Presentation Transcript

1. Announcements EXAMS are graded and will be returnedTOMORROW!! Homework for tomorrow… (Ch. 14, Probs 4, 9, & 10) Office hours… M 3-4 pm TWR 9-10 am F 1-2 pm Tutorial Learning Center – Houston Hall 113 MWR 8 am-6 pm T 8 am-7 pm F 8 am-5 pm
2. Timeline… Monday: Chapter 14, Lecture 1 Tuesday: Chapter 14, Lecture 2 Wednesday: Post-Diagnostic Exam + Evaluations Thursday: Final Exam Review FINAL EXAM: Wednesday, 12/14 @ 10-11:50 am

3. Chapter 14

   Gravitation (Newton’s Law of Gravitation & Superposition)
4. Section 14.2:Newton’s Law of Gravitation The force of gravity between any two bodies is proportional to the product of their masses and inversely proportional to the square of their separation where
5. Newton’s Law of Gravitation continued… Notice: The forces and form a Newton’s3rd Law force pair The value of r is always the center-to-center separation of the two objects
6. Law of Gravitation - Restrictions Masses must be small compared to their separation (“point-like”) or Masses must be uniform spheres OK OK Not OK
7. 1 2 3 4 Quiz Question 1 (from the MCAT…) If the gravitational force between Earth and the space station could suddenly be eliminated, which of the following diagrams would best describe the path taken by the station?
8. Quiz Question 2 (from the MCAT…) Which of the following expressions gives the acceleration due to gravity at the surface of the Earth? (Note: M is the mass of Earth, m is the mass of an observer at the surface of the Earth, and r is the radius of the Earth.) GM/r GM/r2 GmM/r GmM/r2
9. Quiz Question 3 (from the MCAT…) Calculations were done to estimate the forces that would affect the International Space Station while it orbited Earth. The space station would be placed in a circular orbit at a distance of 1.2 x 107 m from the center of Earth (radius 6 x 106 m). (The Gravitational constant G= 6.67 x 10-11 Nm2/kg2 and g is 9.8 m/s2 ). What percentage of the gravitational force that exists at the surface of Earth would be present at the altitude of the station? 5 % 25 % 50 % 100 %
10. Section 14.3: Gravitation and Superposition What is ? mA mB mC mD
11. Gravitation and Superposition, continued… This is the Principle of Superposition. mA mB mC mD
12. Gravitation and Superposition, continued… For n interacting particles?
13. Quiz Question 4 Four point masses, each with mass m, are arranged symmetrically about the origin on the x-axis. A fifth point mass, with mass M, is on the y-axis. The direction of the gravitational force on M is: Up Down Up and to the left Down and to the right Depends whether m>M or m<M y M m x m m m
14. Reading Exercise 14.3: A particle is to be placed, in turn, at the same distance, r, from the center of the four objects, shown in the figure, each of mass m: A small uniform solid sphere A small uniform spherical shell A large uniform spherical shell A large uniform solid sphere In each situation, the distance between the particle and the center of the object is r. Rank the objects according to the magnitude of the gravitational force they exert on the particle, greatest first.