Energy Types and Conservation

Overview of Energy Types

• Energy exists in various forms and transforms between types.

• Categories:

  • Mechanical Energy

  • Kinetic Energy (KE): Energy due to motion, defined as KE = \frac{1}{2}mv^2, where (m) is mass and (v) is speed.

  • Potential Energy (PE): Energy stored due to position, further divided into:

    • Elastic Potential Energy (Ue): Energy stored in springs, defined as Ue = \frac{1}{2}kx^2, where (k) is spring constant and (x) is deformation.

    • Gravitational Potential Energy (Ug): Energy stored due to height, defined as Ug = mgh, where (h) is height.

  • Non-Mechanical Energy: Includes thermal, electrical, light, and sound energy.

Conservation of Energy

• Energy cannot be created or destroyed, only transformed.

• Unit of Energy: Joule (J).

• Work-Energy Theorem: W_{net} = \Delta KE (change in kinetic energy).

Types of Collisions

• Momentum is conserved in all types of collisions.

• Types:

  • Elastic Collision: Both momentum and kinetic energy conserved.

  • Inelastic Collision: Momentum conserved, kinetic energy not conserved.

  • Perfectly Inelastic Collision: Objects stick together post-collision.

Work Done by Forces

• Work is defined as energy transfer resulting in motion or change.

• Work done by gravity calculated as Wg = -\Delta Ug.

Kinetic and Potential Energy Relationships

• As objects fall, gravitational potential energy converts to kinetic energy.

• Changes in potential energy correspond to work done by gravity.

• Energy transitions define motion behavior under forces.

Problem Solving Strategy

1. Define points of interest (e.g., before and after collision).

2. Apply conservation of momentum for collision phase.

3. Apply conservation of energy for motion phase post-collision.

4. Solve for unknowns using the appropriate equations.

5. Analyze results to confirm energy and momentum consistency.