2. If it is known that A is directly proportional to B, how would A change if B is increased by a factor of 2? 1. Increase by a factor of 2 2. Increase by a factor of 4 3. Decrease by a factor of 2 4. Decrease by a factor of 4

3. If it is known that A is directly proportional to B 2, how would A change if B is increased by a factor of 2? 1. Increase by a factor of 2 2. Increase by a factor of 4 3. Decrease by a factor of 2 4. Decrease by a factor of 4

4. If it is known that A is inversely proportional to B 2, How would A change if B is increased by a factor of 2? 1. Increase by a factor of 2 2. Increase by a factor of 4 3. Decrease by a factor of 2 4. Decrease by a factor of 4

5. If it is known that A is inversely proportional to B 2, how would A change if B is decreased by a factor of 2? 1. Increase by a factor of 2 2. Increase by a factor of 4 3. Decrease by a factor of 2 4. Decrease by a factor of 4

6. Proportionality  Direct proportion  Inverse proportion  Inverse square law

7.  When objects fall towards the earth they accelerate  Galileo found objects accelerate toward the earth at the same rate regardless of their mass  Newton observed that planets experience a force on them due to the sun  He saw that this force varied inversely with the square of the distance between the planet and the sun  He also observed that an apple’s acceleration in free fall agreed with the

8.  The force the earth exerts on the apple is equal to the force the apple exerts on the earth  This attraction of two objects must be proportional to the objects’ masses  This is known as a Gravitational force  Newton felt this would work anywhere in the universe  This leads to a universal law that objects attract other objects with a force proportional to their masses and inversely proportional to the distance between them

9. Newton’s Law of Universal Gravitation ChangeResultChangeResult

10. If the gravitational attraction of two objects is 100 N. What would it be if the distance between them were doubled? 1. 25 N 2. 50 N 3. 100 N 4. 200 N 5. 400 N 0 of 20

11. What would the force be if the distance is cut in half? 1. 25 N 2. 50 N 3. 100 N 4. 200 N 5. 400 N

12. What if each mass is doubled? 1. 25 N 2. 50 N 3. 100 N 4. 200 N 5. 400 N

13. What is G???????  Henry Cavendish  Used two large and two small lead spheres  Found the value of G 6.67x10 -11  Found mass of the Earth

14. Calculate the mass of the Earth

15. Acceleration due to gravity  Anything experiencing a net force will accelerate  All objects on the earth are experiencing a gravitational force from the earth, and they are all the same distance from the center of the earth (radius of the earth)  Mass of the earth does not change

17. What is the gravitation force on a person with a mass of 75 kg by the earth if they are 6378 km apart? (M E =5.97*10 24 kg) 1. 734 N 2. 73400 N 3. 7.34*10 6 N 4. 7.34*10 8 N

18. A satellite is one earth’s radius above the earth. How does it’s acceleration compare to that on the surface of the earth? 1. ¼ g 2. ½ g 3. g 4. 2g 5. 4g

19. Jupiter is 300 times as massive as the earth and has a radius of 10 times that of the earth. Estimate g on Jupiter. 1. 3g 2. 9g 3. 30g 4. 90g

20. Velocity of satellites  Satellites experience a gravitational force  This force is the centripetal force

21. A satellite obits the earth 225 km above the surface. What is the satellite’s speed? (mass earth 5.97x10 24 kg, radius of earth 6.38x10 6 m) 1. 1.33x10 6 m/s 2. 4.2x10 4 m/s 3. 7.76x10 3 m/s 4. 1.5x10 3 m/s

22. How far above the earth’s surface is a satellite that is moving with a speed of 2.7x10 3 m/s? 1. 5.46x10 7 m 2. 4.82x10 7 m 3. 5.46x10 4 m 4. 4.82x10 4 m 0 of 20

23. A satellite moving at a constant speed of 8x10 3 m/s, is 200 km from the earth’s surface. What is the mass of the satellite? 1. 1.2x10 3 kg 2. 2.5x10 4 kg 3. 4.7x10 4 kg 4. I don’t know because I can’t calculate it 0 of 20

24. To calculate the mass of an unknown planet, a satellite is sent into orbit around it at a distance of 3.45x10 6 m from its center. If the satellite is moving at a speed of 3.74x10 5 m/s, what is the mass of the planet? 1. 1.93x10 22 kg 2. 7.23x10 27 kg 3. 8.25x10 27 kg 4. 3.69x10 29 kg 0 of 20

25. Tom has a mass of 70 kg, Sally has a mass of 50 kg. Tom and Sally are standing on a dance floor 20 m apart. Sally looks up and sees Tom. She feels an attraction. Assuming it is gravitational, find the attraction. 1. 1.17x10 -8 N 2. 2.74x10 -8 N 3. 4.62x10 -10 N 4. 5.84x10 -10 N 0 of 20

26. Two particles of equal mass are 1 m apart and attract each other with a gravitational force of 5.54x10 -71 N. What is the mass of each particle? 1. 4.73x10 -29 kg 2. 9.11x10 -31 kg 3. 1.81x10 -30 kg 4. 9.46x10 -32 kg 0 of 20

27. Two spheres are placed so that their centers are 2.6 m apart. If the gravitational force of a attraction between them is 2.75x10 -12 N, what is the mass of each sphere if one is twice the mass of the other? 1. 0.37;0.74 kg 2. 0.23;0.46 kg 3. 0.27;0.55 kg 4. 0.14;0.27 kg 0 of 20