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8: Work and Energy

Last updated

Jun 23, 2019
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- 7.19: Angular vs. Linear Quantities
- 8.1: Prelude to Work and Kinetic Energy

Boundless
Boundless

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Topic hierarchy

8.1: Prelude to Work and Kinetic Energy
In this chapter, we discuss some basic physical concepts involved in every physical motion in the universe, going beyond the concepts of force and change in motion. These concepts are work, kinetic energy, and power. We explain how these quantities are related to one another, which will lead us to a fundamental relationship called the work-energy theorem. In the next chapter, we generalize this idea to the broader principle of conservation of energy.
8.2: Work
In physics, work represents a type of energy. Work is done when a force acts on something that undergoes a displacement from one position to another. Forces can vary as a function of position, and displacements can be along various paths between two points. We first define the increment of work dW done by a force acting through an infinitesimal displacement as the dot product of these two vectors. Then, we can add up the contributions for infinitesimal displacements, along a path between two po
8.3: Kinetic Energy
Kinetic energy related to the forces acting on a body and was referred to as “the energy of motion.” The kinetic energy of a particle is one-half the product of the particle’s mass m and the square of its speed v.
8.4: Work-Energy Theorem
Work-Energy Theorem argues the net work done on a particle equals the change in the particle’s kinetic energy. According to this theorem, when an object slows down, its final kinetic energy is less than its initial kinetic energy, the change in its kinetic energy is negative, and so is the net work done on it. If an object speeds up, the net work done on it is positive.
8.5: Power
The concept of work involves force and displacement; the work-energy theorem relates the net work done on a body to the difference in its kinetic energy, calculated between two points on its trajectory. None of these quantities or relations involves time explicitly, yet we know that the time available to accomplish a particular amount of work is frequently just as important to us as the amount itself.
8.6: Work and Kinetic Energy (Exercises)
8.7: Work and Kinetic Energy (Summary)
8.9: Introduction
Work is the energy associated with the action of a force.
8.10: Work Done by a Constant Force
The work done by a constant force is proportional to the force applied times the displacement of the object.
8.11: Work Done by a Variable Force
Integration is used to calculate the work done by a variable force.
8.12: Work-Energy Theorem
The work-energy theorem states that the work done by all forces acting on a particle equals the change in the particle’s kinetic energy.
8.13: Prelude to Potential Energy and Conservation of Energy
In George Rhoads’ rolling ball sculpture, the principle of conservation of energy governs the changes in the ball’s kinetic energy and relates them to changes and transfers for other types of energy associated with the ball’s interactions.
8.14: Potential Energy of a System
In Work, we saw that the work done on an object by the constant gravitational force, near the surface of Earth, over any displacement is a function only of the difference in the positions of the end-points of the displacement. This property allows us to define a different kind of energy for the system than its kinetic energy, which is called potential energy. We consider various properties and types of potential energy in the following subsections.
8.15: Conservative and Non-Conservative Forces
A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
8.16: Conservation of Energy
A conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particle stays constant. For one-dimensional particle motion, in which the mechanical energy is constant and the potential energy is known, the particle’s position, as a function of time, can be found by evaluating an integral that is derived from the conservation of mechanical energy.
8.17: Potential Energy Diagrams and Stability
Interpreting a one-dimensional potential energy diagram allows you to obtain qualitative, and some quantitative, information about the motion of a particle. For example, the negative of the slope of the potential energy curve, for a particle, equals the one-dimensional component of the conservative force on the particle. Also, at a turning point, the potential energy equals the mechanical energy and the kinetic energy is zero, indicating that the direction of the velocity reverses there.
8.18: Sources of Energy
Energy can be transferred from one system to another and transformed or converted from one type into another. Some of the basic types of energy are kinetic, potential, thermal, and electromagnetic. Renewable energy sources are those that are replenished by ongoing natural processes, over human time scales. Non-renewable energy sources are those that are depleted by consumption, over human time scales.
8.19: Potential Energy and Conservation of Energy (Exercises)
8.20: Potential Energy and Conservation of Energy (Summary)
8.21: Potential Energy and Conservation of Energy
Conservative force—a force with the property that the work done in moving a particle between two points is independent of the path it takes.
8.22: Power
In physics, power is the rate of doing work—the amount of energy consumed per unit time.
8.23: CASE STUDY: World Energy Use
The most prominent sources of energy used in the world are non-renewable (i.e., unsustainable).
8.24: Further Topics
Thermal, chemical, electric, radiant, nuclear, magnetic, elastic, sound, mechanical, luminous, and mass are forms that energy can exist in.

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