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Newton’s third law: law of reciprocal actions

Newton’s third law. The skaters’ forces on each other are equal in magnitude, but act in opposite directions.Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.
”To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions”.
A more direct translation than the one just given above is:

LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. — Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinges upon another, and by its force changes the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, as the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium.

In the above, as usual, motion is Newton’s name for momentum, hence his careful distinction between motion and velocity.

The Third Law means that all forces are interactions, and thus that there is no such thing as a unidirectional force. If body A exerts a force on body B, body B simultaneously exerts a force of the same magnitude on body A— both forces acting along the same line. As shown in the diagram opposite, the skaters’ forces on each other are equal in magnitude, but act in opposite directions. Although the forces are equal, the accelerations are not: the less massive skater will have a greater acceleration due to Newton’s second law. It is important to note that the action and reaction act on different objects and do not cancel each other out. The two forces in Newton’s third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car’s tires, then it is also a frictional force that Newton’s third law predicts for the tires pushing backward on the road).

Newton used the third law to derive the law of conservation of momentum;[24] however from a deeper perspective, conservation of momentum is the more fundamental idea (derived via Noether’s theorem from Galilean invariance), and holds in cases where Newton’s third law appears to fail, for instance when force fields as well as particles carry momentum, and in quantum mechanics.

Newton’s second law states that the force applied to a body produces a proportional acceleration; the relationship between the two is where F is the force applied, m is the mass of the body, and a is the body’s acceleration. If the body is subject to multiple forces at the same time, then the acceleration is proportional to the vector sum (that is, the net force. The second law can also be shown to relate the net force and the momentum p of the body. Therefore, Newton’s second law also states that the net force is equal to the time derivative of the body’s momentum. Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude (see time derivative). The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. This can be said easily. Net force is equal to rate of change of momentum for those that don’t know calculus. This definition holds even when the speed of the object approaches the speed of light.

Both statements of the second law are valid only for constant-mass systems, since any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems.

Newton’s second law requires modification if the effects of special relativity are to be taken into account, since it is no longer true that momentum is the product of inertial mass and velocity.
Variable-mass systems
Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law.[15] The reasoning, given in An Introduction to Mechanics by Kleppner and Kolenkow and other modern texts, is that Newton’s second law applies fundamentally to particles.[16] In classical mechanics, particles by definition have constant mass. In case of a well-defined system of particles, Newton’s law can be extended by summing over all the particles in the system.

Newton’s first law of motion states that objects continue to move in a state of constant velocity unless acted upon by an external net force or resultant force. This law is an extension of Galileo’s insight that constant velocity was associated with a lack of net force (see a more detailed description of this below). Newton proposed that every object with mass has an innate inertia that functions as the fundamental equilibrium “natural state” in place of the Aristotelian idea of the “natural state of rest”. That is, the first law contradicts the intuitive Aristotelian belief that a net force is required to keep an object moving with constant velocity. By making rest physically indistinguishable from non-zero constant velocity, Newton’s first law directly connects inertia with the concept of relative velocities. Specifically, in systems where objects are moving with different velocities, it is impossible to determine which object is “in motion” and which object is “at rest”. In other words, to phrase matters more technically, the laws of physics are the same in every inertial frame of reference, that is, in all frames related by a Galilean transformation.
For example, while traveling in a moving vehicle at a constant velocity, the laws of physics do not change from being at rest. A person can throw a ball straight up in the air and catch it as it falls down without worrying about applying a force in the direction the vehicle is moving. This is true even though another person who is observing the moving vehicle pass by also observes the ball follow a curving parabolic path in the same direction as the motion of the vehicle. It is the inertia of the ball associated with its constant velocity in the direction of the vehicle’s motion that ensures the ball continues to move forward even as it is thrown up and falls back down. From the perspective of the person in the car, the vehicle and every thing inside of it is at rest: It is the outside world that is moving with a constant speed in the opposite direction. Since there is no experiment that can distinguish whether it is the vehicle that is at rest or the outside world that is at rest, the two situations are considered to be physically indistinguishable. Inertia therefore applies equally well to constant velocity motion as it does to rest.

Do you know the story of the three kings?Well,I heard about the story of the three kings.. There’s a lot of story about the three kings. It is the one of the popular story before and after Christmas day. And almost of us believe the story about the three kings.

