Chapter_13_mod - Chapter13:KineticsofaParticle:...

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1 Chapter 13: Kinetics of a Particle: Force and Acceleration Chapter 13 Objectives To state Newton’s Second Law of Motion and to define mass and weight To analyze the accelerated motion of a particle using the equation of motion with different coordinate systems To investigate central force motion and apply it to problems in space mechanics
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2 13.1: Newton’s Second Law of Motion Kinetics deals with the relationship between the change in motion of a body and the forces that cause this change The foundation of kinetics is with Newton’s Second Law It states that when an unbalanced force acts on a particle, the particle will accelerate in the direction of force. The magnitude of acceleration is proportional to the force. Mathematical form of Newton’s Second Law As stated, there is a constant of proportionality, which relates the unbalanced force and the acceleration of the particle This is the mass of the particle (assuming that the mass does not change with time) ܨ Ԧ ൌ݉ܽ Ԧ ܨ Ԧ ݀ ݀ݐ ݉ݒ Ԧ Einstein found that the equation of motion is limited by the speed of the body If the bodies speed is close to the speed of light then this equation does not predict the forces well This equation is also limited if the particles are on the size of atoms
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3 Newton’s Law of Gravitational Attraction Newton developed a law for the mutual attraction between any two particles It can be represented as ܨൌܩ ݉ ݉ ݎ ܨ ൌ ݂݋ݎܿ݁ ݋݂ ܽݐݐݎܽܿݐ݅݋݊ ܩ ൌ ݑ݊݅ݒ݁ݎݏ݈ܽ ܿ݋݊ݏݐܽ݊ݐ ݋݂ ݃ݎܽݒ݅ݐܽݐ݅݋݊, ܩ ൌ66 .73 10 ିଵଶ ݉ ݇݃ݏ ݉ ൌ ݉ܽݏݏ ݋݂ ݌ܽݎݐ݈݅ܿ݁ 1 ܽ݊݀ 2 ݎ ൌ ݀݅ݏݐܽ݊ܿ݁ ܾ݁ݐݓ݁݁݊ ݐ݄݁ ܿ݁݊ݐ݁ݎݏ ݋݂ ݐ݄݁ ݐݓ݋ ݌ܽݎݐ݈݅ܿ݁ݏ Particle’s Near Earth For particles near Earth, the only force that is appreciable is the gravitational force from Earth Therefore: ܨ ൌ 66.73 10 ିଵଶ ݉ ݇݃ݏ ݉ ௣௔௥௧௜௖௟௘ ݉ ா௔௥௧௛ ݎ ா௔௥௧௛ ݉ ா௔௥௧௛ ൌ 5.9736 10 ଶସ ݇݃ ݎ ா௔௥௧௛ ൌ 6371݇݉ ݃ൌ 66.73 10 ିଵଶ ݉ /݇݃ݏ ∗ 5.9736 10 ଶସ ݇݃ 6371 10 ݉ ൌ9 .81 ݉ ݏ ൌ 32.2 ݂ݐ ݏ ܹൌ݉ ௣௔௥௧௜௖௟௘ ∗݃ g is defined at sea level at 45 latitude
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4 Weight in the SI/English system Weight is defined from mass in the SI system A mass of 1kg has a weight of 9.81N ܹൌ݉݃ Mass is defined from weight in the English system A weight of 32.2 lb has a mass of 1 slug ݉ൌ ܹ ݃ 13.2: The Equation of Motion When more than one force acts on a particle, the net resultant force may cause acceleration Therefore, ∑ ܨ Ԧ ൌ݉ܽ Ԧ If the acceleration is zero, the particle moves at a constant (maybe zero) velocity
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5 Inertial Reference Frame It is important that accelerations should be measured from a fixed reference frame or one that moves with a constant velocity
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Chapter_13_mod - Chapter13:KineticsofaParticle:...

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