comes from integrating Newton’s second law in time and the conservation law for energy comes © Springer International Publishing Switzerland 2015 A. Malthe-Sørenssen, Elementary Mechanics Using Matlab, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-3-319-19587-2_11
303
304
11 Energy
from integrating along a path, integration along the x-axis in one dimension, as introduced through the work-energy theorem. Overview: In this chapter, we introduce the concept of energy and energy conservation through two examples: A vertical bowshot and an atom moving along a surface. Based on the examples, we introduce the concept of potential energy for a positiondependent force, a positional energy, to complement the kinetic energy, an energy of motion. For objects subject only to position-dependent force, the sum of the potential and kinetic energy is constant. We can therefore interpret a motion as a transfer of energy betw
Data Loading...
