Elastic Collision Physics Calculator

Elastic Collision 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):

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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 principles in physics.

2. How Does the Calculator Work?

The calculator uses the elastic collision 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: This equation calculates the final velocity of the first object after a perfectly elastic collision, considering both masses and their initial velocities.

3. Importance of Elastic Collision Calculation

Details: Understanding elastic collisions is fundamental in physics for analyzing particle interactions, studying conservation laws, and solving problems in mechanics and engineering applications.

4. Using the Calculator

Tips: Enter all masses in kilograms and velocities in meters per second. Mass values must be positive and non-zero for accurate calculations.

5. Frequently Asked Questions (FAQ)

Q1: What makes a collision perfectly elastic?
A: A perfectly elastic collision conserves both momentum and kinetic energy, with no energy lost to deformation, heat, or sound.

Q2: How does mass ratio affect the final velocity?
A: When m1 >> m2, v1f ≈ v1i; when m1 << m2, v1f ≈ -v1i + 2v2i; when m1 = m2, the objects exchange velocities.

Q3: Are real-world collisions perfectly elastic?
A: Most real collisions are not perfectly elastic, but some approximations like billiard ball collisions or atomic collisions are very close.

Q4: What about the final velocity of the second object?
A: The equation for v2f is: \( v_{2f} = \frac{2 m_1 v_{1i}}{m_1 + m_2} + \frac{(m_2 - m_1) v_{2i}}{m_1 + m_2} \)

Q5: Can this be used for 2D or 3D collisions?
A: This equation is for 1D collisions. For 2D/3D, vector components and conservation laws must be applied separately in each dimension.