Unit 3.4: Conservation of Energy

Introduction

Conservation of energy is a fundamental principle of physics stating that the total energy of an isolated system remains constant. Energy may transform from one form to another—such as from potential to kinetic energy—but the overall energy is conserved.

Key Concepts

Conservation of Energy: Energy cannot be created or destroyed, only transformed. In an isolated system, the total energy remains constant.
Mechanical Energy: The sum of kinetic and potential energy.
Non-Conservative Forces: Forces like friction convert mechanical energy into thermal energy, which may cause the mechanical energy of the system to decrease even though total energy is conserved.
Energy Transformation: In problems where no non-conservative forces do work, the mechanical energy at the start equals the mechanical energy at the end.

Tip: When solving problems, clearly write the initial and final energy states and account for any work done by non-conservative forces.

Graphical Representations

Energy conservation can be visualized using energy bar graphs or energy vs. time graphs. In these graphs, the sum of kinetic and potential energy remains constant, while individual energy forms may vary.

Exam Strategy: Verify that the total mechanical energy remains constant throughout the process unless work is done by non-conservative forces.

Mathematical Routines

To apply conservation of energy, follow these steps:

Identify all forms of energy in the system (kinetic, gravitational potential, elastic potential, etc.).
Write the conservation equation: E_initial = E_final.
If non-conservative forces are present, modify the equation to: E_initial + W_nc = E_final.

Tip: Make sure all energy values are expressed in the same units (typically joules) before solving.

Practice Activities

Activity 1: Energy Conversion in a Pendulum

A pendulum of length 2 m and mass 1 kg is released from a height of 0.5 m above its lowest point. Using energy conservation, calculate its speed at the bottom of the swing.

Activity 2: Roller Coaster Energy

A roller coaster starts at a height of 40 m and descends to 10 m. Assuming no friction, calculate the change in kinetic energy of the roller coaster.

Activity 3: Work Done Against Friction

A block slides down a frictional incline. Given the initial height and the work done by friction, determine the block's final speed using energy conservation.

Summary & Exam Preparation Tips

Conservation of energy is a powerful tool for solving physics problems. Key takeaways include:

The total energy in an isolated system remains constant.
Mechanical energy is the sum of kinetic and potential energy.
Non-conservative forces, such as friction, convert mechanical energy into other forms.
Setting up the energy conservation equation correctly is crucial to solving problems.

Mastering energy conservation will help you analyze a wide range of problems on the AP Physics exam.