Totally Elastic Collision Formula

Totally Elastic Collision Equation:

\[ v_{1f} = \frac{m_1 - m_2}{m_1 + m_2} v_1 + \frac{2 m_2}{m_1 + m_2} v_2 \]

Mass 1 (m₁):

Mass 2 (m₂):

Initial Velocity 1 (v₁):

m/s

Initial Velocity 2 (v₂):

m/s

Final Velocity for Object 1 (v₁f):

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1. What is the Totally Elastic Collision Formula?

The Totally Elastic Collision Formula calculates the final velocity of object 1 after a perfectly elastic one-dimensional collision. In elastic collisions, both momentum and kinetic energy are conserved, making this formula essential for physics and engineering applications.

2. How Does the Calculator Work?

The calculator uses the elastic collision equation:

\[ v_{1f} = \frac{m_1 - m_2}{m_1 + m_2} v_1 + \frac{2 m_2}{m_1 + m_2} v_2 \]

Where:

\( v_{1f} \) — Final velocity of object 1 (m/s)
\( m_1 \) — Mass of object 1 (kg)
\( m_2 \) — Mass of object 2 (kg)
\( v_1 \) — Initial velocity of object 1 (m/s)
\( v_2 \) — Initial velocity of object 2 (m/s)

Explanation: This formula is derived from the conservation of momentum and conservation of kinetic energy principles in one-dimensional elastic collisions.

3. Importance of Elastic Collision Calculation

Details: Understanding elastic collisions is crucial for analyzing particle interactions, designing safety systems, studying molecular dynamics, and solving physics problems involving conservation laws.

4. Using the Calculator

Tips: Enter all masses in kilograms and velocities in meters per second. Masses must be positive values greater than zero. The calculator provides the final velocity of object 1 after collision.

5. Frequently Asked Questions (FAQ)

Q1: What defines a perfectly elastic collision?
A: A perfectly elastic collision is one where both momentum and kinetic energy are conserved, with no energy lost to heat, sound, or deformation.

Q2: How do I calculate the final velocity of object 2?
A: The formula for object 2 is: \( v_{2f} = \frac{2 m_1}{m_1 + m_2} v_1 + \frac{m_2 - m_1}{m_1 + m_2} v_2 \)

Q3: What are real-world examples of elastic collisions?
A: Billiard ball collisions, atomic and molecular collisions, and some types of particle collisions in particle accelerators.

Q4: What if the masses are equal?
A: If \( m_1 = m_2 \), then \( v_{1f} = v_2 \) and \( v_{2f} = v_1 \) - the objects simply exchange velocities.

Q5: Are there limitations to this formula?
A: This formula applies only to one-dimensional collisions and assumes perfect elasticity. Real-world collisions often involve some energy loss and may be multi-dimensional.