Collision Elastic Calculator

Collision Elastic Calculator — calculate collision elastic with the correct physics formula. Worked example and unit notes included.

A multi-field classical mechanics calculator handles problems that require three or more inputs — centripetal force, gravitational attraction, aerodynamic drag and lift, thermal expansion, elastic and inelastic collisions, and centre of mass. These cannot be served by a simple two-field formula widget because the physics involves multiple independent variables that each affect the result. The calculator organises these into five tabs: radial mechanics, fluid forces, thermal expansion, collision analysis, and static equilibrium.

Classical mechanics underpins aerospace engineering, structural design, vehicle dynamics, manufacturing tolerances, and sports physics. The formulas here are all derivable from Newton's three laws of motion and the conservation laws of momentum and energy.

Compare Collision Inelastic Calculator, Centre of Mass Calculator, and Equilibrium Calculator when the same physical system crosses between related topics. These companions help connect the input variables, but they do not make the underlying model interchangeable: keep the measured quantity, unit convention, reference direction, and material or medium beside every result.

Physics estimates remain conditional on their assumptions. Decide whether the problem uses an ideal wave, a point mass, a rigid body, a steady flow, a reversible cycle, or a quantum approximation before entering values. State temperature, pressure, geometry, boundary conditions, and significant figures with the output so another reader can reproduce the calculation and judge whether the result is useful.

A simple sanity check should accompany any important result: inspect the dimensions, vary one input at a time, and confirm that the direction of change matches the governing equation. A plausible number is not enough if a wavelength, force, energy, momentum, or temperature was entered in the wrong unit or with the wrong sign convention.

Select the tab for your calculation type: Centripetal & Gravity, Drag & Lift, Thermal Expansion, Collision, or Centre of Mass.
Enter all required values — each tab clearly labels every input field with its physical unit.
Results update instantly as you change any input.
For collisions, the calculator shows both elastic (kinetic energy conserved) and inelastic (perfectly sticky) outcomes from the same initial conditions.

Key mechanics formulas

Centripetal force: F = mv² ÷ r (m = mass, v = speed, r = radius of circular path)

Universal gravitation: F = G × m₁m₂ ÷ r² (G = 6.674×10⁻¹¹ N·m²/kg²)

Drag force: F_D = ½ρCdAv² (ρ = fluid density, Cd = drag coefficient, A = reference area)

Lift force: F_L = ½ρClAv² (Cl = lift coefficient)

Thermal expansion: ΔL = α × L₀ × ΔT (α = coefficient of linear expansion)

Elastic collision: v₁ʼ = ((m₁−m₂)v₁ + 2m₂v₂) ÷ (m₁+m₂)

Inelastic collision: v = (m₁v₁ + m₂v₂) ÷ (m₁+m₂)

Centre of mass: x_cm = (m₁x₁ + m₂x₂) ÷ (m₁+m₂)

Interpreting your mechanics results

Typical magnitudes to check against

Centripetal force for a 1,500 kg car cornering at 20 m/s on a 50 m radius bend: F = 1500 × 400 ÷ 50 = 12,000 N (1.2 tonnes) — comfortably within tyre friction for dry tarmac. Gravitational force between Earth and a 75 kg person at the surface: F = 6.674×10⁻¹¹ × 5.97×10²⁴ × 75 ÷ (6.371×10⁶)² ≈ 735 N (body weight, as expected).

Thermal expansion of a 100 m steel bridge over 50°C seasonal change: ΔL = 12×10⁻⁶ × 100,000 mm × 50 = 60 mm — this is why expansion joints exist. Drag on a cyclist at 10 m/s (36 km/h): ½ × 1.225 × 1.0 × 0.5 × 100 ≈ 30.6 N, requiring about 306 W to sustain — consistent with power-meter data for competitive cyclists.

Physics tips and best practices

For centripetal calculations, centripetal force is not a "new" force — it is the net inward force supplied by friction, tension, gravity, or normal force depending on the scenario.
Drag coefficient Cd varies significantly with shape: a sphere is 0.47, a streamlined teardrop is about 0.05, and a flat plate perpendicular to flow is about 1.2. Use wind tunnel data or published values for specific vehicles.
Thermal expansion coefficients are per °C (or per K — the same numerically). For 2D expansion, the area coefficient is approximately 2α; for 3D (volume), it is 3α.
In a perfectly elastic collision between equal masses where one is stationary, the moving object stops completely and the stationary one takes on all the velocity — a counter-intuitive result confirmed by Newton's cradle.
Centre of mass for complex shapes can be found by dividing the shape into simple parts, computing each part's individual centre of mass, then applying the weighted average formula iteratively.

Formula 1 cars generate approximately 3.5 g of lateral acceleration in high-speed corners — centripetal force ≈ 3.5 × car weight. The driver experiences this as 3.5× their body weight pushing them sideways.
The International Space Station orbits at 408 km altitude where gravitational acceleration is still about 8.7 m/s² (89% of surface gravity) — it is in free fall, which is what orbital motion is.
Thermal expansion caused the Millennium Bridge in London to oscillate synchronously with pedestrians on opening day in 2000, leading to its immediate closure for redesign.
A car-to-car head-on collision at 50 km/h each is equivalent in energy terms to hitting a fixed wall at 50 km/h (not 100 km/h) — momentum is shared, not doubled.

Common mistakes to avoid

Confusing centripetal force with centrifugal force — centrifugal force is a fictitious force felt in a rotating reference frame, not a real force acting on the object.
Using diameter instead of radius in the centripetal or gravitational force formula — always use radius (half the diameter) for circular-motion calculations.
Forgetting to square velocity in drag force calculations — drag increases with v², so doubling speed quadruples drag and power required increases eightfold.
Assuming collisions are elastic when they are not — most everyday collisions (cars, balls, billiards) are partially inelastic; perfectly elastic collisions are idealised and rare.
Mixing units for thermal expansion — always use consistent units; α in /°C, L₀ in mm, ΔT in °C gives ΔL in mm; switching to metres requires no unit change for α or ΔT.

These calculations assume ideal conditions: rigid bodies, uniform materials, incompressible fluids, and constant coefficients. Real engineering design must account for material variability, safety factors, dynamic loading, fatigue, and regulatory requirements. Always verify structural, aerospace, and safety-critical calculations with a qualified engineer and applicable standards (BS, EN, ASCE, etc.).