Final Velocity After Collision Formula

Final Velocity After Inelastic Collision:

\[ v_f = \frac{m_1 \times v_1 + m_2 \times v_2}{m_1 + m_2} \]

Mass 1 (m1):

Initial Velocity 1 (v1):

m/s

Mass 2 (m2):

Initial Velocity 2 (v2):

m/s

Final Velocity (v_f):

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1. What is the Final Velocity After Collision Formula?

The Final Velocity After Collision Formula calculates the resulting velocity when two objects collide and stick together in a perfectly inelastic collision. This formula is derived from the principle of conservation of momentum.

2. How Does the Calculator Work?

The calculator uses the conservation of momentum formula:

\[ v_f = \frac{m_1 \times v_1 + m_2 \times v_2}{m_1 + m_2} \]

Where:

\( v_f \) — Final velocity after collision (m/s)
\( m_1 \) — Mass of object 1 (kg)
\( v_1 \) — Initial velocity of object 1 (m/s)
\( m_2 \) — Mass of object 2 (kg)
\( v_2 \) — Initial velocity of object 2 (m/s)

Explanation: In a perfectly inelastic collision, the two objects stick together after impact, and momentum is conserved while kinetic energy is not conserved.

3. Importance of Final Velocity Calculation

Details: Calculating final velocity after collision is crucial in physics, engineering, accident reconstruction, and sports science to understand the outcome of impacts and collisions.

4. Using the Calculator

Tips: Enter masses in kilograms and velocities in meters per second. All mass values must be positive. Velocities can be positive or negative depending on 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 after impact and move with a common final velocity.

Q2: Does this formula work for elastic collisions?
A: No, this formula is specifically for perfectly inelastic collisions where objects stick together. Elastic collisions require different calculations.

Q3: What if the objects are moving in opposite directions?
A: Use negative values for velocities in the opposite direction. The calculator will properly account for direction in the calculation.

Q4: Is momentum conserved in this type of collision?
A: Yes, momentum is always conserved in collisions. However, kinetic energy is not conserved in inelastic collisions.

Q5: What are real-world examples of inelastic collisions?
A: Car accidents where vehicles lock together, a bullet embedding in a target, or two pieces of clay sticking together after collision.