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Dynamics of Circular Motion and Gravitation

Explore the dynamics of circular motion, Newton's Law of Gravitation, satellite motion, and more in this chapter. Understand centripetal forces, gravitational interactions, and satellite orbit calculations.

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Dynamics of Circular Motion and Gravitation

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  1. CHAPTER 6 CIRCULAR MOTION AND GRAVITATION

  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 study the motion of objects in orbit as a special application of Newton’s Law of Gravitation.

  3. Uniform circular motion is due to a centripetal acceleration This aceleration is alwayspointing to the center This aceleration is dur to a net force

  4. Period = the time for one revolution • Circular motion in horizontal plane: - flat curve - banked curve - rotating object 2) Circular motion in vertical plane

  5. Rounding a flat curve • The centripetal force coming only from tire friction.

  6. Rounding a banked curve • The centripetal force comes from friction and a component of force from the car’s mass

  7. A tetherball problem

  8. Dynamics of a Ferris Wheel

  9. HOMEWORK CH6 3; 5; 8; 13; 15; 19; 22; 29; 36; 40

  10. Each stride is taken as one in a series of arcs

  11. Spherically symmetric objects interact gravitationally as though all the mass of each were concentrated at its center

  12. A diagram of gravitational force

  13. Newton’s Law of Gravitation • Always attractive. • Directly proportional to the masses involved. • Inversely proportional to the square of the separation between the masses. • Masses must be large to bring Fg to a size even close to humanly perceptible forces.

  14. Use Newton’s Law of Universal Gravitation with the specific masses and separation.

  15. Cavendish Balance • The slight attraction of the masses causes a nearly imperceptible rotation of the string supporting the masses connected to the mirror. • Use of the laser allows a point many meters away to move through measurable distances as the angle allows the initial and final positions to diverge.

  16. WEIGHT

  17. Gravitational force falls off quickly • If either m1 or m2 are small, the force decreases quickly enough for humans to notice.

  18. What happens when velocity rises? • Eventually, Fg balances and you have orbit. • When v is large enough, you achieve escape velocity.

  19. Satellite Motion

  20. The principle governing the motion of the satellite is Newton’s second law; the force is F, and the acceleration is v2/r, so the equation Fnet = ma becomes GmmE/r 2 = mv 2/r v =GmE/r Larger orbits correspond to slower speeds and longer periods.

  21. We want to place a satellite into circular orbit 300km above the earth surface. What speed, period and radial acceleration it must have?

  22. A 320 kg satellite experiences a gravitational force of 800 N. What is the radius of the of the satellite’s orbit? What is its altitude? F = GmEmS/r 2 r 2 = GmEmS/ F r 2 = (6.67 x 10 -11 N.m2/kg2) (5.98 x 10 24 kg) (320 kg ) / 800 N r 2= 1.595 x 1014m2 r = 1.26 x 107m Altitude = 1.26 x 107m – radius of the Earth Altitude = 1.26 x 107m – 0.637 x 107 = 0.623 x 107 m

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