# Simple Machine Efficiency

Compare pulley systems, inclined planes, and levers through force, work, friction losses, and efficiency.

> Canonical page: https://elysiatools.com/en/visualizations/simple-machine-efficiency

- **Category:** Physics

## Overview

Interactive simulation of simple machine efficiency comparing three fundamental machines: pulley systems, inclined planes, and levers. Features efficiency calculation η = (W_ideal / W_actual) × 100% = (F_ideal / F_actual) × 100%, where W_ideal = F_ideal·d (theoretical work without friction) and W_actual = F_actual·d (real work including energy losses). Physics formulas for each machine: Pulley system with mechanical advantage MA = 2n (n = number of pulleys), ideal force F_ideal = mg/(2n), actual force F_actual = F_ideal + μ·mg/n accounting for pulley friction. Inclined plane: ideal force F_ideal = mg·sin(θ), actual force F_actual = mg·sin(θ) + μ·mg·cos(θ) including friction, work ratio W_useful/W_total = sin(θ)/(sin(θ) + μ·cos(θ)). Lever: ideal mechanical advantage MA = L_effort/L_resistance, ideal force F_ideal = F_resistance/MA, actual force includes friction losses F_actual = F_ideal + μ·F_resistance. Three machine types with switchable interface, each with specific parameters (pulley count, load mass, friction; incline angle, length, mass; lever arm lengths, resistance force). Real-time force comparison bar chart showing ideal vs actual force. Work analysis diagram displaying energy flow from input to output with efficiency percentage. Energy flow chart breaking down total work into useful work (green) and friction losses (red). Machine efficiency comparison panel showing η values for all three types simultaneously. Dynamic parameter adjustment with instant efficiency recalculation. Educational content covering ideal vs real machines, friction effects, mechanical advantage concepts, energy conservation, practical applications in engineering and daily life. Multi-language support (zh, en, es, fr, de, ru, pt).

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