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Elastic Collision (1D) Calculator

This calculator determines the final velocities of two objects after a one-dimensional elastic collision. Enter the masses and initial velocities of both objects to find their velocities after impact, using the conservation of momentum and kinetic energy principles.

This calculator determines the final velocities of two objects after a one-dimensional elastic collision. Enter the masses and initial velocities of both objects to find their velocities after impact, using the conservation of momentum and kinetic energy principles.

Elastic Collision 1D Calculator

Input Fields
If enabled, the result will update automatically when you change any value.

Elastic Collision Formulas

Formula
$$ v_1 = \frac{m_1 – m_2}{m_1 + m_2} u_1 + \frac{2m_2}{m_1 + m_2} u_2 \\[1em] v_2 = \frac{2m_1}{m_1 + m_2} u_1 + \frac{m_2 – m_1}{m_1 + m_2} u_2 $$

Where:

  • $$m_1$$ and $$m_2$$ are the masses of the two objects.
  • $$u_1$$ and $$u_2$$ are the initial velocities.
  • $$v_1$$ and $$v_2$$ are the final velocities after the collision.

These formulas are derived from the conservation of momentum and conservation of kinetic energy, which both hold true in a perfectly elastic collision.

Elastic Collision – Calculation Example

Example: A 2 kg object moving at 5 m/s collides with a 1 kg object at rest.

$$m_1 = 2\text{ kg},\quad u_1 = 5\text{ m/s},\quad m_2 = 1\text{ kg},\quad u_2 = 0\text{ m/s}$$

$$v_1 = \frac{2 – 1}{2 + 1} \cdot 5 + \frac{2 \cdot 1}{2 + 1} \cdot 0 = \frac{1}{3} \cdot 5 + 0 = 1.667\text{ m/s}$$

$$v_2 = \frac{2 \cdot 2}{2 + 1} \cdot 5 + \frac{1 – 2}{2 + 1} \cdot 0 = \frac{4}{3} \cdot 5 + 0 = 6.667\text{ m/s}$$

Result: $$v_1 = 1.667\text{ m/s}$$, $$v_2 = 6.667\text{ m/s}$$

This tool is useful for physics students, engineers, and educators studying collision dynamics. It instantly computes the outcome of 1D elastic collisions without manual algebra, saving time and reducing calculation errors.

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