Perfect Elastic Collision Formula

Perfect Elastic Collision Formula:

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

Mass 1 (m1):

Mass 2 (m2):

Initial Velocity 1 (v1i):

m/s

Initial Velocity 2 (v2i):

m/s

Final Velocity 1 (v1f):

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1. What Is Perfect Elastic Collision?

A perfect elastic collision is a collision where both momentum and kinetic energy are conserved. In such collisions, objects bounce off each other without any loss of kinetic energy to other forms like heat or sound.

2. How Does The Formula Work?

The calculator uses the perfect elastic collision formula:

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

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: This formula calculates the final velocity of the first object after a perfectly 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 for analyzing particle interactions, billiard ball collisions, gas molecule behavior, and various engineering applications where energy conservation is important.

4. Using The Calculator

Tips: Enter all masses in kilograms and velocities in meters per second. Masses must be positive values greater than zero for accurate calculations.

5. Frequently Asked Questions (FAQ)

Q1: What makes a collision perfectly elastic?
A: A collision is perfectly elastic when both momentum and kinetic energy are conserved throughout the collision process.

Q2: What is the formula for the second object's final velocity?
A: The formula for the second object is: \( v_{2f} = \frac{(m_2 - m_1) v_{2i}}{(m_1 + m_2)} + \frac{2 m_1 v_{1i}}{(m_1 + m_2)} \)

Q3: Are perfect elastic collisions common in real life?
A: Perfectly elastic collisions are idealized situations. Most real collisions are somewhat inelastic, but some like collisions between gas molecules or billiard balls are very close to elastic.

Q4: What happens when masses are equal?
A: When masses are equal (\( m_1 = m_2 \)), the objects simply exchange velocities in a head-on collision.

Q5: Can this formula be used for 2D collisions?
A: No, this formula is for one-dimensional collisions. For 2D collisions, vector components and conservation laws must be applied separately in each direction.