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Mechanical principles of dynamic engineering systems
Published in Alan Darbyshire, Charles Gibson, Mechanical Engineering, 2023
Alan Darbyshire, Charles Gibson
Wherever acceleration occurs, there must be a force present. For a body travelling in a circular path, this is the centripetal force pulling or pushing it towards the centre of the path. If the body shown in Figure 2.25 were attached to the centre of its path by a cord, this would all the time be pulling it inwards and the tension in the cord would be the centripetal force. For a body of mass m kg, the centripetal force is obtained using expression (2.51) or (2.52) and applying the formula F = ma: F=mω2rorF=mv2r
Dialectics of Nature: Inspiration for Computing
Published in Nazmul Siddique, Hojjat Adeli, Nature-Inspired Computing, 2017
Isaac Newton (1643–1727) published his three laws of motion in his book Mathematical Principles of Natural Philosophy in 1687 (see Newton, 1999). The three physical laws laid the foundation of classical mechanics, which describe the relationship between a body and the forces acting upon it, and its motion in response to said forces. The laws cover the law of inertia, the law of force, and the law of action and reaction. The first law of inertia states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving at constant speed in the same direction. The second law of force states that the acceleration a (also defined as the rate of change of velocity) is directly proportional to applied force F and inversely proportional to mass m of the body. The third law also referred to as the law of action and reaction states that every action has an equal and opposite reaction.
Introduction to Dynamics: Implications on the Design of Precision Machines
Published in Richard Leach, Stuart T. Smith, Basics of Precision Engineering, 2017
Patrick Baird, Stuart T. Smith
Newton’s first law of motion, sometimes called the law of inertia because it refers to inertial or nonaccelerating frames of reference, sets the background. Newton’s first law of motion states that all objects stay at rest or continue in motion with constant velocity (a constant speed in a straight line) unless acted on by an external force. In this case, inertia can be described as the property of mass to resist a change in motion, but the term must be used more carefully, or avoided, in the context of moments. This nonaccelerating frame of reference is a starting point for the application of the other laws of motion: for an object not under the influence of forces, a reference frame can be specified in which the object has no acceleration. Newton’s first law can be restated including the requirement of an inertial reference frame for the observer also, to avoid confusion from any apparent acceleration of an object as seen by an observer moving in a non-inertial or accelerating frame.
Investigation of iron ore particle size and shape on green pellet quality
Published in Canadian Metallurgical Quarterly, 2020
Armin Abazarpoor, Mohammad Halali, Rasool Hejazi, Majid Saghaeian, Vahid Sheikh Zadeh
Different modes of breakage are illustrated in Figure 6. Pellet failure occurs when an applied external force (resultant of Fx and Fy) exceeds any of FSS, FS, FL, or FSL forces. If FSL is weaker than other forces, failure type (b) occurs and crack propagates from the solid–liquid interface. In the case of low cohesion force in the liquid, failure type (c) occurs. For failure type (d), low solid bond energy is necessary. It is not likely to happen in this system. Considering the nature of the mentioned forces, type (b) or (c) is more probable to occur.
An improved gravitational search algorithm to the hybrid flowshop with unrelated parallel machines scheduling problem
Published in International Journal of Production Research, 2021
Cuiwen Cao, Yao Zhang, Xingsheng Gu, Dan Li, Jie Li
By Newton’s second law, the acceleration of the object is proportional to the force it receives, and is inversely proportional to its mass. Hence, the acceleration of the job i in individual ia is defined as Equation (15). Finally, the velocity and position of the individual iais updated as Equations (16) and (17).
Optimum economic operation of coordinated power system based on turbulent water flow optimization
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2022
V.P. Sakthivel, K. Thirumal, P.D. Sathya, S. Seenivasan, R. Shivakumar
In whirlpool, the water begins to rotate around its center and a funnel-like structure with a small cavity is formed. The surrounding objects are then spined and confined to the centre of whirlpool. Centripetal force is perpendicular to the velocity of the object. Centrifugal force acts in the opposite direction of centripetal force while maintaining a constant magnitude.