Conservation of Energy

Topic Overview

• Subject: Conservation of energy

• Instructor: Vaughn Vic

• Institution: Christchurch Episcopal School, Greenville, South Carolina

• Focus: Use of energy bar charts to represent energy transformations

Previous Concepts

• Work: Defined as the amount of mechanical energy transferred into or out of a system.

• Types of Mechanical Energy:

  • Kinetic Energy (KE): Energy of a moving object.

  • Gravitational Potential Energy (GPE): Energy stored due to an object’s height above the ground.

  • Spring Potential Energy: Energy stored in a compressed or stretched spring.

Energy Transformations and Bar Charts

• Graphical Representation: Energy bar charts can depict energy transformations in a defined system.

  • Example: A box held at a height that drops to the ground.

  • Before the drop: No kinetic energy (KE = 0)

  • At ground level: Gains kinetic energy as it accelerates towards the ground.

• System Consideration: When analyzing energy, it is important to define the system.

  • In the previous example, the system is considered as just the box.

Conservation of Energy Principles

• Law of Conservation of Energy: States that energy cannot be created or destroyed, only transformed from one type to another.

  • Energy before = Energy after

• Example with Box and Earth System:

  • The system is defined as the box and the Earth combined, allowing for gravitational potential energy to be considered.

  • At the top: Has gravitational potential energy given by the formula:
    GPE = mgh

  • Where:

    • m = mass of the box

    • g = acceleration due to gravity

    • h = height of the box above ground.

  • As it drops, GPE converts into kinetic energy.

• Bar Chart Representation:

  • Initial state (Top of drop): 4 units of GPE

  • Final state (Ground level): 4 units of KE

  • Shows conservation of energy since total energy is consistent (no losses due to non-conservative forces).

Practical Example of Energy Types and Conservation

• New Scenario with a Spring:

  • Box compresses a spring then releases. The box travels up a ramp after being launched.

  • **Types of energy present: **

  • Beginning: Spring Potential Energy (initially compressed)

  • End: Kinetic Energy (as the box moves) and Gravitational Potential Energy (at the peak height).

  • Since the ramp is frictionless (no non-conservative forces), the energy transformation follows:

  • ext{Energy before} = 4 ext{ units (spring potential energy)}

  • ext{Energy at the highest point of the ramp} = 2 ext{ units (kinetic)} + 2 ext{ units (gravitational potential)}

• Conclusion from the example:

  • These units add up (2 + 2 = 4) showing that energy remains constant, illustrating the principle of conservation of energy.

Key Takeaways

• The energy present in a system depends on how the system is defined.

  • Single object systems can only exhibit kinetic energy.

  • Combined systems (like box and Earth) can exhibit both gravitational potential and kinetic energy.

• Energy bar charts are a useful tool for visually representing energy changes and transformations.

• Conservation of energy holds true in the absence of non-conservative forces (like friction or air resistance).

• Emphasis on total energy consistency:

  • Total energy before = Total energy after

Closing Remarks

• Understanding the types of energy and how they transform based on system definitions is essential for application in physics.

• Energy bar charts serve as an effective means to illustrate these concepts in scenarios involving energy transformations.