Board Work

1. Board Work • A satellite revolves around its planet in a perfectly circular orbit at a constant speed. • At each of the four positions, draw an arrow representing the net force on the satellite. Label all the arrows F. • At each position, draw an arrow to represent the satellite’s velocity. Label each arrow v.

2. Announcements • Homework 10 is due • Homework 11 posted; due Wednesday • Quiz nezt week on HW 10 standards

3. Board Work • Are all forces the same magnitude? • Are all velocities the same magnitude? • What is the angle between F and v at any position of the satellite?

4. Gravity The laws of physics are universal

5. What’s the point? • Gravity is one of the fundamental forces.

6. Objectives • Determine the gravitational attraction between objects.

7. Historical Background • Earthly and celestial objects thought fundamentally different • Earthly objects seek a lowly position • Celestial objects move in perfect circles

8. Newton’s Insight • The force pulling us to the ground is the same force curving the moon’s path: gravity!

9. Poll Question Which is greater? • The pull of gravity from the earth on the moon. • The pull of gravity from the moon on the earth. • Both forces are equally strong. • Cannot tell without more information.

10. m1m2 F=G d2 Newton’s Law of Universal Gravitation Force between two objects: m1, m2: masses of the objects d: distance between objects’ centers of mass G: universal gravitational constant, 6.672  10–11 Nm2/kg2

11. m1m2 F=G d2 Properties of Gravity • direction is toward the other object • magnitude decreases as (distance)2 increases • never becomes zero • infinite at zero separation (?!)

12. Poll Question Two satellites orbit at the same distance from a planet. One has twice the mass of the other. How do their gravitational attractions to the planet compare? • They have the same attraction. • The massive satellite is attracted with twice the force of the light satellite. • The massive satellite is attracted with half the force of the light satellite.

13. Poll Question Two satellites orbit at the same distance from a planet. One has twice the mass of the other. How do their gravitational accelerations toward the planet compare? • They have the same acceleration. • The massive satellite accelerates twice as much as the light satellite. • The massive satellite accelerates half as much as the light satellite.

14. F F D D/2 Poll Question When two objects are separated by a distance D, the gravitational force between them is F. If they move closer, to 1/2 the distance (D/2), the force becomes • F/2. • 2F. • 4F. • Cannot tell without more information.

15. GM field =g= d2 Gravitational Field • Gives the force acting on an object of mass m F=m· field • M = mass of object creating the field • d = distance from the object • field is a vector!

16. Poll Question At which position is the satellite speeding up? • Position A. • Position B. • Position C. • Position D. • None of these.

17. Quick Question At which position is the satellite slowing down? • Position A. • Position B. • Position C. • Position D. • None of these.

18. Poll Question At which position is the satellite changing its direction but not its speed? • Position A. • Position B. • Position C. • Position D. • None of these.

19. Board Work • Rank the positions in descending order of: • Gravitational force. • Acceleration. • Speed.

20. . . Gravity between Real Objects The actual force acting on an object is the sum of all forces on all its particles from all the particles of the other object!

21. A Lucky Break The gravitational field around a sphere is the same as would be around a point particle of the same mass at the center of the sphere.

22. (5.976  1024 kg ) g = (6.670  10–11 Nm2/kg2 ) (6378174 m )2 Gravity on Earth • G = 6.670  10–11 Nm2/kg2 • Earth’s mass = 5.976  1024 kg = M • Earth’s radius = 6378174 m = d • so the field g is = 9.8 N/kg look familiar?

23. Reading for Next Time • Work and Power • pp. 54–59