Conservation of Momentum Calculator

Conservation of Momentum Calculator

Object 1

Object 2

Inelastic (Objects stick together) Elastic (Final velocity of Object 1 is known)

Results Overview

Initial Momentum 1: 0 kg·m/s

Initial Momentum 2: 0 kg·m/s

Total System Momentum: 0 kg·m/s

Calculated Final Velocity: 0 m/s

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Understanding the Law of Conservation of Momentum

In physics, the Law of Conservation of Momentum states that within an isolated system, the total momentum remains constant regardless of the interactions between objects. This principle is fundamental for solving problems involving collisions and explosions in classical mechanics.

The Core Formula

The mathematical representation of momentum ($p$) is the product of an object's mass ($m$) and its velocity ($v$):

p = m × v

For a collision between two objects, the total momentum before the collision equals the total momentum after the collision:

(m₁ × u₁) + (m₂ × u₂) = (m₁ × v₁) + (m₂ × v₂)

• m₁: Mass of first object
• u₁: Initial velocity of first object
• m₂: Mass of second object
• u₂: Initial velocity of second object
• v₁: Final velocity of first object
• v₂: Final velocity of second object

Types of Collisions

This calculator handles the two most common problem-solving scenarios:

1. Perfectly Inelastic Collisions: The objects stick together after the collision and move with a single final velocity ($v_f$). The formula simplifies to: $v_f = (m_1u_1 + m_2u_2) / (m_1 + m_2)$.
2. Elastic/Partial Collisions: Kinetic energy may or may not be conserved, but momentum always is. If you know the final velocity of one object, you can solve for the other.

Example Calculation

Imagine Object A (10 kg) is moving at 5 m/s and hits Object B (5 kg) which is stationary (0 m/s). If they stick together (inelastic):

• Initial Momentum = (10 × 5) + (5 × 0) = 50 kg·m/s.
• Total Mass = 10 + 5 = 15 kg.
• Final Velocity = 50 / 15 = 3.33 m/s.

Note: Velocity is a vector. Remember to use negative values for objects moving in the opposite direction!