Examples of law of conservation of energy in the following topics:

 To solve a conservation of energy problem determine the system of interest, apply law of conservation of energy, and solve for the unknown.
 If you know the potential energies ($PE$) for the forces that enter into the problem, then forces are all conservative, and you can apply conservation of mechanical energy simply in terms of potential and kinetic energy.
 If you know the potential energy for only some of the forces, then the conservation of energy law in its most general form must be used:
 where $OE$ stand for all other energies, and $W_{nc}$ stands for work done by nonconservative forces.
 Once you have solved a problem, reexamine the forms of work and energy to see if you have set up the conservation of energy equation correctly.

 The first law of thermodynamics is a version of the law of conservation of energy specialized for thermodynamic systems.
 The law of conservation of energy can be stated like this: The energy of an isolated system is constant.
 If we are interested in how heat transfer is converted into work, then the conservation of energy principle is important.
 The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system .
 The first law of thermodynamics is the conservationofenergy principle stated for a system where heat and work are the methods of transferring energy for a system in thermal equilibrium.

 Mechanical work done by an external force to produce motional EMF is converted to heat energy; energy is conserved in the process.
 We learned in the Atom "Faraday's Law of Induction and Lenz' Law" that Lenz' law is a manifestation of the conservation of energy.
 As we see in the example in this Atom, Lenz' law guarantees that the motion of the rod is opposed because of nature's tendency to oppose a change in magnetic field.
 (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf.
 Apply the law of conservation of energy to describe the production motional electromotive force with mechanical work

 Faraday's law of induction is a basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).
 The minus sign in Faraday's law of induction is very important.
 In fact, if the induced EMF were in the same direction as the change in flux, there would be a positive feedback that would give us free energy from no apparent source—conservation of energy would be violated.
 This is one aspect of Lenz's law—induction opposes any change in flux.
 Express the Faraday’s law of induction in a form of equation

 Kirchhoff's circuit laws are two equations that address the conservation of energy and charge in the context of electrical circuits.
 Fundamentally, they address conservation of energy and charge in the context of electrical circuits.
 Kirchhoff's laws are extremely important to the analysis of closed circuits.
 The voltage law is a simplification of Faraday's law of induction, and is based on the assumption that there is no fluctuating magnetic field within the closed loop.
 Describe relationship between the Kirchhoff's circuit laws and the energy and charge in the electrical circuits

 The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.
 This is an expression for the law of conservation of angular momentum.
 An example of conservation of angular momentum is seen in an ice skater executing a spin, as shown in .
 Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum.
 The work she does to pull in her arms results in an increase in rotational kinetic energy.

 In physics and chemistry there are many conservation laws—among them, the Law of Conservation of Nucleon Number, which states that the total number of nucleons (nuclear particles, specifically protons and neutrons) cannot change by any nuclear reaction.
 Chain reactions of nuclear fission release a tremendous amount of energy, but follow the Law of Conservation of Nucleon Number.
 Finally, nuclear fusion follows the Law of Conservation of Nucleon Number.
 It is well understood that the tremendous amounts of energy released by nuclear fission and fusion can be attributed to the conversion of mass to energy.
 Describe the process of conversion of matter to energy during the nuclear fusion and fission

 Conservation of mechanical energy states that the mechanical energy of an isolated system remains constant without friction.
 Conservation of mechanical energy states that the mechanical energy of an isolated system remains constant in time, as long as the system is free of all frictional forces.
 This equation is a form of the workenergy theorem for conservative forces; it is known as the conservation of mechanical energy principle.
 Remember that the law applies to the extent that all the forces are conservative, so that friction is negligible.
 Express the principle of the conservation of the mechanical energy in the form of an equation

 Gravitational energy is the potential energy associated with gravitational force (a conservative force), as work is required to elevate objects against Earth's gravity.
 Gravitational potential energy near the Earth can be expressed with respect to the height from the surface of the Earth.
 (The surface will be the zero point of the potential energy.
 For the computation of the potential energy we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation (with respect to the distance r between the two bodies).
 Using that definition, the gravitational potential energy of a system of masses m and M at a distance r using gravitational constant G is:

 Spring force is conservative force, given by the Hooke's law : F = kx, where k is spring constant, measured experimentally for a particular spring and x is the displacement .
 From the conservation of mechanical energy (Check our Atom on "Conservation of Mechanical Energy), the work should be equal to the potential energy stored in spring.
 If the block is gently released from the stretched position (x = xf), the stored potential energy in the spring will start to be converted to the kinetic energy of the block, and vice versa.
 Neglecting frictional forces, Mechanical energy conservation demands that, at any point during its motion,$\begin{align} Total ~Energy &= \frac{1}{2} m v^2 + \frac{1}{2}k x^2 \\ &= \frac{1}{2} k x_f^2 = constant.
 From the energy conservation, we can estimate that, by the time the block reaches x=0 position, its speed will be $v(x=0) =\sqrt{\frac{k}{m}}x_f$.