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From Wikipedia
The law of conservation of energy is an empirical law of physics. It states that the total amount of energy in an isolated system remains constant over time (is said to be conserved over time). A consequence of this law is that energy can neither be created nor destroyed: it can only be transformed from one state to another. The only thing that can happen to energy in a closed system is that it can change form: for instance chemical energy can become kinetic energy.
Albert Einstein's theory of relativity shows that energy and mass are the same thing, and that neither one appears without the other. Thus in closed systems, both mass and energy are conserved separately, just as was understood in prerelativistic physics. The new feature of relativistic physics is that "matter" particles (such as those constituting atoms) could be converted to nonmatter forms of energy, such as light; or kinetic and potential energy (example: heat). However, this conversion does not affect the total mass of systems, because the latter forms of nonmatter energy still retain their mass through any such conversion.
Today, conservation of â€œenergyâ€� refers to the conservation of the total system energy over time. This energy includes the energy associated with the rest mass of particles and all other forms of energy in the system. In addition, the invariant mass of systems of particles (the mass of the system as seen in its center of mass inertial frame, such as the frame in which it would need to be weighed) is also conserved over time for any single observer, and (unlike the total energy) is the same value for all observers. Therefore, in an isolated system, although matter (particles with rest mass) and "pure energy" (heat and light) can be converted to one another, both the total amount of energy and the total amount of mass of such systems remain constant over time, as seen by any single observer. If energy in any form is allowed to escape such systems (see binding energy), the mass of the system will decrease in correspondence with the loss.
A consequence of the law of energy conservation is that perpetual motion machines can only work perpetually if they deliver no energy to their surroundings.
History
Ancientphilosophers as far back as Thales of Miletus had inklings of the conservation of which everything is made. However, there is no particular reason to identify this with what we know today as "massenergy" (for example, Thales thought it was water). In 1638, Galileo published his analysis of several situationsâ€”including the celebrated "interrupted pendulum"â€”which can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. It was Gottfried Wilhelm Leibniz during 1676â€“1689 who first attempted a mathematical formulation of the kind of energy which is connected with motion (kinetic energy). Leibniz noticed that in many mechanical systems (of several masses, m_{i}each withvelocityv_{i}),
 \sum_{i} m_i v_i^2
was conserved so long as the masses did not interact. He called this quantity the vis vivaor living force of the system. The principle represents an accurate statement of the approximate conservation ofkinetic energy in situations where there is no friction. Many physicists at that time held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum:
 \,\!\sum_{i} m_i v_i
was the conserved vis viva. It was later shown that, under the proper conditions, both quantities are conserved simultaneously such as in elastic collisions.
It was largely engineers such as John Smeaton, Peter Ewart, Karl Hotzmann, GustaveAdolphe Hirn and Marc Seguin who objected that conservation of momentum alone was not adequate for practical calculation and who made use of Leibniz's principle. The principle was also championed by some chemists such as William Hyde Wollaston. Academics such as John Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the second law of thermodynamics but in the 18th and 19th centuries, the fate of the lost energy was still unknown. Gradually it came to be suspected that the heat inevitably generated by motion under friction, was another form of vis viva. In 1783, Antoine Lavoisier and PierreSimon Laplace reviewed the two competing theories of vis viva and caloric theory. Count Rumford's 1798 observations of heat generation during the boring of cannons added more weight to the view that mechanical motion could be converted into heat, and (as importantly) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat). Vis viva now started to be
A conservative force is a force with the property that the work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the net work done (the sum of the force acting along the path multiplied by the distance travelled) by a conservative force is zero.
It is possible to define a numerical value of potential at every point in space for a conservative force. When an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken.
Gravity is an example of a conservative force, while friction is an example of a nonconservative force.
Informal definition
Informally, a conservative force can be thought of as a force that conservesmechanical energy. Suppose a particle starts at point A, and there is a constant force F acting on it. Then the particle is moved around by other forces, and eventually ends up at A again. Though the particle may still be moving, at that instant when it passes point A again, it has traveled a closed path. If the net work done by F at this point is 0, then F passes the closed path test. Any force that passes the closed path test for all possible closed paths is classified as a conservative force.
The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a timeindependent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of nonconservative forces (in both cases, the energy is converted to heat and cannot be retrieved).
