Elastic Collision Calculator

In an elastic collision, use the masses and initial velocities of two objects to determine their final velocities.

The Elastic Collision Calculator calculates the final velocities of two objects after a collision, assuming no kinetic energy is lost. Elastic collisions are commonly analyzed in physics to study momentum and energy conservation.

Formula

For two objects with masses $m_1$ and $m_2$ and initial velocities $v_{i1}$ and $v_{i2}$ :

Momentum Conservation:
$m_1 \cdot v_{i1} + m_2 \cdot v_{i2} = m_1 \cdot v_{f1} + m_2 \cdot v_{f2}$
Final Velocities:
- $v_{f1} = \frac{(m_1 – m_2) \cdot v_{i1} + 2 \cdot m_2 \cdot v_{i2}}{m_1 + m_2}$
- $v_{f2} = \frac{2 \cdot m_1 \cdot v_{i1} – (m_1 – m_2) \cdot v_{i2}}{m_1 + m_2}$

Variable	Description
$m_1$	Mass of object 1
$m_2$	Mass of object 2
$v_{i1}$	Initial velocity of object 1
$v_{i2}$	Initial velocity of object 2
$v_{f1}$	Final velocity of object 1
$v_{f2}$	Final velocity of object 2

Solved Calculations

Example 1:

Step	Calculation
Mass of Object 1 ( $m_1$ )	2 kg
Mass of Object 2 ( $m_2$ )	3 kg
Initial Velocity of Object 1	5 m/s
Initial Velocity of Object 2	-2 m/s
Final Velocity ( $v_{f1}$ )	$\frac{(2 – 3) \cdot 5 + 2 \cdot 3 \cdot (-2)}{2 + 3}$
Result	-0.2 m/s
Final Velocity ( $v_{f2}$ )	$\frac{2 \cdot 2 \cdot 5 – (2 – 3) \cdot (-2)}{2 + 3}$
Result	4.8 m/s

Answer: After the collision, object 1 has a final velocity of -0.2 m/s and object 2 has a final velocity of 4.8 m/s.

Example 2:

Step	Calculation
Mass of Object 1 ( $m_1$ )	7 kg
Mass of Object 2 ( $m_2$ )	2 kg
Initial Velocity of Object 1 ( $vi_1$ )	12 m/s
Initial Velocity of Object 2 ( $vi_2$ )	0 m/s
Final Velocity of Object 2 ( $vf_2$ )	$\frac{2 \cdot 7 \cdot 12 – (7 – 2) \cdot 0}{7 + 2}$
Result	18.67 m/s

Answer: After the collision, the final velocity of Object 2 is 18.67 m/s.

What is an Elastic Collision Calculator?

The Elastic Collision Calculator is a perfectly handy tool. You can go for it if you need to calculate the outcome of collisions where no energy is lost, ensuring both momentum and kinetic energy remain constant.

Broadly speaking, this calculator is extensively used in physics and engineering. In these fields, this tool favors in predicting post-collision velocities for two objects after they interact, as seen in ideal gas molecules or other theoretical scenarios.

Final Words:

For the last part, the Elastic Collision Calculator offers a straightforward solution for analyzing collision outcomes, helping users understand and predict results in scenarios where energy conservation is crucial.

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1 Elastic Collision Calculator