Velocity After Elastic Collision Formula

Velocity After Elastic Collision Formula:

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

Mass 1 (m1):

Mass 2 (m2):

Initial Velocity 1 (v1):

m/s

Initial Velocity 2 (v2):

m/s

Final Velocity of Mass 1 (v1f):

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1. What is the Velocity After Elastic Collision Formula?

The velocity after elastic collision formula calculates the final velocity of an object after a perfectly elastic collision in one dimension. In elastic collisions, both momentum and kinetic energy are conserved, making this calculation essential in physics and engineering applications.

2. How Does the Calculator Work?

The calculator uses the elastic collision formula:

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

Where:

\( v_{1f} \) — Final velocity of mass 1 after collision (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 perfectly elastic collisions.

3. Importance of Elastic Collision Calculations

Details: Understanding elastic collisions is crucial in fields like particle physics, engineering, sports science, and accident reconstruction. These calculations help predict object behavior after impact while conserving energy and momentum.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What defines 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 is the formula for mass 2's final velocity?
A: The final velocity of mass 2 is given by: \( v_{2f} = \frac{2 m_1}{m_1 + m_2} v_1 + \frac{m_2 - m_1}{m_1 + m_2} v_2 \)

Q3: What happens when masses are equal?
A: When m1 = m2, the formula simplifies to v1f = v2 and v2f = v1 - the objects exchange velocities.

Q4: Can this be used for 2D or 3D collisions?
A: No, this formula is for one-dimensional collisions. Multi-dimensional collisions require vector analysis and conservation laws in each dimension.

Q5: What are real-world examples of elastic collisions?
A: Billiard ball collisions, atomic and subatomic particle interactions, and Newton's cradle are common examples of nearly elastic collisions.