Partially Elastic Collision Calculator

Partially Elastic Collision Equation:

\[ v_{1f} - v_{2f} = -e (u_1 - u_2) \]

Initial Velocity of Object 1 (u₁):

m/s

Initial Velocity of Object 2 (u₂):

m/s

Coefficient of Restitution (e):

unitless

Mass of Object 1 (m₁):

Mass of Object 2 (m₂):

Final Velocity of Object 1 (v₁f):

Final Velocity of Object 2 (v₂f):

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1. What is Partially Elastic Collision?

A partially elastic collision is a type of collision where kinetic energy is not fully conserved, but the objects do not stick together. The coefficient of restitution (e) determines how much kinetic energy is lost during the collision, where e = 1 represents a perfectly elastic collision and e = 0 represents a perfectly inelastic collision.

2. How Does the Calculator Work?

The calculator uses the following equations:

\[ v_{1f} - v_{2f} = -e (u_1 - u_2) \] \[ m_1u_1 + m_2u_2 = m_1v_1f + m_2v_2f \]

Where:

\( u_1, u_2 \) — Initial velocities (m/s)
\( v_1f, v_2f \) — Final velocities (m/s)
\( m_1, m_2 \) — Masses of objects (kg)
\( e \) — Coefficient of restitution (0 ≤ e ≤ 1)

Explanation: The first equation defines the relationship between relative velocities before and after collision, while the second equation ensures conservation of momentum.

3. Importance of Coefficient of Restitution

Details: The coefficient of restitution is crucial in understanding energy loss during collisions. It's used in various fields including physics, engineering, sports science, and automotive safety to analyze impact behavior and design protective systems.

4. Using the Calculator

Tips: Enter all initial velocities in m/s, masses in kg, and coefficient of restitution between 0 and 1. Ensure all values are physically meaningful (masses > 0, e between 0-1).

5. Frequently Asked Questions (FAQ)

Q1: What does e = 0.5 mean?
A: A coefficient of restitution of 0.5 means that the relative velocity after collision is half the relative velocity before collision, but in the opposite direction.

Q2: Can e be greater than 1?
A: No, e > 1 would violate energy conservation principles as it would imply kinetic energy increases during collision.

Q3: How is e measured experimentally?
A: e is measured by dropping an object from height h₁ and measuring rebound height h₂, where e = √(h₂/h₁).

Q4: What factors affect the coefficient of restitution?
A: Material properties, temperature, impact velocity, and object geometry all influence the coefficient of restitution.

Q5: Are there real-world perfectly elastic collisions?
A: While no macroscopic collision is perfectly elastic, collisions between gas molecules and some atomic collisions approach perfect elasticity (e ≈ 1).