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2053Lecture5

# 2053Lecture5 - Newton's Law of Motion Topics of Discussion...

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Unformatted text preview: Newton's Law of Motion Topics of Discussion Newton's Laws of Motion Inertial Reference Frames Types of Forces Superposition Isaac Netwon Sir Isaac Newton, (16431727) was an English physicist, mathematician, astronomer, alchemist and natural philosopher, regarded by many as the greatest figure in the history of science. His treatise Philosophiae Naturalis Principia Mathematica, published in 1687, described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics. The unifying and predictive power of his laws was integral to the scientific revolution, and the broader acceptance of the notion that rational investigation can reveal the inner workings of nature. Newton's First Law Law of Inertia Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. Law 1: An object at rest will remain at rest unless acted upon by an external and unbalanced force. An object in motion will remain in motion unless acted upon by an external and unbalanced force. Remarks on the Law of Inertia An object that is not moving will not move until a net force acts upon it. An object that is in motion will not change velocity (accelerate) until a net force acts upon it. Newton's Second Law Law of Acceleration Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur. Law 2: The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction Reformulation of Newton's Second Laws The acceleration of a body is proportional to the resultant force acting on the body and is in the same direction, that is F a or equivalently F = ma, where m is a "physical" constant of proportionality called the mass. Newton's Third Law Law of Reciprocal Action Lex III: Actioni contrariam semper et qualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse quales et in partes contrarias dirigi. Law 3: All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction. Remarks on the Law of Reciprocal Action The law of reciprocal action is sometimes said to be a mathematical version of Murphy's Law, and sometimes it isn't. The phrase "Murphy's law" was coined in 1949 by Edward A Murphy, Jr, an engineer for the US Air Force. At the time he was carrying out a series of tests on human resistance to high accelerations. In one of the tests, the subject had to have a sensor mounted on him. This could be done in two ways. Murphy discovered that someone had applied all the sensors to the subject backwards. This led him to state the following law: If there is a wrong way to do something, then someone will do it. Newton's First Law A body at rest remains at rest, and a body in motion continues to move in a straight line with a constant speed unless and until an external unbalanced force acts upon it. body is directly proportional to the force acting on the body. Summary of Newton's Laws of Motion Newton's Second Law The acceleration of a Newton's Third Law To every action (force applied) there is an equal and opposite reaction (equal force in the opposite direction). Mach's Reformulation of Newton's Laws "When two compact objects, called "point masses", act on each other, they accelerate in opposite directions, and the ratio of their accelerations is always the same," that is a1 / a2 = constant. Inertial Reference Frames Inertia is the tendency of an object to remain in it's current state of motion. The quantitative measurement of inertia is called the mass of the body. All measurements conducted by the observer are from the observers perspective, which we call the observer's reference frame. An inertial reference frame is a reference frame in which Newton's First Law holds. A non-inertial reference frame is a frame of reference that is accelerating or rotating. Relative Motion Let the velocity of observer A relative to observer B be denoted as vAB. Let the velocity of observer B relative to observer C be denoted as vBC. Then the velocity of observer A relative to observer C, denoted by vAC is given by v AC = v AB + v BC . Relative Motion & Newton's Laws Let two observers, in reference frames A and B, record the same phenomenon P. So, we must ask the following question: If Newton's Laws are valid in the reference frame of observer A then do they remain valid in the reference frame of observer B? The answer is a resounding "yes" but for speeds much less than the speed of light (3 108m/s). Types of Forces Action at a Distance Forces: Gravity, Electromagnetism and Nuclear. Contact Forces: Tension, Frictional Forces & the Normal Force. The Universal Law of Gravity Every object is attracted to another object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance r between them, and is given by where m1 and m2 are the masses, G is the universal gravitational constant whose value is 6.673 10-11 Nm2/kg2. m1 m2 F= G 2 r Weight & Tension Let us consider a hanging mass m that is attached to a string. The weight W of the mass is a force that acts down. The string holds the mass by producing a counter-force called the tension T, which acts upward. T m W The Normal Force When a body of mass m exerts a force W perpendicular to the surface of another body, the other body produces a counteracting force, called the normal force N. N m W Static Frictional Forces When attempting to move a motionless body of mass m across a table, the applied force F must overcome a static frictional force fs that is produced by the physical contact of two surfaces as described by the coefficient of static F friction s of the table. f m Dynamic Frictional Forces When a body of mass m is in motion across a table, the dynamic frictional force fd is a force which must be overcome by an applied force F so that the body continues in its motion. The physical contact of two surfaces is described by the coefficient of dynamic F friction d of the table. f m Hooke's Law Empirically, the magnitude of the restoring force Fs is directly proportional to the displacement x, that is Fs x. Hooke's Law says that the restoring force always opposes the displacement, and is given by Fs = kx, where x is the displacement of the spring of mass m and k is the spring constant in kg/s2. k m x Principle of Superposition Let n forces { F1, F2, F3, ..., Fi, ..., Fn } act on a body. Then the principle of superposition states that the total force (or resultant) acting on a body is the sum of all the individual forces that act on the body. n i= 1 Fi = F The Total Mechanical Force Let W, T, N, fs , fd and Fs be the weight, tension, normal force, frictional forces and spring force that act on a body. Then the resultant or total mechanical force is the sum of all the individual forces that act on the body. F = W + T + N + f s + f d + Fs ...
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