Path independence
A direct consequence of the closed path test is that the work done by a conservative force on a particle moving between any two points does not depend on the path taken by the particle. Also the work done by a conservative force is equal to the negative of change in potential energy during that process. For a proof of that, let's imagine two paths 1 and 2, both going from point A to point B. The variation of energy for the particle, taking path 1 from A to B and then path 2 backwards from B to A, is 0; thus, the work is the same in path 1 and 2, i.e., the work is independent of the path followed, as long as it goes from A to B.
For example, if a child slides down a frictionless slide, the work done by the gravitational force on the child from the top of the slide to the bottom will be the same no matter what the shape of the slide; it can be straight or it can be a spiral. The amount of work done only depends on the vertical displacement of the child.
Mathematical description
A force fieldF, defined everywhere in space (or within a simplyconnected volume of space), is called a conservative force or conservative vector fieldif it meets any of these three equivalent conditions:
 1. The curl of F is zero:
 \nabla \times \vec{F} = 0. \,
 2. There is zero net work (W) done by the force when moving a particle through a trajectory that starts and ends in the same place:
 W \equiv \oint_C \vec{F} \cdot \mathrm{d}\vec r = 0.\,
 3. The force can be written as the gradient of a potential, \Phi:
 \vec{F} = \nabla \Phi. \,
The term conservative force comes from the fact that when a conservative force exists, it conserves mechanical energy. The most familiar conservative forces are gravity, the electric force (in a timeindependent magnetic field, see Faraday's law), and spring force.
Many forces (particularly those that depend on velocity) are not force fields. In these cases, the above three conditions are not mathematically equivalent. For example, the magnetic force satisfies condition 2 (since the work done by a magnetic field on a charged particle is always zero), but does not satisfy condition 3, and condition 1 is not even defined (the force is not a vector field, so one cannot evaluate its curl). Accordingly, some authors classify the magnetic force as conservative, while others do not. The magnetic force is an unusual case; most velocitydependent forces, such as friction, do not satisfy any of the three conditions, and therefore are unambiguously nonconservative.
Nonconservative forces
Nonconservative forces can only arise in classical physics due to neglected degrees of freedom. For instance, friction may be treated without resorting to the use of nonconservative forces by considering the motion of individual molecules; however that means every molecule's motion must be considered rather than handling it through statistical methods. For macroscopic systems the nonconservative approximation is far easier to deal with than millions of degrees of freedom. Examples of nonconservative forces are friction and nonelastic material stress.
However, general relativity is nonconservative, as seen in the anomalous precession of Mercury's orbit. However, general relativity can be shown to conserve a stressenergymomentum pseudotensor.
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves.
One particularly important physical result concerning conservation laws is Noether's Theorem, which states that there is a onetoone correspondence between conservation laws and differentiable symmetries of physical systems. For example, the conservation of energy follows from the timeinvariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.
A partial listing of conservation laws that are said to be exact laws, or more precisely have never been shown to be violated:
 Conservation of massenergy
 Conservation of linear momentum
 Conservation of angular momentum
 Conservation of electric charge
 Conservation of color charge
 Conservation of weak isospin
 Conservation of probability density
 CPT symmetry (combining charge, parity and time conjugation)
 Lorentz symmetry
There are also approximate conservation laws. These are approximately true in particular situations, such as low speeds, short time scales, or certain interactions.
