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Unformatted text preview: 6 Circular Motion and Other Applications of Newtons Laws CHAPTER OUTLINE 6.1 Newtons 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 ANSWERS TO QUESTIONS *Q6.1 (i) nonzero. Its direction of motion is changing. (ii) zero. Its speed is not changing. (iii) zero: when v = 0, v 2 / r = 0. (iv) nonzero: its velocity is changing from, say 0.1 m / s north to 0.1 m / s south. Q6.2 (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. Q6.3 The speed changes. The tangential force component causes tangential acceleration. *Q6.4 (a) A > C = D > B = E. At constant speed, centripetal acceleration is largest when radius is smallest. A straight path has infi nite radius of curvature. (b) Velocity is north at A, west at B, and south at C. (c) Acceleration is west at A, nonexistent at B, and east at C, to be radially inward. *Q6.5 (a) yes, point C. Total acceleration here is centripetal acceleration, straight up. (b) yes, point A. Total acceleration here is tangential acceleration, to the right and downward perpendicular to the cord. (c) No. (d) yes, point B. Total acceleration here is to the right and upward. Q6.6 I would not accept that statement for two reasons. First, to be beyond the pull of gravity, one would have to be infi nitely 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 Earths surface. Gravity does its job most clearly on an orbiting spacecraft, because the craft feels no other forces and is in free fall. Q6.7 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. Q6.8 The water has inertia. The water tends to move along a straight line, but the bucket pulls it in and around in a circle. Q6.9 Blood pressure cannot supply the force necessary both to balance the gravitational force and to provide the centripetal acceleration, to keep blood owing up to the pilots brain. *Q6.10 (a) The keys shift backward relative to the students hand. The cord then pulls the keys upward and forward, to make them gain speed horizontally forward along with the airplane. (b) The angle stays constant while the plane has constant acceleration. This experiment is described in the book Science from Your Airplane Window by Elizabeth Wood....
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