Conservation of energy: A fundamental principle of physics

Scientific summary

The Astronoo article presents the conservation of energy as a fundamental principle of physics. It explains that the total energy of an isolated system remains constant, even if it transforms between kinetic energy and potential energy. Through the example of the pendulum, it shows that energy transfers obey precise mathematical relationships, such as E_c = ½ mv^2 and E_p = mgh. The article also emphasizes that friction and exchanges with the outside eventually dissipate mechanical energy, which prohibits perpetual motion without external input.

Why is energy conserved?

This article answers a central question in physics: why is energy conserved? The conservation of energy stems from the uniformity of time: physical laws do not change over time, which implies, through Noether's theorem, the existence of a conserved quantity called energy. In an isolated system, energy can change form, pass from kinetic energy to potential energy, transform into heat or radiation, but its total balance remains constant. The article illustrates this principle with a pendulum: at each oscillation, energy is continuously exchanged between motion and position, while the sum of the two remains theoretically unchanged. In practice, friction, internal vibrations and thermal exchanges dissipate part of the mechanical energy, often as heat. This dissipation does not cancel global conservation: it simply distributes energy across a greater number of degrees of freedom. Understanding this law allows us to analyze motions, machines, chemical reactions and even cosmic evolution. It is therefore a common thread linking mechanics, thermodynamics and astrophysics.

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Kinetic energy

Definition and nature of kinetic energy

Kinetic energy is a fundamental property of physics. It is a form of energy associated with the motion of an object due to its speed. Kinetic energy is a scalar quantity, that is, it has a magnitude but no direction; it is a quantity defined solely by a number.

Transfers between kinetic energy and potential energy

When a pendulum is in motion, it continuously exchanges energy between its kinetic energy (associated with its motion) and its potential energy (associated with its position). At each oscillation of the pendulum, the total energy of the system (the sum of its kinetic energy and its potential energy) remains constant, although energy is continuously transferred between the two forms of energy.

Historical origin and equation of kinetic energy

The concept of kinetic energy, introduced under the name of "living force" of an object, was formulated by Leibniz (1646-1716) and Émilie du Châtelet (1706-1749).

The equation is as follows: \[ E_c = \frac{1}{2} m v^2 \] where \(E_c\) represents kinetic energy, \(m\) is the mass (kg) of the object, and \(v\) is its speed (m/s).

Kinetic energy therefore depends directly on the mass and the square of the speed, multiplied by the factor \(\frac{1}{2}\). This is why faster or heavier vehicles generally require more energy to maintain their motion.

Potential energy

Definition and origin of potential energy

Potential energy is a form of energy associated with the position in a gravitational field. The higher the object, the more potential energy it has. This energy is used every day in hydroelectric dams.

Equation and parameters of potential energy

The equation is as follows:

\[ E_p = m g h \]

Potential energy therefore depends directly on the mass of the body \(m\) (kg), the gravity \(g\) (9.81 m/s²) and also on the height \(h\) (m) at which it is located relative to a reference level.

Conversion and free fall

Potential energy can be converted into other forms of energy, such as kinetic energy (associated with motion) or thermal energy (associated with heat), through appropriate physical processes. For example, an object in free fall converts its gravitational potential energy into kinetic energy as it accelerates toward the ground.

\[ m g h = \frac{1}{2} m v^2 \] \[ v^2 = 2 g h \] \[ h = \frac{1}{2} g v^2 \]

N.B.:
Potential energy is a relative quantity and depends on the choice of a specific reference position, and only the difference in potential energy between two positions is significant for calculations.

Key takeaways

Principle of conservation: The total energy of an isolated system remains constant over time; it can neither be created nor destroyed, but only transformed.
Temporal origin: This conservation stems from the uniformity of time (symmetry under time translation) and Noether's theorem, making energy a fundamental conserved quantity of space-time.
Mechanical conversion: In the case of a pendulum, energy continuously switches between kinetic energy (\(E_c = \frac{1}{2} m v^2\)), linked to speed, and potential energy (\(E_p = m g h\)), linked to position and height.
Dissipation and motion: Internal friction, vibrations and thermal transfers progressively dissipate mechanical energy, making perpetual motion impossible to achieve without external input.

References

FAQ: Everything you need to know about energy conservation

What is conservation of energy?

Conservation of energy is a fundamental principle of physics. It states that the total energy of an isolated system remains constant, even if it can transform from one form to another. In other words, energy can neither be created nor destroyed, only converted.

Why is energy conserved?

Energy is conserved because the laws of physics are invariant under translation in time. This symmetry leads, according to Noether's theorem, to the existence of a conserved quantity called energy. Conservation therefore results from a fundamental property of space-time.

What are the main forms of energy?

There are many forms of energy: mechanical, kinetic, potential, thermal, chemical, electrical, nuclear or radiant. In mechanics, the two most studied forms are kinetic energy, linked to motion, and potential energy, linked to position.

How does kinetic energy transform into potential energy?

In a pendulum, kinetic energy decreases as the mass rises and transforms into potential energy. When the pendulum descends again, potential energy is converted back into kinetic energy. The sum of the two remains constant if friction is neglected.

Is conservation of energy valid throughout the entire Universe?

Yes, on the scale of the Universe, conservation of energy is valid in an isolated system. However, in cosmology, the expansion of the Universe complicates the definition of a global total energy. Locally, exchanges always obey a rigorous energy balance, but gravitational energy must be taken into account.

What is energy dissipation?

Energy dissipation is the process by which part of the mechanical energy transforms into heat or other less organized forms. Friction, vibrations and thermal exchanges are common causes. It does not eliminate energy, but redistributes it into the environment.

Conservation of energy: A fundamental principle of physics

Scientific summary

Why is energy conserved?

Also worth exploring

Kinetic energy

Definition and nature of kinetic energy

Transfers between kinetic energy and potential energy

Historical origin and equation of kinetic energy

Potential energy

Definition and origin of potential energy

Equation and parameters of potential energy

Conversion and free fall

Key takeaways

References

FAQ: Everything you need to know about energy conservation

What is conservation of energy?

Why is energy conserved?

What are the main forms of energy?

How does kinetic energy transform into potential energy?

Is conservation of energy valid throughout the entire Universe?

What is energy dissipation?

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