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Related Concept Videos

Elastic Collisions: Case Study01:15

Elastic Collisions: Case Study

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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...
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Collisions in Multiple Dimensions: Problem Solving01:06

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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...
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Elastic Collisions: Introduction01:00

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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...
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Types of Collisions - II01:19

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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...
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Collisions in Multiple Dimensions: Introduction01:05

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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...
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Types Of Collisions - I01:04

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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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Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
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Hybrid Long-Range Collision Avoidance for Crowd Simulation.

Abhinav Golas, Rahul Narain, Sean Curtis

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    This study introduces new crowd simulation algorithms for smoother, faster agent trajectories. The hybrid approach accurately models crowds at any density, improving realism and efficiency.

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    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Computational Physics

    Background:

    • Existing local collision avoidance algorithms in crowd simulation have limitations.
    • Ignoring distant agents leads to abrupt trajectory changes.
    • Discrete and continuum methods have different applicability ranges.

    Purpose of the Study:

    • To develop novel algorithms for crowd simulation.
    • To improve trajectory smoothness and simulation speed.
    • To create a hybrid approach for simulating crowds at any density.

    Main Methods:

    • Proposed an approximate, long-range collision avoidance algorithm.
    • Developed a hybrid technique blending continuum and discrete methods.
    • Algorithm performance evaluated against real-world crowd data.

    Main Results:

    • Simulated crowds exhibit smoother trajectories and faster computation rates.
    • The hybrid approach accurately and efficiently simulates crowds across all densities.
    • Improved speed sensitivity to density, mimicking human crowd behavior.

    Conclusions:

    • The novel algorithms enhance crowd simulation realism and efficiency.
    • The hybrid method provides a robust solution for diverse crowd scenarios.
    • Interactive rates achieved for large-scale crowd simulations on portable systems.