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Understanding Gravity, Orbital Velocity, and Waves: Key Concepts and Sample Problems

In this educational overview, we explore crucial topics from Chapters 9, 11.1, and 11.2 relating to gravity, orbital motion, and wave mechanics. The focus includes essential concepts such as gravitational force, escape velocity, and orbital velocity, alongside practical sample problems involving an astronaut's weight in various scenarios. We also delve into the characteristics of waves, including frequency, period, wavelength, and amplitude. This session is a preparation for the in-class Quiz #4 on Chapters 8 and 9, providing a concise review without a reading quiz.

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Understanding Gravity, Orbital Velocity, and Waves: Key Concepts and Sample Problems

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  1. Gravity Continued and Waves Chapters 9, 11.1, and 11.2

  2. Reminders • No lab this week. • In-class Quiz #4 will take place on Thursday, October 23, focusing on Chapters 8 and 9. • No reading quiz prior to class on Thursday as today’s quiz covered all of Chapter 11.

  3. Gravity - Review

  4. Orbital Velocity In orbital motion, Fg = Fc, hence

  5. Escape Velocity

  6. Examples • Force between two objects: • Orbital velocity: • Escape velocity: • G = 6.67x10-11Nm2/kg2 • M = 5.97x1024kg • r = 6,371,000m

  7. Sample Problems 1 • What is the gravitational force between a proton and an electron in a Hydrogen atom? • mp = 1.673x10–27kg • me = 9.109x10–31kg • ro = 5.29x10–11m • G = 6.67x10–11Nm2/kg2 • F = Gmemp/ro2

  8. Sample Problems 2 • How much does a 53-kg astronaut weigh on the surface of Earth? Wt= mg • How much does a 53-kg astronaut weigh 400km up in Earth orbit? Fg= -Fc • How much would a 53-kg astronaut weigh standing on top of a 400km-hightower? F = Gmame/r2

  9. Sample Problems 3 • What is the orbital velocity of the International Space Station (ISS) whose altitude is 330km? Take the radius of Earth to be 6378.1km. The mass of Earth is 5.97x1024kg • What is the ISS’s orbital period? Recall that Δx = vt which implies 2πr = vP • How does Earth’s escape velocity at the altitude of ISS’s orbit compare with the ISS’s orbital velocity?

  10. Key Concepts Chapter 11, Sec 1-2 • Simple Harmonic Oscillator (a pendulum) • Terms: frequency (f), period (T), wavelength (λ), amplitude (A); note f = 1/T • Wave forms: • Longitudinal • Transverse • Polarization • Δx= vt implies v = λf

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