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Related Concept Videos

Newton's First Law: Introduction01:17

Newton's First Law: Introduction

Motion draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to create spectacular sights, such as that of a dolphin jumping out of the water, the flight of a bird, or the orbit of a satellite. The study of motion is kinematics, but kinematics only describes the way objects move—their velocity and acceleration. Dynamics considers the forces that affect the motion of moving objects and systems. Newton's laws of motion are the foundation of dynamics. These...
Newton's Second Law00:55

Newton's Second Law

Newton's second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes in motion. Newton's second law is quantitative and is used extensively to calculate what happens in situations involving a force. All external forces acting on a system add together to produce a net force Fnet. A larger net external force produces a larger acceleration. This acceleration is directly proportional to, and in the same direction as,...
Newton's Third Law: Examples01:08

Newton's Third Law: Examples

Newton's third law states that every action has an equal and opposite reaction. Consider a swimmer pushing off the side of a pool. They push against the wall of the pool with their feet and accelerate in the direction opposite to that of their push. This occurs because the wall exerts an equal and opposite force on the swimmer. Here, the forces do not cancel out each other as they are acting on different systems. In this case, there are two systems: the swimmer and the wall. If we select the...
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Newton's Law of Motion01:20

Newton's Law of Motion

When we observe objects around us, one question that comes to mind is why they move or stay still. The answer to this question can be explained using Newton's laws of motion. These laws describe the fundamental principles of motion and the effects of forces on objects.
The first law of motion, also known as the law of inertia, states that an object at rest will stay at rest, and an object in motion will continue to move at a constant speed and direction unless acted upon by an external force.
Newton's First Law: Application01:12

Newton's First Law: Application

Experience suggests that an object at rest remains at rest if left alone, and that an object in motion tends to slow down and stop unless some effort is made to keep it moving. However, Newton's first law gives a deeper explanation of this observation. The study of Newton's laws is like recognizing patterns in nature from which further patterns can be discovered. The genius of Galileo, who first developed the idea for the first law of motion, and Newton, who clarified it, was to ask the...

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Assessment and Evaluation of the High Risk Neonate: The NICU Network Neurobehavioral Scale
19:15

Assessment and Evaluation of the High Risk Neonate: The NICU Network Neurobehavioral Scale

Published on: August 25, 2014

Two-ball Newton's cradle.

Paul Glendinning1

  • 1School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis, University of Manchester, Manchester M13 9PL, UK. p.a.glendinning@manchester.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
PubMed
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Newton

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Area of Science:

  • Physics
  • Applied Mathematics
  • Mechanical Engineering

Background:

  • Newton's cradle is a classic demonstration of the conservation of momentum and energy.
  • The Hertzian contact model describes the elastic deformation of contacting bodies.
  • Hybrid systems combine different physical phenomena, leading to complex dynamics.

Purpose of the Study:

  • To analyze the dynamics of a two-ball Newton's cradle with Hertzian interactions.
  • To derive exact return maps for the motion between collisions.
  • To investigate the independence of results from the specific interaction potential details.

Main Methods:

  • Modeling the Newton's cradle as a hybrid system.
  • Deriving exact return maps for inter-collision motion.
  • Numerical determination of a key constant for explicit solutions.
  • Comparison of analytical solutions with simulation results.

Main Results:

  • Exact return maps were derived for the two-ball Newton's cradle with Hertzian interactions.
  • Solutions are explicitly written in terms of a numerically determined constant.
  • The study found that the results are independent of the specific interaction potential details.

Conclusions:

  • The hybrid system approach allows for exact derivation of return maps.
  • Explicit solutions can be obtained despite the complexity of the three-halves interaction law.
  • The findings highlight the robustness of the derived solutions concerning interaction potentials.