How To Calculate Elastic Collision Velocity

Elastic Collision Velocity Equation:

\[ v_{1f} = \frac{(m_1 - m_2) v_{1i}}{(m_1 + m_2)} + \frac{2 m_2 v_{2i}}{(m_1 + m_2)} \]

Mass 1 (m1):

Mass 2 (m2):

Initial Velocity 1 (v1i):

m/s

Initial Velocity 2 (v2i):

m/s

Final Velocity 1 (v1f):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Elastic Collision Velocity?

Elastic collision velocity calculation determines the final velocity of objects after a perfectly elastic collision where both momentum and kinetic energy are conserved. This is fundamental in physics for analyzing collisions between particles, billiard balls, and other objects.

2. How Does the Calculator Work?

The calculator uses the elastic collision velocity equation:

\[ v_{1f} = \frac{(m_1 - m_2) v_{1i}}{(m_1 + m_2)} + \frac{2 m_2 v_{2i}}{(m_1 + m_2)} \]

Where:

\( v_{1f} \) — Final velocity of object 1 (m/s)
\( m_1 \) — Mass of object 1 (kg)
\( m_2 \) — Mass of object 2 (kg)
\( v_{1i} \) — Initial velocity of object 1 (m/s)
\( v_{2i} \) — Initial velocity of object 2 (m/s)

Explanation: The equation calculates the final velocity of the first object after an elastic collision, considering the conservation of both momentum and kinetic energy.

3. Importance of Elastic Collision Calculation

Details: Understanding elastic collisions is crucial in physics, engineering, and various applications including particle physics, mechanical engineering, sports science, and accident reconstruction.

4. Using the Calculator

Tips: Enter all masses in kilograms and velocities in meters per second. Ensure masses are positive values. The calculator provides the final velocity of object 1 after collision.

5. Frequently Asked Questions (FAQ)

Q1: What is an elastic collision?
A: An elastic collision is one where both momentum and kinetic energy are conserved. No energy is lost to heat, sound, or deformation.

Q2: What are real-world examples of elastic collisions?
A: Billiard ball collisions, atomic and subatomic particle collisions, and collisions between hard steel balls are close approximations of elastic collisions.

Q3: How do I calculate the final velocity of object 2?
A: Use the complementary equation: \( v_{2f} = \frac{(m_2 - m_1) v_{2i}}{(m_1 + m_2)} + \frac{2 m_1 v_{1i}}{(m_1 + m_2)} \)

Q4: What if the masses are equal?
A: For equal masses (\( m_1 = m_2 \)), the objects simply exchange velocities: \( v_{1f} = v_{2i} \) and \( v_{2f} = v_{1i} \)

Q5: When is this equation not applicable?
A: This equation applies only to perfectly elastic collisions in one dimension. For inelastic collisions or two-dimensional collisions, different equations are needed.