 Conservation of mass (applies for nonrelativistic speeds and when there are no nuclear reactions)
 Conservation of baryon number (See chiral anomaly)
 Conservation of lepton number (In the Standard Model)
 Conservation of flavor (violated by the weak interaction)
 Conservation of parity
 Invariance under Charge conjugation
 Invariance under time reversal
 CP symmetry, the combination of charge and parity conjugation (equivalent to time reversal if CPT holds)
From Encyclopedia
energy in physics, the ability or capacity to do work or to produce change. Forms of energy include heat , light , sound , electricity , and chemical energy. Energy and work are measured in the same unitsâ€”footpounds, joules, ergs, or some other, depending on the system of measurement being used. When a force acts on a body, the work performed (and the energy expended) is the product of the force and the distance over which it is exerted. Potential and Kinetic Energy Potential energy is the capacity for doing work that a body possesses because of its position or condition. For example, a stone resting on the edge of a cliff has potential energy due to its position in the earth's gravitational field. If it falls, the force of gravity (which is equal to the stone's weight; see gravitation ) will act on it until it strikes the ground; the stone's potential energy is equal to its weight times the distance it can fall. A charge in an electric field also has potential energy because of its position; a stretched spring has potential energy because of its condition. Chemical energy is a special kind of potential energy; it is the form of energy involved in chemical reactions. The chemical energy of a substance is due to the condition of the atoms of which it is made; it resides in the chemical bonds that join the atoms in compound substances (see chemical bond ). Kinetic energy is energy a body possesses because it is in motion. The kinetic energy of a body with mass m moving at a velocity v is one half the product of the mass of the body and the square of its velocity, i.e., KE = 1/2 mv2 . Even when a body appears to be at rest, its atoms and molecules are in constant motion and thus have kinetic energy. The average kinetic energy of the atoms or molecules is measured by the temperature of the body. The difference between kinetic energy and potential energy, and the conversion of one to the other, is demonstrated by the falling of a rock from a cliff, when its energy of position is changed to energy of motion. Another example is provided in the movements of a simple pendulum (see harmonic motion ). As the suspended body moves upward in its swing, its kinetic energy is continuously being changed into potential energy; the higher it goes the greater becomes the energy that it owes to its position. At the top of the swing the change from kinetic to potential energy is complete, and in the course of the downward motion that follows the potential energy is in turn converted to kinetic energy. Conversion and Conservation of Energy It is common for energy to be converted from one form to another; however, the law of conservation of energy, a fundamental law of physics, states that although energy can be changed in form it can be neither created nor destroyed (see conservation laws ). The theory of relativity shows, however, that mass and energy are equivalent and thus that one can be converted into the other. As a result, the law of conservation of energy includes both mass and energy. Many transformations of energy are of practical importance. Combustion of fuels results in the conversion of chemical energy into heat and light. In the electric storage battery chemical energy is converted to electrical energy and conversely. In the photosynthesis of starch, green plants convert light energy from the sun into chemical energy. Hydroelectric facilities convert the kinetic energy of falling water into electrical energy, which can be conveniently carried by wires to its place of use (see power, electric ). The force of a nuclear explosion results from the partial conversion of matter to energy (see nuclear energy ).
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Answers:There is no energy loss ... only there is energy transformation from one form of energy to another.
Answers:10% law of energy transfer through trophic levels? I guess their similar in that energy is not destroyed. Only about 10% of the energy at one trophic level is passed on to the next. The rest is lost as heat (through metabolism) or decays. They are different in that usable energy is created in ecosystems (primary production by plants).
Answers:"What is the effect of air resistance on the conservation of energy?" It doesn't change the idea of conservation of energy, but it makes calculations using it more difficult. "Is it because energy is lost due to work done on the air?" Yes. Air resistance creates lower final energy values than we calculate if we neglect it. So the ball wouldn't go as high or fall back as fast as you would predict if you neglected air resistance. Without air resistance conservation of energy tells us that: mv^2/2 = mgh where v is the velocity at which the ball left your hand and h is the maximum height. The mass m cancels and we can write: v^2/2 = gh, so h = v^2/2g If we consider air resistance we have to write: mv^2/2 = mgh + A Where A is the energy lost to air resistance. Notice that mass no longer cancels. We can solve for h : v^2/2g  A/mg = h this is less than v^2/2g
Answers:All the initial energy stored in the spring will be dissipated by the kinetic friction, that is 1/2 k Xo^2 = Fr d where Xo is the initial compression in the spring and Fr d is the work done by the kinetic friction which will turn into heat. Solving for d we get d = 1/2 K Xo^2 / Fr = 1/2 K Xo^2 / (uk mg) = 0.5 * 650 * (0.11)^2 / (0.45*1.2*9.8) = 0.74 m since this distance d is larger than the initial compression of the spring then the mass will oscillate back and forth with an smaller and smaller amplitude until it stops. Thus, assuming that the maximum static friction (which you do not provide) is equal to the kinetic friction, then the mass, after so many oscillations, will stop at x = 0.45*1.2*9.8 / 650 = 0.008 m this distance could be either positive or negative, depending on how many cycles it takes to stop the mass.
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