1D Elastic & Inelastic Collision Momentum & Velocity Calculator

Solve 1D conservation of linear momentum with adjustable restitution (e).

Post-Collision Velocity of Body 1 (v₁′)
-4.65 m/s
Post-Collision Velocity of Body 2 (v₂′) 8.1 m/s
Total Conserved Momentum 30 kg·m/s
Kinetic Energy Dissipated 74.93 J
Inputs
kg
Mass of body 1 in kilograms.
m/s
Initial velocity of body 1 in m/s.
kg
Mass of body 2 in kilograms.
m/s
Initial velocity of body 2 in m/s.
e
Coefficient of restitution e (1 = elastic, 0 = sticky inelastic).
Results & Graph
Post-Collision Velocity of Body 1 (v₁′)
-4.65 m/s
Post-Collision Velocity of Body 2 (v₂′)
8.1 m/s
Total Conserved Momentum
30 kg·m/s
Kinetic Energy Dissipated
74.93 J

Post-Collision Velocity of Body 1 (v₁′)

Graph 1 • Mass1 Kg Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
-8.8 m/s -3.9 m/s 1.1 m/s 50%: -8.81 m/s -8.8 50% 75%: -6.5 m/s -6.5 75% 100%: -4.65 m/s -4.7 100% 125%: -3.14 m/s -3.1 125% 150%: -1.87 m/s -1.9 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Post-Collision Velocity of Body 1 (v₁′) -4.65 m/s Post-Collision Velocity of Body 2 (v₂′) 8.1 m/s Total Conserved Momentum 30 kg·m/s Kinetic Energy Dissipated 74.93 J
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Post-Collision Velocity of Body 1 (v₁′)-4.65 m/sPost-Collision Velocity of Body 2 (v₂′)8.1 m/sTotal Conserved Momentum30 kg·m/sKinetic Energy Dissipated74.93 J
Summary: With restitution e=0.85, post-collision velocities are v₁′ = -4.65 m/s and v₂′ = 8.1 m/s, dissipating 74.93 J of kinetic energy.
Summary: With restitution e=0.85, post-collision velocities are v₁′ = -4.65 m/s and v₂′ = 8.1 m/s, dissipating 74.93 J of kinetic energy.
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Formula & Mathematical Methodology: Collision Momentum Physics & Engineering Equation

v₁′ = [m₁v₁ + m₂v₂ − m₂·e·(v₁ − v₂)] / (m₁ + m₂)
v₂′ = [m₁v₁ + m₂v₂ + m₁·e·(v₁ − v₂)] / (m₁ + m₂)
v₁′ = [m₁v₁ + m₂v₂ − m₂·e·(v₁ − v₂)] / (m₁ + m₂); v₂′ = [m₁v₁ + m₂v₂ + m₁·e·(v₁ − v₂)] / (m₁ + m₂)
  • mass1Kg: Mass1 Kg (kg)
  • velocity1Mps: Velocity1 Mps (m/s)
  • mass2Kg: Mass2 Kg (kg)
  • velocity2Mps: Velocity2 Mps (m/s)
  • restitutionCoeff: Restitution Coeff (e)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Collision Momentum

Solve 1D conservation of linear momentum with adjustable restitution (e).

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: v₁′ = [m₁v₁ + m₂v₂ − m₂·e·(v₁ − v₂)] / (m₁ + m₂); v₂′ = [m₁v₁ + m₂v₂ + m₁·e·(v₁ − v₂)] / (m₁ + m₂).
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Collision Momentum via v₁′ = [m₁v₁ + m₂v₂ − m₂·e·(v₁ − v₂)] / (m₁ + m₂); v₂′ = [m₁v₁ + m₂v₂ + m₁·e·(v₁ − v₂)] / (m₁ + m₂).

Frequently Asked Questions

What equation powers the 1D Elastic & Inelastic Collision Momentum & Velocity Calculator?

It evaluates v₁′ = [m₁v₁ + m₂v₂ − m₂·e·(v₁ − v₂)] / (m₁ + m₂); v₂′ = [m₁v₁ + m₂v₂ + m₁·e·(v₁ − v₂)] / (m₁ + m₂) using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Classical Mechanics & Kinematics

1D Elastic & Inelastic Collision Momentum & Velocity Calculator: inputs, method, and how to read the result

Solve 1D conservation of linear momentum with adjustable restitution (e).

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Mass1 Kg: Mass of body 1 in kilograms.
  • Velocity1 Mps: Initial velocity of body 1 in m/s.
  • Mass2 Kg: Mass of body 2 in kilograms.
  • Velocity2 Mps: Initial velocity of body 2 in m/s.

What the calculation includes

With the default values shown, Post-Collision Velocity of Body 1 (v₁′) is -4.65 m/s. The calculation follows Collision Momentum Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Mass1 Kg from 4 kg to 5 kg changes Post-Collision Velocity of Body 1 (v₁′) from -4.65 m/s to -3.14 m/s. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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