Work and Energy in Physics: Kinetic, Potential, and Conservation Laws
In physics, energy is the quantitative capability to perform work. Work occurs when an applied force causes an object to displace across a distance in the direction of the force.
💡 Plain-English Analogy
Pushing against a brick wall for an hour makes you tired, but in physics, you did zero "work" on the wall because the wall never moved! Work only happens when a force physically moves something over a distance.
⚙️ Architecture & Under the Hood
Mechanical work is defined as the line integral of force over displacement: W = ∫ F · dr = F · d · cos(θ). The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy (W_net = ΔKE). Energy cannot be created or destroyed, only transformed between forms (kinetic, potential, thermal, electrical).
Core Energy Equations
The two primary mechanical energy forms are Kinetic Energy (motion) and Gravitational Potential Energy (stored position).
- Mechanical Work: W = F × d × cos(θ) [Measured in Joules, J]
- Kinetic Energy (Motion): KE = 0.5 × m × v²
- Gravitational Potential Energy (Height): PE = m × g × h (where g ≈ 9.81 m/s²)
- Conservation Law: Total Mechanical Energy (KE + PE) remains constant in a closed conservative system.
Frequently Asked Questions
Why does braking distance quadruple when driving speed doubles?
Because kinetic energy is proportional to velocity squared (KE = 0.5 · m · v²). Doubling your speed from 30 mph to 60 mph quadruples your vehicle's kinetic energy, requiring the brakes to perform four times as much friction work to bring the car to a stop.