CH6%20Some%20Appl%20of%20N%20Laws%20%5bCompatibility%20Mode%5d

CH6%20Some%20Appl%20of%20N%20Laws%20%5bCompatibility%20Mode%5d

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1 Chapter 6 Circular Motion and Other Applications of Newton’s Laws Circular Motion Two analysis models using Newton’s Laws of Motion have been developed. The models have been applied to linear motion. Newton’s Laws can be applied to other situations: Obj t tl i iil th Objects traveling in circular paths Motion observed from an accelerating frame of reference Motion of an object through a viscous medium Many examples will be used to illustrate the application of Newton’s Laws to a variety of new circumstances. Introduction Uniform Circular Motion, Acceleration 2 c v a r = A particle moves with a constant speed in a circular path of radius r with an acceleration. The magnitude of the acceleration is given by The centripetal acceleration, , is directed toward the center of the circle. The centripetal acceleration is always perpendicular to the velocity. c a G Section 6.1 Uniform Circular Motion, Force r F G A force, , is associated with the centripetal acceleration. The force is also directed toward the center of the circle. Applying Newton’s Second Law along the radial direction gives 2 c v Fm a m r == Section 6.1 Uniform Circular Motion, cont. A force causing a centripetal acceleration acts toward the center of the circle. It causes a change in the direction of the velocity vector. If the force vanishes, the object would move in a straight line path tangent to the circle. See various release points in the active figure Section 6.1 Conical Pendulum The object is in equilibrium in the vertical direction . It undergoes uniform circular motion in the horizontal direction direction. F y = 0 T cos θ = mg F x = T sin θ = m a c v is independent of m sin tan vL g θ = Section 6.1
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2 Motion in a Horizontal Circle The speed at which the object moves depends on the mass of the object and the tension in the cord. The centripetal force is supplied by the tension The centripetal force is supplied by the tension. The maximum speed corresponds to the maximum tension the string can withstand. Tr v m = Section 6.1 Horizontal (Flat) Curve Model the car as a particle in uniform circular motion in the horizontal direction. Model the car as a particle in equilibrium in the vertical direction. The force of static friction supplies the centripetal force. The maximum speed at which the car can negotiate the curve is: Note, this does not depend on the mass of the car. s vg r μ = Section 6.1 Banked Curve These are designed with friction equaling zero. Model the car as a particle in equilibrium in the vertical direction. Model the car as a particle in uniform circular motion in the horizontal direction.
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CH6%20Some%20Appl%20of%20N%20Laws%20%5bCompatibility%20Mode%5d

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