Collision in 1D with momentum and energy conservations

Collision in One Dimension Experiment – For Schools, Teachers, and Students

Definition

A collision in one dimension (1D) occurs when two objects move along the same straight line before and after the collision. This type of collision is analyzed using the law of conservation of momentum and, in certain cases, conservation of kinetic energy.

This concept is demonstrated in Dencity – Online Science Lab and Simulations to enhance interactive learning.

Theory

In 1D collisions, the law of conservation of linear momentum states:

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

where:

• m₁, m₂ = Masses of the two objects
• u₁, u₂ = Initial velocities of the objects
• v₁, v₂ = Final velocities of the objects

Types of 1D Collisions

1. Elastic Collisions:
   • Both momentum and kinetic energy are conserved.
   • The equation for kinetic energy conservation is:
     (1/2) m₁ u₁² + (1/2) m₂ u₂² = (1/2) m₁ v₁² + (1/2) m₂ v₂²
   • The final velocities are given by:
     v₁ = ((m₁ – m₂) u₁ + 2 m₂ u₂) / (m₁ + m₂)
     v₂ = ((m₂ – m₁) u₂ + 2 m₁ u₁) / (m₁ + m₂)
2. Inelastic Collisions:
   • Momentum is conserved, but kinetic energy is not.
   • Some kinetic energy is converted into heat, sound, or deformation.
   • Completely Inelastic Collision: The two objects stick together after the collision, and their final velocity (v) is:
     v = (m₁ u₁ + m₂ u₂) / (m₁ + m₂)

Examples of 1D Collisions

1. Elastic Collision:
   • Two billiard balls collide on a pool table. Both momentum and kinetic energy are conserved.
2. Inelastic Collision:
   • A car crash where two vehicles collide and deform. Momentum is conserved, but some kinetic energy is lost.
3. Completely Inelastic Collision:
   • A lump of clay sticks to another after collision, moving together as one mass.

Real-World Applications

The principles of 1D collisions are used in:

• Traffic Accident Analysis: Predicting collision outcomes in vehicle crashes.
• Particle Physics: Studying interactions in atomic and nuclear collisions.
• Conservation Law Studies: Demonstrating fundamental physics principles in labs.
• Car Safety Design: Engineering crumple zones to minimize damage in collisions.
• Online Science Lab: Allows students to simulate 1D collisions interactively.

Observations and Key Learnings

• In elastic collisions, the relative speed of separation equals the relative speed of approach:
  |u₁ – u₂| = |v₂ – v₁|
• In inelastic collisions, kinetic energy after the collision is lower than before.
• In completely inelastic collisions, the two objects move together with the same final velocity.
• The amount of energy lost depends on the type of collision (elastic, inelastic, or completely inelastic).

This collision in one dimension experiment helps students understand how momentum is conserved in elastic, inelastic, and completely inelastic collisions. While elastic collisions conserve both momentum and kinetic energy, inelastic collisions result in energy loss as heat, sound, or deformation.

Using our app for science students, learners can explore real-world applications like traffic accident analysis, particle physics, and car safety design. The science experiments lab and physics practical simulations provide interactive online science experiments, making it easier to visualize and analyze different types of 1D collisions dynamically.