chapter_06-actualmap - 6 Circular Motion and Other...

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6 CHAPTER OUTLINE 6.1 Newton’s Second Law Applied to Uniform Circular Motion 6.2 Nonuniform Circular Motion 6.3 Motion in Accelerated Frames 6.4 Motion in the Presence of Resistive Forces 6.5 Numerical Modeling in Particle Dynamics Circular Motion and Other Applications of Newton’s Laws ANSWERS TO QUESTIONS Q6.1 Mud flies off a rapidly spinning tire because the resultant force is not sufficient to keep it moving in a circular path. In this case, the force that plays a major role is the adhesion between the mud and the tire. Q6.2 The spring will stretch. In order for the object to move in a circle, the force exerted on the object by the spring must have a size of mv r 2 . Newton’s third law says that the force exerted on the object by the spring has the same size as the force exerted by the object on the spring. It is the force exerted on the spring that causes the spring to stretch. Q6.3 Driving in a circle at a constant speed requires a centripetal acceleration but no tangential acceleration. Q6.4 (a) The object will move in a circle at a constant speed. (b) The object will move in a straight line at a changing speed. Q6.5 The speed changes. The tangential force component causes tangential acceleration. Q6.6 Consider the force required to keep a rock in the Earth’s crust moving in a circle. The size of the force is proportional to the radius of the circle. If that rock is at the Equator, the radius of the circle through which it moves is about 6400 km. If the rock is at the north pole, the radius of the circle through which it moves is zero! Q6.7 Consider standing on a bathroom scale. The resultant force on you is your actual weight minus the normal force. The scale reading shows the size of the normal force, and is your ‘apparent weight.’ If you are at the North or South Pole, it can be precisely equal to your actual weight. If you are at the equator, your apparent weight must be less, so that the resultant force on you can be a downward force large enough to cause your centripetal acceleration as the Earth rotates. Q6.8 A torque is exerted by the thrust force of the water times the distance between the nozzles. 157
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158 Circular Motion and Other Applications of Newton’s Laws Q6.9 I would not accept that statement for two reasons. First, to be “beyond the pull of gravity,” one would have to be infinitely far away from all other matter. Second, astronauts in orbit are moving in a circular path. It is the gravitational pull of Earth on the astronauts that keeps them in orbit. In the space shuttle, just above the atmosphere, gravity is only slightly weaker than at the Earth’s surface. Gravity does its job most clearly on an orbiting spacecraft, because the craft feels no other forces and is in free fall. Q6.10 This is the same principle as the centrifuge. All the material inside the cylinder tends to move along a straight-line path, but the walls of the cylinder exert an inward force to keep everything moving around in a circular path.
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This note was uploaded on 03/22/2008 for the course PHYS phys230 taught by Professor Hadley during the Spring '08 term at A.T. Still University.

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chapter_06-actualmap - 6 Circular Motion and Other...

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