Elastic Collision Calculator at 90 Degrees

This elastic collision calculator at 90 degrees helps you determine the final velocities of two objects after they collide perpendicularly. Elastic collisions conserve both momentum and kinetic energy, making them fundamental in physics and engineering applications.

Introduction

An elastic collision at 90 degrees occurs when two objects collide perpendicularly and bounce off without losing kinetic energy. This type of collision is common in physics problems and has practical applications in fields like sports, vehicle safety, and material science.

When two objects collide at 90 degrees, their velocities change according to the conservation of momentum and kinetic energy. The calculator uses these principles to determine the final velocities of the objects after the collision.

Formula

For an elastic collision at 90 degrees, the final velocities (v₁' and v₂') of two objects with masses m₁ and m₂ and initial velocities v₁ and v₂ can be calculated using the following formulas:

Final velocity of object 1: v₁' = (2m₂v₂ + v₁(m₁ - m₂)) / (m₁ + m₂)

Final velocity of object 2: v₂' = (2m₁v₁ + v₂(m₂ - m₁)) / (m₁ + m₂)

These formulas are derived from the conservation of momentum and kinetic energy principles. The calculator applies these formulas to provide accurate results for any given input values.

How to Use the Calculator

Enter the mass of the first object (m₁) in kilograms.
Enter the initial velocity of the first object (v₁) in meters per second.
Enter the mass of the second object (m₂) in kilograms.
Enter the initial velocity of the second object (v₂) in meters per second.
Click the "Calculate" button to compute the final velocities.
Review the results and use the chart to visualize the velocity changes.

The calculator will display the final velocities of both objects after the collision and provide a chart showing the velocity changes.

Example Calculation

Example Scenario

Object 1: Mass = 2 kg, Initial Velocity = 5 m/s

Object 2: Mass = 3 kg, Initial Velocity = 4 m/s

Final Velocity of Object 1: 1.2 m/s

Final Velocity of Object 2: 4.4 m/s

In this example, the calculator determines that after the collision, Object 1 will have a final velocity of 1.2 m/s and Object 2 will have a final velocity of 4.4 m/s. The chart will show how the velocities change during the collision.

Physics of Elastic Collisions

Elastic collisions are characterized by the conservation of both momentum and kinetic energy. For a collision at 90 degrees, the following principles apply:

Conservation of Momentum: The total momentum before the collision equals the total momentum after the collision.
Conservation of Kinetic Energy: The total kinetic energy before the collision equals the total kinetic energy after the collision.
Perpendicular Collision: The collision occurs at a 90-degree angle, simplifying the calculation of final velocities.

Understanding these principles is essential for accurately predicting the outcomes of elastic collisions in various scenarios.

FAQ

What is an elastic collision?

An elastic collision is a type of collision where both momentum and kinetic energy are conserved. The objects involved in the collision do not lose any kinetic energy to heat or deformation.

How do I calculate the final velocities in an elastic collision at 90 degrees?

Use the formulas provided in the "Formula" section of this page. Enter the masses and initial velocities of the two objects, and the calculator will compute the final velocities.

What happens if the masses of the objects are equal?

If the masses are equal, the objects will exchange velocities. The final velocity of each object will be equal to the initial velocity of the other object.

Can this calculator be used for inelastic collisions?

No, this calculator is specifically designed for elastic collisions at 90 degrees. For inelastic collisions, a different set of formulas would be required.