Work, Energy, and Conservation in Classical Mechanics

Work, energy, and conservation are like the pieces of a puzzle that fit together in physics.

1. Work: We say work is done when a force moves something. It can be thought of like this:

   • Work (W) = Force (F) x Distance (d) x Cosine of the angle (θ).
   • Here, Force is how hard we push or pull, Distance is how far the object moves, and the angle tells us how the force is applied.

2. Energy: This is the ability to do work. There are two main types:

   • Kinetic Energy (KE) is the energy of moving things. It can be calculated with this formula: KE = 1/2 x mass (m) x speed (v) squared.

   • Potential Energy (PE) is stored energy based on height. It’s shown by this formula: PE = mass (m) x gravity (g) x height (h).

3. Conservation Principles: In a closed system (like a box where nothing goes in or out), energy can’t be made or destroyed. Instead, it changes form. This means the total energy (from both kinetic and potential energy) stays the same.

In simple terms, these ideas help us understand how things move and work, from everyday life to more complicated science problems.