Chapter5 - CHAPTER 5 DYNAMICS OF UNIFORM CIRCULAR MOTION...

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CHAPTER 5 DYNAMICS OF UNIFORM CIRCULAR MOTION CONCEPTUAL QUESTIONS ____________________________________________________________________________________________ 1. REASONING AND SOLUTION The car will accelerate if its velocity changes in magnitude, in direction, or both. If a car is traveling at a constant speed of 35 m/s, it can be accelerating if its direction of motion is changing. ____________________________________________________________________________________________ 2. REASONING AND SOLUTION Consider two people, one on the earth's surface at the equator, and the other at the north pole. If we combine Equations 5.1 and 5.2, we see that the centripetal acceleration of an object moving in a circle of radius r with period T can be written as a r T C = ( ) / 4 2 2 π . The earth rotates about an axis that passes approximately through the north pole and is perpendicular to the plane of the equator. Since both people are moving on the earth's surface, they have the same period T . The person at the equator moves in a larger circle so that r is larger for the person at the equator. Therefore, the person at the equator has a larger centripetal acceleration than the person at the north pole. ____________________________________________________________________________________________ 3. REASONING AND SOLUTION The equations of kinematics (Equations 3.3 - 3.6) cannot be applied to uniform circular motion because an object in uniform circular motion does not have a constant acceleration. While the acceleration vector is constant in magnitude a v r = 2 / c h , its direction changes constantly -- it always points toward the center of the circle. As the object moves around the circle the direction of the acceleration must constantly change. Because of this changing direction, the condition of constant acceleration that is required by Equations 3.3 – 3.6 is violated. ____________________________________________________________________________________________ 4. REASONING AND SOLUTION Acceleration is the rate of change of velocity. In order to have an acceleration, the velocity vector must change either in magnitude or direction, or both. Therefore, if the velocity of the object is constant, the acceleration must be zero. On the other hand, if the speed of the object is constant, the object could be accelerating if the direction of the velocity is changing. ____________________________________________________________________________________________ 5. REASONING AND SOLUTION When the car is moving at constant speed along the straight segments (i.e., AB and DE ) , the acceleration is zero. Along the curved segments, the magnitude of the acceleration is given by v r 2 / . Since the speed of the car is constant, the magnitude of the acceleration is largest where the radius r is smallest. Ranked from smallest to largest the magnitudes of the accelerations in each of the four sections are: AB or DE, CD, BC . ____________________________________________________________________________________________
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241 DYNAMICS OF UNIFORM CIRCULAR MOTION 6. REASONING AND SOLUTION From Example 7, the maximum safe speed with which a car can round an unbanked horizontal curve of radius r is given by v gr s = μ . Since the acceleration due to gravity on the moon is roughly one sixth that on earth, the safe speed for the same curve on the moon would be less than that on earth. In other words, other things being equal, it would be more difficult to drive at high speed around an unbanked curve on the moon as compared to driving around the same curve on the earth.
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