Force Converter

The dyne (dyn) is the CGS unit of force: 1 dyn = 10⁻⁵ N = 1 g·cm/s². It is the force needed to accelerate 1 gram at 1 cm/s². Surface tension is naturally expressed in dyn/cm: water ~72 dyn/cm = 72 mN/m. In older physics and biophysics literature, forces are still sometimes given in dynes, particularly for forces in the 10⁻⁴ to 10² dyn (1 nN to 10 μN) range relevant to cells and molecules.

The poundal (pdl) is the FPS unit of force: 1 pdl = the force needed to accelerate 1 pound mass at 1 ft/s² = 0.138255 N. Unlike the pound-force (lbf), the poundal is a true force unit consistent with Newton's second law in FPS units (F = ma, with m in pounds and a in ft/s²). The poundal is rarely used today; lbf is more common in US engineering.

Thrust comparison: typical model rocket ~5-20 N; SpaceX Merlin 1D (Falcon 9) 845 kN sea level; SpaceX Raptor 2 (Starship) 2.2 MN; Space Shuttle main engine (SSME) 1.86 MN each; Space Shuttle total liftoff 30.1 MN; Saturn V F-1 engine 6.7 MN each, 5 engines = 33.4 MN; SpaceX Super Heavy booster (33 Raptors) ≈ 72.7 MN — the most powerful rocket in history.

Van der Waals forces are the weak attractive forces between all molecules, arising from instantaneous and induced dipole moments. Their magnitude per atom: ~10 pN (piconewtons). Despite being weak individually, they are collectively responsible for surface adhesion, the stickiness of geckos (which use millions of fine hair tips providing ~10 nN each, totaling ~1 N per mm²), and the condensation of noble gases into liquids at low temperatures.

Atomic Force Microscopy (AFM) measures forces from ~1 pN to ~10 μN using a cantilever with a sharp tip (~10 nm radius). Force sensitivity: cantilever spring constant k × displacement z; typical k = 0.01-100 N/m; displacement measured by laser deflection to ~0.01 nm → force resolution ~0.1 pN. AFM has measured: single bond rupture (~1-10 nN), DNA-protein binding (10-100 pN), and protein unfolding forces.

The strong force (QCD) between quarks inside a nucleon operates over distances of ~1 fm = 10⁻¹⁵ m, with a coupling strength αs ≈ 0.12-1 depending on energy scale. The force between two nucleons at 1 fm separation is roughly 10,000-100,000 N (!) — but it only acts over ~10⁻¹⁵ m range, which is why we don't notice it in everyday life. The corresponding potential energy (~100 MeV) is what holds nuclei together.

For a typical car at 100 km/h (27.8 m/s): aerodynamic drag F_drag = ½ ρ Cd A v² ≈ ½ × 1.2 × 0.3 × 2.0 × 27.8² ≈ 278 N; rolling resistance F_roll = μ_r × m × g ≈ 0.01 × 1500 × 9.8 ≈ 147 N; total resistance ≈ 425 N; engine power to maintain speed = F × v = 425 × 27.8 ≈ 11.8 kW = 15.8 hp. At 200 km/h, drag quadruples to ~1112 N, requiring ~62 kW (83 hp) just to overcome air resistance.

The Casimir effect is a quantum mechanical force between two uncharged perfectly conducting plates in vacuum, arising from zero-point fluctuations of the electromagnetic field: F/A = −π²ℏc/(240 d⁴), where d is the plate separation. At d = 100 nm: F/A ≈ 1.3 × 10⁻⁴ N/m² = 0.13 mPa. First measured precisely in 1997 (Lamoreaux), the Casimir force is significant in MEMS devices at sub-micrometer separations.

Surface tension γ (N/m or equivalently J/m²) is the force per unit length along a surface. Water: γ = 72.8 mN/m at 20°C. The force to pull a 1 cm wire from water's surface: F = 2γL = 2 × 0.0728 × 0.01 = 1.46 mN (factor 2 for two interfaces). Surface tension explains why water forms droplets (spherical minimizes surface area), insects can walk on water (water strider feet exert ~1.6 mN downward, balanced by surface tension force ~2.5 mN), and capillary action in plants.