Partially Elastic Collision Formula

Partially Elastic Collision Formula:

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

Mass 1 (m₁):

Mass 2 (m₂):

Initial Velocity 1 (v₁ᵢ):

m/s

Initial Velocity 2 (v₂ᵢ):

m/s

Restitution Coefficient (e):

(0-1)

Final Velocity 1 (v₁f):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is Partially Elastic Collision?

A partially elastic collision is one where kinetic energy is not fully conserved, but momentum is conserved. The degree of elasticity is determined by the coefficient of restitution (e), which ranges from 0 (perfectly inelastic) to 1 (perfectly elastic).

2. How Does The Formula Work?

The formula for final velocity in partially elastic collision:

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

Where:

\( v_{1f} \) — Final velocity of object 1 (m/s)
\( m_1, m_2 \) — Masses of objects 1 and 2 (kg)
\( e \) — Coefficient of restitution (0-1)
\( v_{1i}, v_{2i} \) — Initial velocities of objects 1 and 2 (m/s)

Explanation: This formula calculates the final velocity of object 1 after a partially elastic collision, accounting for both conservation of momentum and the energy loss through the restitution coefficient.

3. Understanding Restitution Coefficient

Details: The coefficient of restitution (e) represents the ratio of relative velocity after collision to relative velocity before collision. e=1 means perfectly elastic (no energy loss), e=0 means perfectly inelastic (maximum energy loss, objects stick together).

4. Using The Calculator

Tips: Enter masses in kilograms, velocities in m/s, and restitution coefficient between 0 and 1. All mass values must be positive, and restitution coefficient must be between 0 and 1 inclusive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between elastic and partially elastic collision?
A: In perfectly elastic collisions, kinetic energy is conserved (e=1). In partially elastic collisions, some kinetic energy is lost as heat, sound, or deformation (0<e<1).

Q2: How is restitution coefficient determined?
A: The coefficient of restitution is experimentally determined and depends on the materials involved. It can be calculated as e = (v₂f - v₁f) / (v₁i - v₂i).

Q3: What are typical e values for common materials?
A: Glass balls: ~0.95, Steel balls: ~0.8-0.9, Wood: ~0.5, Clay: ~0.1-0.3. These values vary with impact velocity and conditions.

Q4: Can this formula be used for 2D collisions?
A: No, this formula is for 1D collisions along a straight line. For 2D collisions, vector components must be considered separately.

Q5: What happens when e=0?
A: When e=0, the collision is perfectly inelastic and the formula simplifies to the common velocity case where both objects move together after collision.