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Elastic Collisions: Case Study

Elastic Collisions: Case Study

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...

Types of Collisions - II

Types of Collisions - II

When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...

Elastic Collisions: Introduction

Elastic Collisions: Introduction

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...

Collisions in Multiple Dimensions: Problem Solving

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...

Collisions in Multiple Dimensions: Introduction

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...

Types Of Collisions - I

Types Of Collisions - I

When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...

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Related Experiment Video

Updated: Apr 18, 2026

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

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Published on: February 1, 2020

New algorithms for computing the time-to-collision in freeway traffic simulation models.

Jia Hou¹, George F List², Xiucheng Guo¹

¹School of Transportation, Southeast University, No. 2 Sipailou, Nanjing 210096, China.

Computational Intelligence and Neuroscience

|January 29, 2015

Summary

This summary is machine-generated.

New algorithms estimate time-to-collision in traffic simulations by analyzing vehicle trajectories. These computational methods offer efficient conflict assessment for improved traffic safety analysis.

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Area of Science:

Traffic simulation and computational geometry
Vehicle dynamics and collision avoidance

Background:

Traditional traffic models rely on lane-based vehicle positions.
Accurate time-to-collision estimation is crucial for traffic safety.

Purpose of the Study:

To explore novel algorithms for estimating time-to-collision.
To evaluate computational procedures for trajectory conflict assessment in traffic simulations.

Main Methods:

Utilizing a two-dimensional coordinate system to track vehicle trajectories.
Employing vector-based kinematic variables for calculations.
Analyzing algorithms based on geometric shapes (boxes, circles, ellipses).

Main Results:

Developed fast and efficient algorithms for time-to-collision estimation.
Evaluated algorithm performance based on computational complexity and solution time.
A combined computational approach demonstrated high effectiveness.

Conclusions:

The examined algorithms show promise for effective and efficient trajectory conflict analysis.
Advanced computational methods can enhance the accuracy and speed of traffic safety assessments.
Further research into combined computational processes is warranted for practical applications.