Slide 1

Chapter 6 Lecture Chapter 6: Circular Motion and Gravitation 2016 Pearson Education, Inc. Slide 2 Goals for Chapter 6 To understand the dynamics of circular motion. To study the unique application of circular motion as it applies to Newton's law of gravitation. To examine the idea of weight and relate it to mass and Newton's law of gravitation. To study the motion of objects in orbit as a special application of Newton's law of gravitation. 2016 Pearson Education, Inc. Slide 3 In Section 3.4 We studied the kinematics of circular motion. Centripetal acceleration Changing velocity vector Uniform circular motion We acquire new terminology. Radian Period (T) Frequency (f) 2016 Pearson Education, Inc. Slide 4 Velocity Changing from the Influence of a rad Figure 6.1 A review of the relationship between and a rad. The velocity changes direction, not magnitude. The magnitude of the centripetal acceleration is: In terms of the speed and period (time to make one complete revolution) 2016 Pearson Education, Inc. Slide 5 Circular motion and Gravitation Slide 6 Details of Uniform Circular Motion An object moves in a circle because of a centripetal bet force. Notice how becomes linear when F rad vanishes. 2016 Pearson Education, Inc. Slide 7 You whirl a ball of mass m in a fast vertical circle on a string of length R. At the top of the circle, the tension in the string is five times the ball's weight. The ball's speed at this point is given by a) gR b) 4gR c) 6gR d) 6 gR 2016 Pearson Education, Inc. Clicker question Slide 8 You whirl a ball of mass m in a fast vertical circle on a string of length R. At the bottom of the circle, the tension in the string is five times the ball's weight. The ball's speed at this point is given by a) gR b) 4gR c) 6gR d) 6 gR 2016 Pearson Education, Inc. Clicker question Slide 9 The Giant Swing: a)Make a free body diagram of the seat including the person on it. b)Find the time for one revolution for the indicated angle of 30 o c)Does the angle depend on the weight of the passenger? Slide 10 Work out the radial acceleration of the moon around the earth. Slide 11 Ferris wheel Slide 12 Slide 13 2016 Pearson Education, Inc. snowboarding Slide 14 You're snowboarding down a slope. The free-body diagram in the figure represents the forces on you as you a)go over the top of a mogul. b)go through the bottom of a hollow between moguls. c)go along a horizontal stretch. d)go along a horizontal stretch or over the top of a mogul. 2016 Pearson Education, Inc. Clicker question Slide 15 Conical Pendulum Tether Ball Problem Example 6.2 Center-seeking Force: Tension Circular Motion Slide 16 Conical Pendulum Slide 17 No Skidding on a Curve (I) s min = ? Center-seeking Force : Static Friction Slide 18 No Skidding on a Curve (II) r = 50.0 m m = 1000 kg v = 14.0 m/s C Slide 19 Un-Banked Curve Friction force is larger than radial force Slide 20 No Skidding on Banked Curve F rad Slide 21 No Skidding on Banked Curve Slide 22 Slide 23 6-55. As the bus rounds a flat curve at constant speed, a package suspended from the luggage rack on a string makes an angle with the vertical as shown. Slide 24 Gravitation Newtons Law of Gravitation Slide 25 Gravitational attraction Note: Two particles of different mass exert equally strong gravitational force on each other Slide 26 Gravitational Forces (I) Attractive Force M M M E F G = G r 2 MEME M Slide 27 Why is the Aggie not falling off the earth? Remember there is equally strong attraction between the earth and the Aggie and vice versa Slide 28 Cavendish balance Cavendish(1798) announced that he has weighted the earth Slide 29 Cavendish Tension balance (1798) Slide 30 Gravitational Force Falls off Quickly Figure 6.15 The gravitational force is proportional to 1/r 2, and thus the weight of an object decreases inversely with the square of the distance from the earth's center (not distance from the surface of the earth). 2016 Pearson Education, Inc. Slide 31 What is the magnitude of the gravitational force inside, on the surface, and outside the earth?? Slide 32 g = 9.80 m/s 2 R E = 6.37 x 10 6 m M E = 5.96 x 10 24 kg E = 5.50 x 10 3 kg/m 3 = 5.50 g/cm 3 ~ 2 x Rock Average Density of the Earth Slide 33 Projectile Slide 34 Circular orbit The larger r then slower the speed and the larger the period Slide 35 Weather Satellite Slide 36 Geo-synchronous Satellite (at the equator of Earth) Slide 37 If an Object is Massive, Even Photons Cannot Escape A "black hole" is a collapsed sun of immense density such that a tiny radius contains all the former mass of a star. The radius to prevent light from escaping is termed the "Schwarzschild Radius." The edge of this radius has even entered pop culture in films. This radius for light is called the "event horizon." 2016 Pearson Education, Inc. Slide 38 Black hole Steven Hawkins is associated with the department of Physics and Astronomy at TAMU Slide 39 Slide 40