## Lecture 24: Gravitational Forces and Energy

November 30, 2017

• Study: Eq 8.1; Ex 8.1; Fig 8.5; Eq 8.6; Ex 8.5

### Objectives

• (Continuing objective) Relate the concepts of rotational motion and gravity to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
• Calculate the gravitational force acting between point-like or spherical objects using Newton's law of gravitation.
• Apply Newton's second law and Newton's law of gravity to circular orbit problems.
• Using the expression for gravitational potential energy and conservation of mechanical energy, relate speed and distance for objects in free flight. Use conservation of mechanical energy to solve problems involving escape velocity.

### Homework

• Friday's Assigned Problems: CH 8: 5, 11, 12, 15, 25, 27, 31, 43, 57, 68

Answers: CH 8 #12 $2.73 \times 10^{-3}\,\mbox{m/s$^2$}$; CH 8 #68 $13\, \text{km}$.

Notes: For CH 8 #25, calculate the kinetic energy needed, not the total mechanical energy. For CH 8 #31, use conservation of energy (with $E = 0$) instead of the canned escape velocity formula.

• Monday's Hand-In Problems: A44bc, A45; CH 11: 28, 36, 58; CH 8: 16, 26, 30, 52, 66

### Lecture Materials

Answers to Conceptests: (1) 3; (2) 5; (3) 5; (4) 1; (5) 2

• Newton's cannon animation (I don't know if I'll get to this in lecture, but even if I don't, it's fun to play with.)
• And speaking of cool demos to play with, click here for a cool demo that let's you set up as many stars and planets as you want orbiting around each other. NOTE: if more than two, you will get chaotic orbits in general.

### Videos of example problems

To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.
• Video Example #1: This is a two-part example, but it is really the second part that is relevant this year (i.e., figuring things out using Newton's Laws), so you can skip the first part.
• Video Example #2: Applying conservation of energy using the more general form for gravitational potential energy. (Ignore the comments about this being "classic lecture 23 material" -- we changed the lectures around since making this video.)

### Pre-Class Entertainment

• TVC 15, by David Bowie
• Two Against One, by Danger Mouse and Daniele Luppi (fea. Jack White)
• Twist In My Sobriety, by Tanita Tikaram
• Tighten Up, by the Black Keys
• Thank You, by Dido
• Uptown Funk, by Mark Ronson fea. Bruno Mars