Was ist mechanische Energie? Ich brauche eine umfassende Definition

Frage

Was ist mechanische Energie

conservartion-of-mechanical-energy-pendulumin der Physik, mechanische Energie (Emech) is the energy associated with the motion und Position of an object usually in some force field (z.B.. Schwerkraftfeld). Mechanical energy (and also the thermal energy) can be separated into two categories, transient and stored. Transient energy is energy in motion, das ist, energy being transferred from one place to another. Stored energy is the energy contained within a substance or object. Transient mechanical energy is commonly referred to as Arbeit. Stored mechanical energy exists in one of two forms: kinetisch oder potential:

  • Potential energy. Potential energy, die, is defined as the energy stored in an object subjected to a conservative force. Common types include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object.
  • Kinetic energy. The kinetic energy, K, is defined as the energy stored in an object because of its motion. It depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.

Conservation of Mechanical Energy

First the principle of the Conservation of Mechanical Energy was stated:

The total mechanical energy (defined as the sum of its potential and kinetic energies) of a particle being acted on by only conservative forces is constant.

conservartion-of-mechanical-energy-example

Siehe auch: Conservation of Mechanical Energy

An isolated system is one in which no external force causes energy changes. If only conservative forces act on an object and die ist der potenzielle Energie function for the total conservative force, dann

Emech = U + K

The potential energy, die, depends on the position of an object subjected to a conservative force.

potential-energy-equation

It is defined as the object’s ability to do work and is increased as the object is moved in the opposite direction of the direction of the force.

The potential energy associated with a system consisting of Earth and a nearby particle is gravitational potential energy.

gravitational-potential-energy-equation

The kinetic energy, K, depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.

K = ½ mv2

The above mentioned definition (Emech = U + K) assumes that the system is free of friction and other non-conservative forces. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path.

In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. For example the frictional force is a non-conservative force, because it acts to reduce the mechanical energy in a system.

Note that non-conservative forces do not always reduce the mechanical energy. A non-conservative force changes the mechanical energy, there are forces that increase the total mechanical energy, like the force provided by a motor or engine, is also a non-conservative force.

Block sliding down a frictionless incline slope

Das 1 kg block starts out a height H (let say 1 m) über dem Boden, mit potenzielle Energie mgH und kinetische Energie that is equal to 0. It slides to the ground (without friction) and arrives with no potential energy and kinetic energy K = ½ mv2. Calculate the velocity of the block on the ground and its kinetic energy.

Emech = U + K = const

=> ½ mv2 = mgH

=> v = √2gH = 4.43 Frau

=> K2 = ½ x 1 kg x (4.43 Frau)2 = 19.62 kg.m2.s-2 = 19.62 J.

Pendulum

conservartion-of-mechanical-energy-pendulumAssume a pendulum (ball of mass m suspended on a string of length L that we have pulled up so that the ball is a height H < L above its lowest point on the arc of its stretched string motion. The pendulum is subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible.

We release it from rest. How fast is it going at the bottom?

conservartion-of-mechanical-energy-pendulum2

The pendulum reaches greatest kinetic energy und least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. Auf der anderen Seite, it will have its least kinetic energy und greatest potential energy Beverly Hills extreme positions of its swing, because it has zero speed and is farthest from Earth at these points.

If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, ist:

period-of-pendulum-conservation-of-energy

woher L is the length of the pendulum and G is the local acceleration of gravity. For small swings the period of swing is approximately the same for different size swings. Das ist, the period is independent of amplitude.

Verweise:
Reactor Physics and Thermal Hydraulics:

  1. J.. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, lesen, MA (1983).
  2. J.. R. Lamarsh, EIN. J.. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Zweite Ausgabe. CRC Press; 2 Auflage, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. UNS. Energiebehörde, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volumen 1, 2 und 3. Juni 1992.

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