Live Momentum & Energy Diagnostics
Before Collision (Initial)
After Collision (Final)
Kinetic Energy Comparison (KE = ½ m v²)
In Elastic collisions, kinetic energy is strictly conserved.
| Reading # | Mode | Collision | m₁ (kg) | m₂ (kg) | u₁ (m/s) | u₂ (m/s) | v₁ (m/s) | v₂ (m/s) | Pinitial (kg·m/s) | Pfinal (kg·m/s) | ΔP (kg·m/s) | KEinitial (J) | KEfinal (J) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| No readings recorded yet. Click "RECORD DATA" to save the current simulation state. | |||||||||||||
Working Principle & Physics Framework
1. Concept of Linear Momentum
Linear momentum (p) is defined as the product of an object's mass (m) and its velocity vector (v):
Momentum is a vector quantity possessing both magnitude and direction. In one-dimensional motion, direction is indicated by algebraic sign: rightward motion is positive (+), and leftward motion is negative (−).
2. Law of Conservation of Linear Momentum
According to Newton's third law of motion, when two objects collide in an isolated system (where external net forces ΣFext = 0), the internal forces exerted by the objects on each other are equal and opposite. Consequently:
The total linear momentum of the system remains strictly constant before and after the collision.
3. Elastic vs. Inelastic Collisions
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Elastic Collision (e = 1.0): Both total momentum and total kinetic energy are conserved. The post-collision velocities are:
v₁ = [(m₁ - m₂)u₁ + 2m₂u₂] / (m₁ + m₂)
v₂ = [2m₁u₁ + (m₂ - m₁)u₂] / (m₁ + m₂) -
Perfectly Inelastic Collision (e = 0.0): Objects lock together and move at a common final velocity (vf). Maximum kinetic energy is transformed into thermal and deformation energy:
v₁ = v₂ = vf = (m₁u₁ + m₂u₂) / (m₁ + m₂)
4. Real-World Engineering Applications
- Automotive Safety Testing: Designing crumple zones and air-bag deployment algorithms based on collision impulse (J = Δp).
- Ballistics & Particle Physics: Analyzing subatomic collisions in hadron colliders and recoil velocities in aerospace launch systems.
- Orbital Gravity Assists: Leveraging planetary momentum transfer to accelerate interplanetary space probes (e.g., Voyager, James Webb).