Work-Energy Theorem - Interactive Visualization

Interactive visualization of the work-energy theorem - explore the relationship between work, kinetic energy, and velocity changes with adjustable parameters

Energy Analysis

Initial KE (½mv₁²) 0.00 J
Work Done (W = Fs) 0.00 J
Final KE (½mv₂²) 0.00 J
ΔEk = Ek₂ - Ek₁ = W 0.00 J
Initial Velocity (v₁) 0.00 m/s
→
Final Velocity (v₂) 0.00 m/s

Current State

Position 0.00 m
Velocity 0.00 m/s
Kinetic Energy 0.00 J
Work Done 0.00 J

Parameters

Positive: Acceleration

Work-Energy Theorem

Main Theorem: W合 = ΔEk = Ek₂ - Ek₁
Kinetic Energy: Ek = ½mv²
Work Done: W = F · s
Velocity Relation: v₂² = v₁² + 2Fs/m
Expanded Form: Fs = ½mv₂² - ½mv₁²

What is the Work-Energy Theorem?

The work-energy theorem states that the work done by the net force on an object equals the change in its kinetic energy. This fundamental principle connects the concepts of force, displacement, and energy in mechanics.

Key Concepts

Work (W = F·s)

Work is done when a force causes displacement. Positive work (force in direction of motion) increases kinetic energy, while negative work (force opposite to motion) decreases it.

Kinetic Energy (Ek = ½mv²)

Kinetic energy is the energy of motion. It depends on both mass and velocity, with velocity having a squared relationship - doubling velocity quadruples kinetic energy.

The Theorem (W = ΔEk)

The work-energy theorem provides a powerful method for solving mechanics problems without analyzing forces and accelerations at every instant. Instead, we relate initial and final states directly.

Applications

Scenario Explanations

Horizontal Acceleration

When an applied force acts in the direction of motion (F > 0), positive work is done. The object gains kinetic energy, and v₂ > v₁.

Horizontal Deceleration

When friction or braking force opposes motion (F < 0), negative work is done. The object loses kinetic energy, and v₂ < v₁.

Vertical Throw

When throwing upward, gravity does negative work. Kinetic energy converts to gravitational potential energy. At the peak, v₂ = 0 and all initial KE becomes PE.