Collision Position Calculator

This collision position calculator determines the final positions of two objects after an elastic or inelastic collision. Understanding these calculations helps in physics problems, engineering simulations, and real-world scenarios where momentum conservation is important.

How to Use This Calculator

To calculate the final positions of two objects after a collision:

Enter the mass of the first object in kilograms (kg).
Enter the initial velocity of the first object in meters per second (m/s).
Enter the mass of the second object in kilograms (kg).
Enter the initial velocity of the second object in meters per second (m/s).
Select whether the collision is elastic or inelastic.
Click "Calculate" to see the results.

The calculator will display the final velocities and positions of both objects after the collision.

Formula Explained

For elastic collisions, momentum is conserved, and kinetic energy is also conserved. The final velocities are calculated using the following formulas:

Final velocity of object 1 (v₁'):

v₁' = [(m₁ - m₂)v₁ + 2m₂v₂] / (m₁ + m₂)

Final velocity of object 2 (v₂'):

v₂' = [2m₁v₁ + (m₂ - m₁)v₂] / (m₁ + m₂)

For inelastic collisions, momentum is conserved, but kinetic energy is not. The final velocity is calculated using:

Final velocity (v'):

v' = (m₁v₁ + m₂v₂) / (m₁ + m₂)

Where:

m₁ = mass of object 1
m₂ = mass of object 2
v₁ = initial velocity of object 1
v₂ = initial velocity of object 2

Worked Example

Let's calculate the final positions of two objects after an elastic collision:

Object 1: mass = 2 kg, initial velocity = 4 m/s
Object 2: mass = 3 kg, initial velocity = -2 m/s

Using the elastic collision formulas:

v₁' = [(2 - 3)(4) + 2(3)(-2)] / (2 + 3) = [(-2)(4) + (-12)] / 5 = (-8 - 12) / 5 = -20/5 = -4 m/s

v₂' = [2(2)(4) + (3 - 2)(-2)] / (2 + 3) = [16 + (1)(-2)] / 5 = (16 - 2) / 5 = 14/5 = 2.8 m/s

The final velocities are -4 m/s for object 1 and 2.8 m/s for object 2.

Interpreting Results

The results show the final velocities of both objects after the collision. A negative velocity indicates the object is moving in the opposite direction of its initial motion.

For inelastic collisions, both objects will have the same final velocity since they stick together. The calculator will show this unified velocity.

Note: This calculator assumes ideal conditions with no external forces acting on the objects during the collision.

FAQ

What is the difference between elastic and inelastic collisions?

An elastic collision preserves both momentum and kinetic energy, while an inelastic collision preserves only momentum. Inelastic collisions often result in the objects sticking together.

Can this calculator handle three-dimensional collisions?

No, this calculator is designed for one-dimensional collisions. For multi-dimensional collisions, you would need to consider each axis separately.

What units should I use for mass and velocity?

Use kilograms (kg) for mass and meters per second (m/s) for velocity. The calculator will handle the conversion internally.

Is there a limit to the numbers I can enter?

The calculator can handle a wide range of values, but extremely large numbers may affect precision. Keep values within reasonable physical limits.