AP_Physics_Topic_5_Student_Notes.doc

AP_Physics_Topic_5_Student_Notes.doc - Topic 5 Conservation...

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Topic 5 Conservation of Linear Momentum I. Introduction. a. One of the most important principles in physics is the law of conservation of momentum, which says that the total momentum of a system and its surroundings does not change. Whenever the momentum of a system changes, we can account for the change by the appearance or disappearance of momentum somewhere else. b. In this chapter, we introduce the ideas of impulse and linear momentum, and show how integrating Newton’s second law produces an important theorem known as the impulse–momentum theorem. We will also determine if the momentum of a system remains constant, and how to exploit constant momentum to solve problems involving collisions between objects. In addition, we examine a new reference frame, known as the center-of-mass reference frame, and explore situations in which a system has a continuously changing mass. II. Conservation of Linear Momentum. a. When Newton devised his second law, he considered the product of mass and velocity as a measure of an object’s “quantity of motion.” Today, we call the product of a particle’s mass and velocity linear momentum b. Linear momentum is a vector quantity, it is the product of a vector (velocity) and a scalar (mass). Its magnitude is and it has the same direction as . The units of momentum are units of mass times speed, so the SI units of momentum are kg•m/s. c. Momentum may be thought of as a measurement of the effort needed to bring a particle to rest. i. Thus, the net force acting on a particle equals the time rate of change of the particle’s momentum. ii. d. The total momentum of a system of particles is the vector sum of the momenta of the individual particles. i. 1
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Topic 5 Conservation of Linear Momentum ii. But according to Newton’s second law for a system of particles, equals the net external force acting on the system. iii. e. When the sum of the external forces acting on a system of particles remains zero, the rate of change of the total momentum remains zero and the total momentum of the system remains constant. i. ii. This result is known as the law of conservation of momentum. iii. iv. This law is one of the most important in physics. It is more widely applicable than the law of conservation of mechanical energy because internal forces exerted by one particle in a system on another are often not conservative. The nonconservative internal forces can change the total mechanical energy of the system, though they effect no change of the system’s total momentum. If the total momentum of a system remains constant, then the velocity of the center of mass of the system remains constant. The law of conservation of momentum is a vector relation, so it is valid component by component. f. Finding Velocities Using Momentum Conservation ( Equation 8-5 ) i. PICTURE Determine that the net external force (or ) on the system is negligible for some interval of time. If the net force is determined not to be negligible, do not proceed.
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