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Related Concept Videos

Types of Collisions - II01:19

Types of Collisions - II

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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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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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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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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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Impact01:30

Impact

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Impact occurs when two bodies collide, leading to the application of impulsive forces between them. Analyzing impact mechanics involves considering two colliding particles moving along a line known as the line of impact, which passes through their centers and is perpendicular to the contact plane.
When particles with different initial velocities collide, they induce deformation by applying equal and opposite impulses. At the point of maximum deformation, the particles move together with...
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Elastic Collisions: Case Study01:15

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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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Related Experiment Video

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Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System
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Collisions, rebounds and skimming.

Kevin Liu1, Frank T Smith2

  • 1Department of Mathematics, UCL, Gower Street, London WC1E 6BT, UK f.smith@ucl.ac.uk.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 18, 2014
PubMed
Summary
This summary is machine-generated.

Mathematical modeling reveals that the speed of impacts and rebounds significantly influences shallow water dynamics. This study focuses on repeated oblique impacts of solid bodies on water surfaces.

Keywords:
bodybouncesfluidmathematical modellingskimming

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Area of Science:

  • Fluid dynamics
  • Solid mechanics
  • Applied mathematics

Background:

  • Understanding the complex interactions between solid bodies and fluids is crucial in various scientific and engineering fields.
  • Previous models often simplify the dynamics of repeated impacts, limiting predictive accuracy.

Purpose of the Study:

  • To develop a novel mathematical model for analyzing repeated oblique impacts and rebounds of solid bodies on shallow water.
  • To enhance the prediction of fluid-body interactions during skimming events.

Main Methods:

  • Mathematical modeling of oblique impacts and rebounds.
  • Nonlinear analysis and computation for thin body shapes and small inclinations.
  • Investigation of fluid-body dynamics over short time-scales.

Main Results:

  • A new formulation for predicting impacts and rebounds on shallow water is presented.
  • The study highlights the significance of impact velocity (fast vs. slow) on the interaction dynamics.
  • Analysis reveals that small inclinations are relevant as skimming evolves.

Conclusions:

  • The developed mathematical model provides improved predictions for solid body impacts on shallow water.
  • The speed of collisions and rebounds is a critical factor influencing the overall phenomenon.
  • Further research can explore more complex body shapes and impact scenarios.