Force Resolution - Interactive Simulation

Interactive simulation of force resolution into rectangular components using trigonometry with pendulum application

Fx Component: 0.00 N
Fy Component: 0.00 N

Force Resolution Formulas

Fx = F·cos(θ)
Fy = F·sin(θ)
Pythagorean: F² = Fx² + Fy²

Application Scenario

Basic force resolution: decompose a force into horizontal and vertical components.

Parameters

Real-time Calculations

Angle θ 30.00°
cos(θ) 0.866
sin(θ) 0.500
Fx = F·cos(θ) 86.60 N
Fy = F·sin(θ) 50.00 N
Verification: F² = Fx² + Fy² 10000 = 10000

What is Force Resolution?

Force resolution is the process of breaking down a single force into two or more component forces that, when combined, produce the same effect as the original force. The most common resolution is into perpendicular (rectangular) components along the x and y axes. This technique is fundamental in physics and engineering for analyzing forces in different directions.

Trigonometric Principles

Force resolution uses basic trigonometry. If a force F acts at an angle θ from the horizontal, its horizontal component is Fx = F·cos(θ) and its vertical component is Fy = F·sin(θ). These relationships come from a right triangle where the force is the hypotenuse, and the components are the adjacent and opposite sides. The Pythagorean theorem ensures that F² = Fx² + Fy², verifying the conservation of magnitude.

Applications

Structures & Bridges

Resolving tension and compression forces in trusses and beams to ensure structural integrity.

Projectile Motion

Breaking initial velocity into horizontal and vertical components to analyze trajectory.

Pendulum Analysis

Resolving gravitational force into tangential and radial components to study oscillatory motion.