Conservation of Energy Study Pack

Kibin's free study pack on Conservation of Energy includes a 3-section study guide, 8 quiz questions, 10 flashcards, and 1 open-ended Explain review question. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.

Last updated May 21, 2026

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Conservation of Energy Study Guide

Master the law of conservation of energy by working through the relationship between kinetic energy (KE = ½mv²) and gravitational potential energy (PE = mgh) and how they continuously convert into each other. This pack covers mechanical energy in isolated systems, the impact of non-conservative forces like friction on energy transfer, and how to solve for unknown velocities and heights using energy analysis alone.

Key Takeaways

  • •The law of conservation of energy states that the total mechanical energy of an isolated system remains constant, meaning energy is neither created nor destroyed, only converted between forms.
  • •Mechanical energy is the sum of kinetic energy (energy of motion) and potential energy (energy stored due to position or configuration), and their interconversion drives most observable motion.
  • •Kinetic energy is calculated as KE = ½mv², making it proportional to mass and to the square of velocity, while gravitational potential energy is calculated as PE = mgh, depending on mass, gravitational acceleration, and height.
  • •When non-conservative forces such as friction or air resistance are present, mechanical energy is not conserved — some is converted to thermal energy or sound — but total energy across all forms is still conserved.
  • •Work done by non-conservative forces equals the change in mechanical energy of a system, allowing energy analysis even in real-world situations involving friction.
  • •Energy conservation principles are applied in physics to solve for unknown velocities, heights, and forces without needing to track the details of motion at every instant.

The Law of Conservation of Energy

Conservation of energy is one of the most fundamental principles in physics, describing a universal constraint on how energy behaves in any physical system.

Core Statement of the Law

  • •Energy cannot be created from nothing, nor can it be made to disappear — it can only change from one form to another.
  • •In an isolated system (one with no energy entering or leaving), the total amount of energy remains constant over time.
  • •This applies across all physical processes: mechanical, thermal, electromagnetic, chemical, and nuclear.

Distinction Between Isolated and Non-Isolated Systems

  • •An isolated system exchanges neither energy nor matter with its surroundings, making total energy strictly constant.
  • •A non-isolated system can gain or lose energy through work done by external forces or through heat transfer, but the energy that enters or leaves is fully accounted for elsewhere.
  • •In everyday problems, 'the system' is often defined to include all relevant objects so that energy transfers remain internal.

Kinetic Energy and Potential Energy as Forms of Mechanical Energy

Mechanical energy is the category of energy directly associated with the motion and position of objects, and understanding its two components is essential to applying conservation principles.

Kinetic Energy: Energy of Motion

  • •Kinetic energy (KE) is the energy an object possesses because it is moving, calculated by KE = ½mv², where m is mass in kilograms and v is speed in meters per second.
  • •Because velocity is squared, doubling an object's speed increases its kinetic energy by a factor of four.
  • •Kinetic energy is always a positive scalar quantity — direction of motion does not affect its value.

Gravitational Potential Energy: Energy of Position

  • •Gravitational potential energy (PE) is the energy stored in an object due to its height above a reference point, calculated by PE = mgh, where g ≈ 9.8 m/s² near Earth's surface and h is height.
  • •The choice of reference height (where PE = 0) is arbitrary, but it must remain consistent throughout a single problem.
  • •As an object rises, it gains gravitational PE; as it falls, gravitational PE converts into kinetic energy.

Elastic Potential Energy: Energy Stored in Deformation

  • •Springs and other elastic materials store elastic potential energy when compressed or stretched, calculated as PE_elastic = ½kx², where k is the spring constant and x is the displacement from equilibrium.
  • •This energy converts fully to kinetic energy when the spring returns to its natural length, assuming no friction.

About this Study Pack

Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.

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