Common Velocity After Collision Formula

Common Velocity Formula:

\[ v_{common} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \]

Mass 1 (m1):

Velocity 1 (v1):

m/s

Mass 2 (m2):

Velocity 2 (v2):

m/s

Common Velocity (v_common):

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1. What is Common Velocity After Collision?

The common velocity after collision formula calculates the final velocity when two objects stick together after a perfectly inelastic collision. This occurs when kinetic energy is not conserved but momentum is conserved.

2. How Does the Calculator Work?

The calculator uses the common velocity formula:

\[ v_{common} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \]

Where:

\( v_{common} \) — Common velocity after collision (m/s)
\( m_1 \) — Mass of first object (kg)
\( v_1 \) — Velocity of first object before collision (m/s)
\( m_2 \) — Mass of second object (kg)
\( v_2 \) — Velocity of second object before collision (m/s)

Explanation: The formula is derived from the conservation of momentum principle, where the total momentum before collision equals the total momentum after collision in a perfectly inelastic collision.

3. Importance of Common Velocity Calculation

Details: Calculating common velocity is essential in physics for analyzing collisions, understanding energy transfer, and solving problems in mechanics and engineering applications.

4. Using the Calculator

Tips: Enter all masses in kilograms and velocities in meters per second. Masses must be positive values. The calculator handles both positive and negative velocities (indicating direction).

5. Frequently Asked Questions (FAQ)

Q1: What is a perfectly inelastic collision?
A: A perfectly inelastic collision is one where the colliding objects stick together and move with a common velocity after impact, maximizing kinetic energy loss.

Q2: Is kinetic energy conserved in this type of collision?
A: No, kinetic energy is not conserved in perfectly inelastic collisions. Some kinetic energy is converted to other forms like heat, sound, or deformation energy.

Q3: Can this formula be used for elastic collisions?
A: No, this formula is specifically for perfectly inelastic collisions where objects stick together. Elastic collisions require different equations.

Q4: What if the objects are moving in opposite directions?
A: Use negative values for velocity to indicate opposite directions. The calculator will properly account for the vector nature of velocity.

Q5: Are there real-world applications of this formula?
A: Yes, this formula is used in automotive safety (car crashes), ballistics, sports physics, and various engineering applications involving impacts.