Elastic Collision Calculator 1d And 2d

Elastic Collision Formula (1D):

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

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 one-dimensional elastic collisions, objects bounce off each other without any loss of kinetic energy.

2. How Does the Calculator Work?

The calculator uses the 1D 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 in one dimension, where both momentum and kinetic energy are conserved.

3. Importance of Elastic Collision Calculation

Details: Understanding elastic collisions is crucial in physics, engineering, and various applications including particle physics, vehicle safety design, sports science, and animation/game physics.

4. Using the Calculator

Tips: Enter all mass values in kilograms and velocity values in meters per second. All mass values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between elastic and inelastic collisions?
A: In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not.

Q2: How do I calculate the final velocity of the second object?
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: What if the masses are equal?
A: If m1 = m2, the objects simply exchange velocities: v1f = v2i and v2f = v1i.

Q4: Does this work for 2D collisions?
A: No, this formula is for 1D collisions only. 2D collisions require vector decomposition and conservation of momentum in both x and y directions.

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