Elastic Collision Calculator

About the Elastic Collision Calculator

The Elastic Collision Calculator computes the final velocities (\( v_1 \), \( v_2 \)) of two objects after a one-dimensional elastic collision, where both momentum and kinetic energy are conserved. This tool is designed for physics students, engineers, and educators analyzing collision dynamics.

Formulas used:

• Final Velocity of Object 1: \( v_1 = \frac{m_1 - m_2}{m_1 + m_2} u_1 + \frac{2 m_2}{m_1 + m_2} u_2 \)
• Final Velocity of Object 2: \( v_2 = \frac{2 m_1}{m_1 + m_2} u_1 + \frac{m_2 - m_1}{m_1 + m_2} u_2 \)

This calculator is ideal for studying mechanics, such as in billiards, particle physics, or vehicle collision analysis.

• Features:
  • Calculates final velocities for two objects in a 1D elastic collision.
  • Supports unit conversions: mass (kg, g), velocity (m/s, cm/s).
  • Validates inputs: positive masses; numeric velocities (positive or negative).
  • Keypad includes digits, decimal point, scientific notation (E), and negative sign (-).
  • Clear and backspace functionality, with a "Copy" button for results.
• Practical Applications: Useful in physics education, mechanical engineering (e.g., analyzing collisions in machinery), sports science (e.g., billiards, hockey), and accident reconstruction.
• How to Use:
  • Enter the mass of Object 1 (\( m_1 \)) and select the unit (kg, g).
  • Enter the initial velocity of Object 1 (\( u_1 \)) and select the unit (m/s, cm/s).
  • Enter the mass of Object 2 (\( m_2 \)) and select the unit (kg, g).
  • Enter the initial velocity of Object 2 (\( u_2 \)) and select the unit (m/s, cm/s).
  • Use the keypad to insert digits, decimal point, scientific notation (E), or negative sign (-).
  • Click "Calculate" to compute the final velocities, then use "Copy" to copy the result.
  • Use "Clear" to reset, or "⌫" to delete the last character.
  • Share or embed the calculator using the action buttons.
• Helpful Tips:
  • Ensure masses are positive.
  • Velocities can be positive (e.g., moving right) or negative (e.g., moving left).
  • Use scientific notation (E) for small values (e.g., 1E-3 for 0.001).
  • Final velocities are in \( \text{m/s} \).
  • This calculator assumes a head-on (1D) elastic collision.
• Examples:
  • Example 1: Equal Masses, Opposite Velocities:
    • Input: \( m_1 = 1 \, \text{kg} \), \( u_1 = 5 \, \text{m/s} \), \( m_2 = 1 \, \text{kg} \), \( u_2 = -5 \, \text{m/s} \)
    • Steps:
      • Formula for \( v_1 \): \( v_1 = \frac{m_1 - m_2}{m_1 + m_2} u_1 + \frac{2 m_2}{m_1 + m_2} u_2 \)
      • \( v_1 = \frac{1 - 1}{1 + 1} \cdot 5 + \frac{2 \cdot 1}{1 + 1} \cdot (-5) = 0 + 1 \cdot (-5) = -5 \, \text{m/s} \)
      • Formula for \( v_2 \): \( v_2 = \frac{2 m_1}{m_1 + m_2} u_1 + \frac{m_2 - m_1}{m_1 + m_2} u_2 \)
      • \( v_2 = \frac{2 \cdot 1}{1 + 1} \cdot 5 + \frac{1 - 1}{1 + 1} \cdot (-5) = 1 \cdot 5 + 0 = 5 \, \text{m/s} \)
    • Result: \( v_1 = -5 \, \text{m/s} \), \( v_2 = 5 \, \text{m/s} \)
  • Example 2: Different Masses, One Stationary:
    • Input: \( m_1 = 2 \, \text{kg} \), \( u_1 = 4 \, \text{m/s} \), \( m_2 = 500 \, \text{g} \), \( u_2 = 0 \, \text{cm/s} \)
    • Steps:
      • Convert: \( m_2 = 500 \, \text{g} = 0.5 \, \text{kg} \), \( u_2 = 0 \, \text{cm/s} = 0 \, \text{m/s} \)
      • \( v_1 = \frac{2 - 0.5}{2 + 0.5} \cdot 4 + \frac{2 \cdot 0.5}{2 + 0.5} \cdot 0 = \frac{1.5}{2.5} \cdot 4 + 0 = 0.6 \cdot 4 = 2.4 \, \text{m/s} \)
      • \( v_2 = \frac{2 \cdot 2}{2 + 0.5} \cdot 4 + \frac{0.5 - 2}{2 + 0.5} \cdot 0 = \frac{4}{2.5} \cdot 4 + 0 = 1.6 \cdot 4 = 6.4 \, \text{m/s} \)
    • Result: \( v_1 = 2.4 \, \text{m/s} \), \( v_2 = 6.4 \, \text{m/s} \)
  • Example 3: Small Mass Hits Large Mass:
    • Input: \( m_1 = 0.1 \, \text{kg} \), \( u_1 = 10 \, \text{m/s} \), \( m_2 = 5 \, \text{kg} \), \( u_2 = 0 \, \text{m/s} \)
    • Steps:
      • \( v_1 = \frac{0.1 - 5}{0.1 + 5} \cdot 10 + \frac{2 \cdot 5}{0.1 + 5} \cdot 0 = \frac{-4.9}{5.1} \cdot 10 + 0 \approx -9.6078 \, \text{m/s} \)
      • \( v_2 = \frac{2 \cdot 0.1}{0.1 + 5} \cdot 10 + \frac{5 - 0.1}{0.1 + 5} \cdot 0 = \frac{0.2}{5.1} \cdot 10 + 0 \approx 0.3922 \, \text{m/s} \)
    • Result: \( v_1 \approx -9.61 \, \text{m/s} \), \( v_2 \approx 0.39 \, \text{m/s} \)

Calculate final velocities in elastic collisions with detailed steps using this calculator. Share or embed it on your site!