Loading…
Calculate net force from mass and acceleration (F = ma), find mass from force and acceleration, or solve for acceleration. Also calculates weight force (W = mg), friction force, and normal force using Newton's laws of motion.
Force is any interaction that changes or tends to change an object's state of motion. Newton's Second Law (F = ma) quantifies the relationship: force equals mass times acceleration. The SI unit of force is the Newton (N) — the force required to accelerate 1 kg at 1 m/s². Understanding force is fundamental to all of classical mechanics.
Force is a vector quantity that describes an interaction capable of changing an object's velocity (acceleration) or shape. Isaac Newton's three laws of motion, published in Principia Mathematica (1687), provide the complete mathematical framework for understanding force and motion in the classical (non-relativistic) regime.
Newton's First Law (Law of Inertia): An object at rest remains at rest, and an object in motion remains in motion at constant velocity, unless acted upon by a net external force. Newton's Second Law: The net force on an object equals mass times acceleration: F = ma. Newton's Third Law: For every action force, there is an equal and opposite reaction force.
| Force Type | Formula | Direction/Note |
|---|---|---|
| Gravity | W = mg | Downward, toward Earth center |
| Normal Force | N = mg cos θ | Perpendicular to surface |
| Friction (kinetic) | f_k = μ_k × N | Opposes sliding motion |
| Friction (static) | f_s ≤ μ_s × N | Prevents motion, up to maximum |
| Tension | T = F along rope | Along rope or cable |
| Buoyancy | F_b = ρVg | Upward, in fluid |
| Spring Force | F = -kx (Hooke's Law) | Restoring force |
| Centripetal | F_c = mv²/r | Toward center of circular path |
Mass (kg) is the quantity of matter — it is constant everywhere in the universe. Weight (N) is the gravitational force acting on mass: W = mg. A 70 kg person has mass 70 kg everywhere but weight varies: Earth surface: W = 70 × 9.81 = 686.7 N. Moon: W = 70 × 1.62 = 113.4 N (1/6 Earth). Mars: W = 70 × 3.72 = 260.4 N. Weightlessness in orbit: astronauts are in continuous free fall around Earth — g is only slightly less than at surface, but they feel weightless because everything around them accelerates at the same rate.
Friction force = μ × Normal force. Coefficients of friction (static μ_s / kinetic μ_k): Rubber on dry concrete: 0.7/0.5 (car tire braking). Steel on steel: 0.74/0.57 (rail-wheel contact). Wood on wood: 0.4/0.2. PTFE (Teflon) on steel: 0.04/0.04 (nearly frictionless). Ice on ice: 0.1/0.03. Human joint (synovial fluid): 0.001-0.003 (lowest natural friction system). Static friction (before motion begins) is always ≥ kinetic friction (during sliding). Maximum static friction = μ_s × N — once this threshold is exceeded, motion begins.
Solving force problems requires identifying all forces acting on an object (free body diagram) and calculating net force as the vector sum. Box on inclined plane (angle θ): Weight component along slope = mg sin θ (down slope). Normal force = mg cos θ (perpendicular to slope). Friction (up slope if sliding) = μ_k × mg cos θ. Net force along slope = mg sin θ - μ_k mg cos θ = mg(sin θ - μ_k cos θ). Acceleration = g(sin θ - μ_k cos θ). At angle where tan θ = μ_s, the box is on the verge of sliding — the angle of repose, used in designing conveyor belts and storing granular materials.
Always ensure units are consistent before calculating. This calculator uses SI units (International System): meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, Newtons (N) for force, Joules (J) for energy, Watts (W) for power, and Pascals (Pa) for pressure. When converting from other unit systems (imperial, CGS), convert all values before entering them into the calculator.