Elastic Collision Calculator

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 Elastic Collision?

An elastic collision is a collision where both momentum and kinetic energy are conserved. In such collisions, the total kinetic energy before and after the collision remains the same, making them ideal for studying conservation laws in physics.

2. How Does the Calculator Work?

The calculator uses the 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 masses and initial velocities of both objects.

3. Importance of Elastic Collision Calculation

Details: Understanding elastic collisions is fundamental in physics, particularly in mechanics and particle physics. It helps in analyzing interactions where energy conservation is crucial, such as in atomic and subatomic particle collisions.

4. Using the Calculator

Tips: Enter the masses of both objects in kilograms and their initial velocities in meters per second. All mass values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What distinguishes elastic from inelastic collisions?
A: In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, only momentum is conserved, while kinetic energy is not.

Q2: Are perfectly elastic collisions common in real life?
A: Perfectly elastic collisions are ideal and rare in everyday life but are good approximations for collisions between atoms, molecules, or billiard balls.

Q3: Can this formula be used for objects of any mass?
A: Yes, the formula applies to any two masses, but it assumes a one-dimensional collision without external forces.

Q4: How is the final velocity of the second object calculated?
A: The final velocity of object 2 can be found using a similar formula: \( v_{2f} = \frac{(m_2 - m_1) v_{2i}}{(m_1 + m_2)} + \frac{2 m_1 v_{1i}}{(m_1 + m_2)} \).

Q5: What if one object is initially at rest?
A: If object 2 is at rest (\( v_{2i} = 0 \)), the formula simplifies to \( v_{1f} = \frac{(m_1 - m_2) v_{1i}}{(m_1 + m_2)} \).