law of conservation of mechanical energy

Mind map of the law of conservation of mechanical energy, concept of mechanical energy: the collective name for kinetic energy and potential energy, calculation formula: E=Eₚ Eₖ, law of conservation of mechanical energy: In a system where only gravity and elastic force do work, kinetic energy and potential energy transform into each other, and the total amount of mechanical energy remains unchanged.

Edited at 2023-08-30 11:12:49

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law of conservation of mechanical energy

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Outline

Limitations of Newtonian mechanics and preliminary theory of relativity
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law of conservation of mechanical energy

achievement

Concept: When an object is displaced in the direction of a force, it is said that the force has done work on the object. The work done by a constant force on an object is equal to the product of the magnitude of the constant force, the magnitude of the displacement, and the cosine of the angle between the constant force and the displacement.

Formula: W=Fscosθ

Unit: N·m. In order to commemorate the British physicist Joule, the unit of work is named "Joule" and is represented by the symbol J, that is, 1J=1N·m

power

concept

Power: a physical quantity that describes how quickly work is done

Average power: The ratio of the total work done within a period of time to the working time. When the constant force is in the same direction as the displacement, it is equal to the product of the magnitude of the constant force and the magnitude of the average velocity.

Formula: P=W/t

Instantaneous power: When the direction of the force and the instantaneous velocity are the same, it is equal to the product of the magnitude of the force and the instantaneous velocity.

Formula: P=W/t=Fs/t=Fv

Rated power: the maximum power that the machine should not exceed when working under normal conditions for a long time.

Actual power: the power of the machine when it is actually running

Kinetic Energy Kinetic Energy Theorem

kinetic energy

Concept: The energy an object has due to motion

Formula: Eₖ=0.5mv²

Kinetic energy theorem

Concept: The work done by the resultant force on an object is equal to the change in kinetic energy of the object

Expression: W=ΔEₖ=Eₖₜ-Eₖ₀

gravitational potential energy

Concept: Changes in energy due to changes in the height of an object

Characteristics of work done by gravity: Work done by gravity only depends on the initial and final positions of the object, and has nothing to do with the path the object takes. In other words, along any closed path, the work done by gravity is zero.

Calculation method: Eₚ=mgh

Since the height h is relative, the gravitational potential energy is also relative. The gravitational potential energy can only be determined after selecting a reference plane with zero gravitational potential energy.

If the object is above the zero potential energy surface, then h＞0, Eₚ＞0; if it is below the zero potential energy surface, then h＜0, Eₚ＜0

The relationship between the work done by gravity and the change in gravitational potential energy: ΔEₚ=Eₚₜ-Eₚ₀ / Wɢ=-ΔEₚ

Specifically: when the object falls, gravity does positive work, Wɢ＞0, the object's gravitational potential energy decreases, ΔEₚ＜0; when the object rises, gravity does negative work or overcomes gravity to do work, Wɢ＜0, the object's gravitational potential energy increases, ΔEₚ＞0

The concept of elastic potential energy: the energy possessed by an elastically deformed object due to changes in the relative positions of its parts.

law of conservation of mechanical energy

Mechanical energy concept: a collective term for kinetic energy and potential energy

Calculation formula: E=Eₚ Eₖ

Law of conservation of mechanical energy: In a system where only gravity and elastic force do work, kinetic energy and potential energy are converted into each other, and the total amount of mechanical energy remains unchanged.

Expression: 0.5mv₁² mgh₁=0.5mv₂² mgh₂