Physics 161 Lecture 10: Universal Gravitation. October 4, /6/20 15

Transcription

1 Physics 161 Lecture 10: Universal Gravitation October 4,

2 Midterm announcements 1) The first midterm exam will be Thursday October 18 from 10:00 pm to 11:20 pm in ARC ) The exam will be multiple choice. 3) You may bring an 8 1/2 x 11 hand-written sheet with information and formulas (both sides may be used). You should also bring a calculator. No cell phones allowed during the exam. 4) A practice exam has been posted. Solutions will soon be posted. 5) The exam will cover Chapter 2, 3, 4, 5, 6 and 7 from the textbook. Specific sections are listed in the Syllabus. (exclude sectioon 6.4, glancing collisions). 6) The materials on the exam may come from the textbook, workshops, WebAssign or the lectures. 2 10/1/201 5

3 Office hours Solomon Admasu Friday 2-3pm SRN-232 Shagesh Sridharan Friday 3-4pm SRN-232 Unab Javed Thursday 11am-12pm SRN-232 Prof. Kloet Thursday 12pm-1:30pm SRN-211 Prof. DeBuvitz Friday 10am-12pm SRN /1/201 5

4 Lecture 10: learning objectives Review from lecture 9 - Rotational motion. Uniform circular motion. - Centripetal acceleration and force This lecture 10 You will apply Newton s law of gravitation to calculate gravitational forces and the gravitational potential energy. You will calculate the escape speed from the surface of the earth. We will state Kepler s three laws and apply the third law to determine the motion of orbiting bodies. Sep. 1, 20 4

5 iclicker question: stone-sling A stone is attached to a string and whirled around in a circle. Which way does the stone travel initially if the string is released? a) Direction a. b) Direction b. c) Direction c. d) The stone stops. e) It is unpredictable. (c) (b) (a) 5 9/29/1 5

6 iclicker question: car-upgrade The speedometer in a car measures the number of rotations of the car s wheels. If you replace your wheels with wheels of greater diameter, the reading on the speedometer will be: a) Too slow. b) The same. c) Too fast. 6 9/29/1 5

7 Problem: complete the loop How high (from a point outside of the figure) must we release the cart for it to complete the loop? [This is very similar to Example 7.8.] 7 9/29/1 5

8 Problem: 7.19 One end of a cord is fixed and a small kg object attached to the other end, where it swings in a section of a vertical circle of radius 2 m as shown. When θ = 20.0, the speed of the object is v = 8.00 m/s. At this instant, find: a)the tension in the string. b)the tangential and radial components of the acceleration. c) The total acceleration. d)is your answer changed if the object is swinging down instead of up? e)why? 8 θ r = 2 m v 9/29/1 5

9 Newton s universal gravitation Newton s law of universal gravitation: Two objects attract each other with a force that is proportional to the product of their masses and inversely proportional to their separation. Here the gravitational constant is G = 6.67x10-11 Nm 2 /kg 2. The force that Object 2 exerts on Object 1 is directed toward Object 2 and vice versa. 9 center-to-center distance

10 Origin of g Copyright: Christoph Hormann 10

11 Non-spherical Earth The value of g varies according to your latitude. ( It also depends on Your elevation) 11

12 iclicker question: gravity at a distance Two identical masses each with diameter 2r are separated by a distance 8r, as measured from the surface of each mass. When the two masses are brought in contact with each other, the gravitational force between the two masses: a) Increases by a factor of 8. b) Increases by a factor of 25. c) Increases by a factor of 49. d) Increases by a factor of 64. e) Increases by a factor of /29/1 5

13 Gravitational potential energy Recall the gravitational potential energy near the Earth s surface: But g changes with distance r. The gravitational potential energy at large distances is given by: Here the reference point is at. r 13

14 iclicker question: astronaut Consider an astronaut flying within a space shuttle orbiting around the Earth. She appears to be weightless because: a) The net force on her is zero. b) The gravitational force on her is zero. c) The gravitational force and normal force balance out. d) She falls resulting in a circular orbit around Earth. 14 9/29/1 5

15 Escape speed Escape speed: The speed required for an object to leave a planet and never fall back. (It reaches an infinite distance with zero speed.) Escape speed tells us how fast something has to go to escape the gravitational force of the planet it is escaping.

16 Kepler s first law (orbit) Kepler formulated his three laws of planetary motion between 1609 and 1619 in Germany. (Based on very precise observations of the planet Mars by Tycho Brahe without the help of a telescope) Kepler s first law: All of the planets move in elliptical orbits with the Sun at one of the focal points. 16

17 Conic Sections You do not need to know this diagram for the exam. You need only know that orbiting bodies move in an ellipse. 17

18 Kepler s second law (sweeped area) Kepler formulated his three laws of planetary motion between 1609 and Mars moves faster in its elliptic orbit if it is closer to the sun. Kepler s second law: A line drawn from the Sun to any planet sweeps out equal areas in equal time intervals. 18

19 Kepler s third law (periods) Kepler s third law: The square of the orbital period T of any planet is proportional to the cube of the average distance r of the planet from the Sun. 1. The square of the orbital period divided by the cube of the orbital radius is constant for all the planets of the sun: 19

20 Problem of Earth satellite What is the period of a low-flying satellite of the Earth? (Think Sputnik 4 Oct 1957) R E = m M E = kg G = Nm 2 /kg 2 20

21 21

22 Kepler confirmed It is remarkable that Kepler s Laws were purely based on data previously collected by Tycho Brahe ( ). 50 years after Johannes Kepler ( ) the theory of gravity was proposed by Isaac Newton ( ). The theory of gravity does explain the Kepler s Laws. 22

23 Problem 7.43 A satellite of Mars, called Phoebus, has an orbital radius of 9.4 x 10 6 m and a period of 2.8 x 10 4 s. Assuming the orbit is circular, determine the mass of Mars. 23 9/29/1 5

24 Problem: like 7.41 A satellite goes around the Earth with a period of 127 minutes. What is: a)the satellite s altitude? b)the satellite s speed? c)the value of g at the location of the satellite? 24