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Unformatted text preview: CHAPTER 5 DYNAMICS OF UNIFORM CIRCULAR MOTION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS ____________________________________________________________________________________________ 1. (c) The velocity of car A has a constant magnitude (speed) and direction. Since its velocity is constant, car A does not have an acceleration. The velocity of car B is continually changing direction during the turn. Therefore, even though car B has a constant speed, it has an acceleration (known as a centripetal acceleration). 2. (d) The centripetal (or “centerseeking”) acceleration of the car is perpendicular to its velocity and points toward the center of the circle that the road follows. 3. (b) The magnitude of the centripetal acceleration is equal to v 2 / r , where v is the speed of the object and r is the radius of the circular path. Since the radius of the track is smaller at A compared to B, the centripetal acceleration of the car at A has a greater magnitude. 4. (a) The magnitude a c of the centripetal acceleration is given by a c = v 2 / r . 5. (d) The acceleration (known as the centripetal acceleration) and the net force (known as the centripetal force) have the same direction and point toward the center of the circular path. 6. (a) According to the discussion in Example 7 in Section 5.3, the maximum speed that the cylinder can have is given by max s v gr μ = , where μ s is the coefficient of static friction, g is the acceleration due to gravity, and r is the radius of the path. 7. (d) The radius of path 1 is twice that of path 2. The tension in the cord is the centripetal force. Since the centripetal force is inversely proportional to the radius r of the path, T 1 must be onehalf of T 2 . 8. (a) The centripetal force is given by F c = mv 2 / r . The centripetal forces for particles 1, 2 and 3 are, respectively, 4 m v 2 / r , 3 m v 2 / r , and 2 m v 2 / r . 9. (d) The centripetal force is directed along the radius and toward the center of the circular path. The component F N sin θ of the normal force is directed along the radius and points toward the center of the path. 10. (a) The magnitude of the centripetal force is given by F c = mv 2 / r . The two cars have the same speed v and the radius r of the turn is the same. The cars also have the same mass m , 244 DYNAMICS OF UNIFORM CIRCULAR MOTION even though they have different weights due to the different accelerations due to gravity. Therefore, the centripetal accelerations are the same. 11. (e) The centripetal force acting on a satellite is provided by the gravitational force. The magnitude of the gravitational force is inversely proportional to the radius squared (1/ r 2 ), so if the radius is doubled, the gravitational force is one fourth as great; 1/2 2 = 1/4....
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This note was uploaded on 03/30/2012 for the course PHYSICS 201 taught by Professor Rollino during the Fall '11 term at Rutgers.
 Fall '11
 rollino
 Physics, Acceleration, Circular Motion

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