Conservation of Mechanical Energy: System Analysis | AP Physics

Defining Mechanical Energy and Its Changes

• 💡 Mechanical energy is defined as the sum of a system's kinetic energy and potential energy.
• 🎯 The change in mechanical energy is determined by the work done on the system; positive work increases it, negative work decreases it.

Analyzing Simple Systems

• 🚀 When considering just a block as the system, gravity does positive work as it falls, increasing the block's mechanical (kinetic) energy.
• 🌍 If the Earth-block system is considered, gravity is a conservative force within the system, and its work is accounted for by potential energy, resulting in unchanged mechanical energy.

Systems with Springs

• ⚡ For an Earth-block system with a spring, the spring force acts as an external force doing negative work as it compresses, thus decreasing the system's mechanical energy.
• 🌎 When the Earth-block-spring system is considered, both gravity and spring forces are internal conservative forces, leading to constant mechanical energy.

Incorporating Non-Conservative Forces

• 💨 In the presence of drag force (a non-conservative force), the mechanical energy of the Earth-block-spring system decreases because the drag force does negative work.
• ⚖️ If friction is present and the two-block spring system is considered, gravity does positive work while friction does negative work. The net work determines the change in mechanical energy.
• 🔑 When the two-block spring and Earth system is considered, friction is the only external force doing work, and it reduces the mechanical energy of the system.