Elastic And Inelastic Collision Formula

Collision Equations:

\[ v_f = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \quad \text{(inelastic)} \] \[ v_{1f} = \frac{m_1 - m_2}{m_1 + m_2} v_1 \quad \text{(elastic, m2 at rest)} \]

Collision Type:

Mass 1 (m1):

Velocity 1 (v1):

m/s

Mass 2 (m2):

Velocity 2 (v2):

m/s

Final Velocity:

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1. What Are Elastic And Inelastic Collisions?

Elastic collisions are those where both momentum and kinetic energy are conserved, while inelastic collisions conserve momentum but not kinetic energy (some energy is converted to other forms like heat or sound).

2. How Does The Calculator Work?

The calculator uses the following equations:

\[ v_f = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \quad \text{(inelastic collision)} \] \[ v_{1f} = \frac{m_1 - m_2}{m_1 + m_2} v_1 \quad \text{(elastic collision, m2 at rest)} \]

Where:

\( m_1 \) — Mass of first object (kg)
\( v_1 \) — Initial velocity of first object (m/s)
\( m_2 \) — Mass of second object (kg)
\( v_2 \) — Initial velocity of second object (m/s)
\( v_f \) — Final velocity after inelastic collision (m/s)
\( v_{1f} \) — Final velocity of first object after elastic collision (m/s)

Explanation: The equations represent conservation of momentum for different collision types, with elastic collisions assuming perfect energy conservation.

3. Conservation Laws In Collisions

Details: All collisions conserve momentum. Elastic collisions additionally conserve kinetic energy, while inelastic collisions convert some kinetic energy to other forms.

4. Using The Calculator

Tips: Select collision type, enter masses in kg and velocities in m/s. For elastic collisions, the second object is assumed to be initially at rest (v2 = 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between elastic and inelastic collisions?
A: Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum.

Q2: Are perfectly elastic collisions possible in reality?
A: No real collisions are perfectly elastic, but some (like billiard ball collisions) are very close to elastic.

Q3: What happens to the "lost" energy in inelastic collisions?
A: It's converted to other forms like heat, sound, or deformation energy.

Q4: Why is v2 set to zero for elastic collisions in this calculator?
A: This simplifies the common case where one object is initially stationary, making the calculation more straightforward.

Q5: Can I use this for collisions in two dimensions?
A: No, these equations are for one-dimensional collisions only. Two-dimensional collisions require vector analysis.