Lecture 20 - Lecture 20 NEWTONS LAWS OF MOTION EQUATIONS OF...

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Dynamics: Lecture Notes for Sections 13.1-13.4 1 Lecture 20 NEWTON’S LAWS OF MOTION EQUATIONS OF MOTION & EQUATIONS OF MOTION FOR A SYSTEM OF PARTICLES RECTANGULAR COORDINATES Section 13.1-13.4 (pp 101-126) Problems 13.2,10,25,35,39 Ehab Zalok 2 NEWTON’S LAWS OF MOTION, EQUATIONS OF MOTION, & EQUATIONS OF MOTION FOR A SYSTEM OF PARTICLES Objectives : Students will be able to: 1. Write the equation of motion for an accelerating body. 2. Draw the free-body and kinetic diagrams for an accelerating body.
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Dynamics: Lecture Notes for Sections 13.1-13.4 2 3 APPLICATIONS The motion of an object depends on the forces acting on it. Knowing the drag force; How can we determine the acceleration or velocity of the parachutist at any point in time ? A parachutist relies on the atmospheric drag resistance force to limit his velocity. 4 APPLICATIONS (continued) A freight elevator is lifted using a motor attached to a cable and pulley system as shown. How can we determine the tension force in the cable required to lift the elevator at a given acceleration? Is the tension force in the cable greater than the weight of the elevator and its load?
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Dynamics: Lecture Notes for Sections 13.1-13.4 3 5 NEWTON’S LAWS OF MOTION (Section 13.1) The motion of a particle is governed by Newton’s three laws of motion . First Law: A particle originally at rest, or moving in a straight line at constant velocity, will remain in this state if the resultant force acting on the particle is zero. Second Law: If the resultant force on the particle is not zero, the particle experiences an acceleration in the same direction as the resultant force. This acceleration has a magnitude proportional to the resultant force. Third Law: Mutual forces of action and reaction between two particles are equal, opposite, and collinear. 6 NEWTON’S LAWS OF MOTION (continued) The first and third laws were used in developing the concepts of statics. Newton’s second law forms the basis of the study of dynamics. Mathematically, Newton’s second law of motion can be written F = m a Where: F is the resultant unbalanced force acting on the particle, and a is the acceleration of the particle. The positive scalar m is called the mass of the particle. Newton’s second law cannot be used when the particle’s speed approaches the speed of light, or if the size of the particle is extremely small (~ size of an atom).
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Dynamics: Lecture Notes for Sections 13.1-13.4 4 7 EQUATION OF MOTION (Section 13.2-12.3) The motion of a particle is governed by Newton’s second law, relating the unbalanced forces on a particle to its acceleration. If more than one force acts on the particle, the equation of motion can be written F = F R = m a where F R is the resultant force , which is a vector summation of all the forces. To illustrate the equation, consider a
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This note was uploaded on 02/28/2011 for the course MATH 101 taught by Professor Duke during the Spring '11 term at University of Ottawa.

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Lecture 20 - Lecture 20 NEWTONS LAWS OF MOTION EQUATIONS OF...

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