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state-law-of-energy-conservation

🚀 The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. This principle is closely related to the concepts of kinetic energy (the energy of motion) and potential energy (the energy stored due to an object's position). The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system, the total energy (kinetic + potential) remains constant, even as energy changes forms.

Theory Explanation

Understanding Kinetic Energy

Kinetic energy (KE) is the energy that an object possesses due to its motion. It is given by the formula KE = 1/2 mv², where m is the mass of the object and v is its velocity. This means that the kinetic energy increases with the square of the velocity, indicating that even small increases in speed can lead to significant increases in kinetic energy.

\[ KE = \frac{1}{2} mv^2 \]
Understanding Potential Energy

Potential energy (PE) is the energy stored in an object due to its position or configuration. The most common form of potential energy is gravitational potential energy, which is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above a reference point. This energy can be converted into kinetic energy when the object is allowed to fall.

\[ PE = mgh \]
Law of Conservation of Energy

The law of conservation of energy states that the total energy in a closed system remains constant. This means that the sum of kinetic and potential energy at any point in time will be equal to the total energy of the system. For example, when an object falls, its potential energy decreases while its kinetic energy increases, but the total energy remains the same.

\[ KE + PE = \text{constant} \]

Key Points

  • 🎯 Kinetic energy depends on the mass and the square of the velocity.
  • 🎯 Potential energy depends on the mass, height, and gravitational acceleration.
  • 🎯 The total mechanical energy (kinetic + potential) in a closed system is conserved.

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Examples:💡

A 2 kg object is dropped from a height of 10 m. Calculate its potential energy at the top and its kinetic energy just before it hits the ground.

Solution:

Step 1: Calculate the potential energy at the height of 10 m using PE = mgh.

\[ PE = 2 \times 9.8 \times 10 = 196 J \]

Step 2: Just before hitting the ground, all potential energy is converted to kinetic energy. Therefore, KE = 196 J.

Common Mistakes

  • Mistake: Confusing kinetic energy with potential energy.

    Correction: Remember that kinetic energy is related to motion, while potential energy is related to position.

  • Mistake: Forgetting to account for energy conservation in calculations.

    Correction: Always check that the total energy before and after an event remains constant.

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