But my professor in Theology says that some of the story are not true, what I mean is the three kings where not intended to be factual narrations. Because the source of the story is on the bible, and the bible said that it is wise men not a king,I think its a magi. And it didn’t said that the wise men are three,what if they are four or five and the other men did not bring a present? And they are not sure that the wise men are really a man, what if one of them is a woman.

There are a lot of changes on this story, but this is what they know so we have to respect it. But if you are studying Theology, you will know that not every story that you got from the other is exact from the real story that you can get on the bible.

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This is a picture of a sucket to have an electricity because my topic is about electricity.

The laws of thermodynamics

According to the second law of thermodynamics, work can be totally converted into heat, but not vice versa.This is a mathematical consequence of statistical mechanics. The first law of thermodynamics simply asserts that energy is conserved,[16] and that heat is included as a form of energy transfer. A commonly-used corollary of the first law is that for a “system” subject only to pressure forces and heat transfer (e.g. a cylinder-full of gas), the differential change in energy of the system (with a gain in energy signified by a positive quantity) is given by:

,

where the first term on the right is the heat transfer into the system, defined in terms of temperature T and entropy S (in which entropy increases and the change dS is positive when the system is heated); and the last term on the right hand side is identified as “work” done on the system, where pressure is P and volume V (the negative sign results since compression of the system requires work to be done on it and so the volume change, dV, is negative when work is done on the system). Although this equation is the standard text-book example of energy conservation in classical thermodynamics, it is highly specific, ignoring all chemical, electric, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat, and because it contains a term that depends on temperature. The most general statement of the first law (i.e., conservation of energy) is valid even in situations in which temperature is undefinable.

Energy is sometimes expressed as:

,

which is unsatisfactory[12] because there cannot exist any thermodynamic state functions W or Q that are meaningful on the right hand side of this equation, except perhaps in trivial cases.

Energy and the laws of motion

In classical mechanics, energy is a conceptually and mathematically useful property since it is a conserved quantity.

The Hamiltonian

The total energy of a system is sometimes called the Hamiltonian, after William Rowan Hamilton. The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems. These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics.^[14]

The Lagrangian

Another energy-related concept is called the Lagrangian, after Joseph Louis Lagrange. This is even more fundamental than the Hamiltonian, and can be used to derive the equations of motion. It was invented in the context of classical mechanics, but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy.

Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (like systems with friction).

Energy and thermodynamics

Internal energy

Internal energy – the sum of all microscopic forms of energy of a system. It is related to the molecular structure and the degree of molecular activity and may be viewed as the sum of kinetic and potential energies of the molecules; it comprises the following types of energy

Energy ágain’.

Because where not finish discussing about energy.

Its about energy transfer.

Because energy is strictly conserved and is also locally conserved (wherever it can be defined), it is important to remember that by definition of energy the transfer of energy between the “system” and adjacent regions is work. A familiar example is mechanical work. In simple cases this is written as:

ΔE = W (1)

if there are no other energy-transfer processes involved. Here E is the amount of energy transferred, and W represents the work done on the system.

More generally, the energy transfer can be split into two categories:

ΔE = W + Q (2)

where Q represents the heat flow into the system.

There are other ways in which an open system can gain or lose energy. In chemical systems, energy can be added to a system by means of adding substances with different chemical potentials, which potentials are then extracted (both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without addition of either work or heat). Winding a clock would be adding energy to a mechanical system. These terms may be added to the above equation, or they can generally be subsumed into a quantity called “energy addition term E” which refers to any type of energy carried over the surface of a control volume or system volume. Examples may be seen above, and many others can be imagined (for example, the kinetic energy of a stream of particles entering a system, or energy from a laser beam adds to system energy, without either being either work-done or heat-added, in the classic senses).

ΔE = W + Q + E (3)

Where E in this general equation represents other additional advected energy terms not covered by work done on a system, or heat added to it.

Energy is also transferred from potential energy (E_p) to kinetic energy (E_k) and then back to potential energy constantly. This is referred to as conservation of energy. In this closed system, energy can not be created or destroyed, so the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

E_pi + E_ki = E_pF + E_kF

The equation can then be simplified further since E_p = mgh (mass times acceleration due to gravity times the height) and  (half mass times velocity squared). Then the total amount of energy can be found by adding E_p + E_k = E_total.