Physics of Energy: Mechanical Work, Potential Energy, Kinetic Energy, and Fundamental Laws
Welcome to Unit 2 of Preparatory 1 Science! In this unit, we explore one of the most foundational principles in physics: Energy. In scientific terms, energy is defined as the 'ability to do work or produce a change', and its standard SI unit is the Joule. Work is performed only when an acting force displaces an object in its direction of action: Work (Joules) = Force (Newtons) x Displacement (meters). Potential Energy (PE) is the energy stored within an object due to the work done on it; it depends directly on the object's weight and its height above ground level: PE = Weight x Height (where Weight = Mass x Acceleration due to gravity, w = m x g). Kinetic Energy (KE) is the work done during the motion of an object, directly proportional to half its mass and the square of its velocity: KE = 1/2 x m x v^2. Mechanical Energy is the total sum of an object's potential and kinetic energies.
1. Mechanical Work & Potential Energy
Mathematical relationships governing potential energy:
- Work (J): Work = Force (N) × Displacement (m) → W = F × d.
- Weight (N): Weight = Mass (kg) × Acceleration of Gravity (m/s²) → w = m × g.
- Potential Energy (PE): PE = Weight × Height → PE = w × h.
- Factors affecting PE:
• Object's weight: Direct proportion (w increases → PE increases).
• Height above ground: Direct proportion (h increases → PE increases).
• At ground level: Height = 0 → Potential Energy = 0.
2. Kinetic Energy & Mechanical Energy
Kinetic energy dynamics and conservation:
- Kinetic Energy (KE): KE = 1/2 × Mass × (Velocity)² → KE = 1/2 m v².
- Factors affecting KE:
• Mass of the moving body: Direct proportion.
• Square of velocity: Doubling velocity increases KE by 4 times! - Mechanical Energy (ME): ME = Potential Energy + Kinetic Energy = Constant.
- Energy Interchange: When an object falls, PE decreases while KE increases by the exact same amount.
Solved Physics Problems Step-by-Step:
1. Weight = mass × g = 5 × 10 = 50 N.
2. PE = weight × height = 50 × 10 = 500 Joules.
KE = 1/2 × m × v² = 1/2 × 4 × (6)² = 2 × 36 = 72 Joules.
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