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Calculate linear momentum (p = mv), solve conservation of momentum for elastic and inelastic collisions, and find impulse (J = FΔt). Momentum is conserved in all isolated systems — a fundamental principle of physics.
Momentum (p = mv) is the product of mass and velocity — a measure of how difficult it is to stop a moving object. A heavy truck at slow speed and a light bullet at high speed can have the same momentum. In any isolated system, total momentum before a collision equals total momentum after, regardless of collision type.
Linear momentum (p) is defined as the product of an object's mass and its velocity: p = mv. It is a vector quantity — it has the same direction as velocity. The SI unit of momentum is kg·m/s (equivalent to N·s). Momentum quantifies the "quantity of motion" — a 2000 kg truck at 10 m/s has the same momentum (20,000 kg·m/s) as a 0.02 kg bullet traveling at 1,000,000 m/s (if such speeds were possible).
The Law of Conservation of Momentum states that in an isolated system (no external forces), the total momentum remains constant. This is one of the most fundamental conservation laws in physics, applying from subatomic particle collisions to galaxy cluster interactions. It derives directly from Newton's Third Law: action and reaction forces in a collision are equal and opposite, so momentum transferred between objects cancels exactly.
| Collision Type | Energy | Example |
|---|---|---|
| Perfectly Elastic | KE conserved, objects separate | Billiard balls, atomic collisions |
| Partially Inelastic | Some KE lost to heat/sound | Most real-world collisions |
| Perfectly Inelastic | Maximum KE lost, objects stick | Clay ball hitting wall, car crash |
| Explosive | Objects initially together, fly apart | Explosion, gun firing bullet |
Impulse (J) = Force × time = F × Δt. Impulse equals the change in momentum: J = Δp = m(v_f - v_i). This is why safety features extend collision time — longer time for same momentum change = smaller force. Car crumple zones: extend impact duration from 0.05s to 0.15s, reducing peak force by 3×. Airbags: cushion impact over 0.05-0.15s vs 0.002s for bare impact. Sports: follow-through in baseball/tennis maximizes impulse (force × time contact). Catching: pulling hands back with ball extends time, reduces impact force (hand velocity matches ball before stopping).
Elastic collision (two objects, 1D): Object 1 (m₁, v₁) hits stationary Object 2 (m₂, v₂=0). After: v₁' = v₁(m₁-m₂)/(m₁+m₂). v₂' = 2m₁v₁/(m₁+m₂). Equal masses (m₁=m₂): v₁'=0, v₂'=v₁. Object 1 stops completely — all momentum transferred to Object 2. This is why billiard cue ball stops after hitting another ball head-on. Perfectly inelastic: both stick together. v_final = (m₁v₁+m₂v₂)/(m₁+m₂). A 1500kg car at 20 m/s hits stationary 1500kg car: v_final = (1500×20)/(1500+1500) = 10 m/s. KE lost: ½(3000)(10²) - ½(1500)(20²) = 150,000 - 300,000 = -150,000 J lost to deformation.
Rockets work by conservation of momentum. Exhaust gases are ejected backward with high momentum — equal and opposite momentum is imparted to the rocket (forward). The Tsiolkovsky rocket equation: Δv = v_e × ln(m₀/m_f), where v_e is exhaust velocity, m₀ is initial mass (full fuel), m_f is final mass (empty). To reach orbit (~7,800 m/s), with v_e = 3,000 m/s: m₀/m_f = e^(7800/3000) = e^2.6 = 13.5. Must be 93% fuel by mass. This is why rockets are mostly fuel and why staged rockets are used — discarding empty tanks reduces m₀ for subsequent stages.
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.
Sports science relies heavily on classical mechanics to analyze and improve athletic performance. Projectile motion governs the trajectory of every thrown, kicked, or hit ball in sport. Torque analysis explains joint loading and muscle force requirements in weight training. Momentum and impulse calculations underpin collision analysis in contact sports and help design protective equipment that extends impact duration to reduce peak force. Power output measurement guides training intensity for cyclists, rowers, and sprinters. Understanding these physics principles gives athletes and coaches a quantitative framework for performance optimization.