1. PHYS16 – Lecture 26 Gravitation November 8, 2010

2. Review of Last Week…

3. Practice Question 1 I want to use a wheelbarrow to move 30 kg of yard waste with a center of mass 0.2 m from the wheel axle. If the handle is located at 1 m from the wheel axle how much force should I use to keep the wheelbarrow lifted? A)300 N B)60 N C)50 N D)1500 N What is my mechanical advantage? F=(30kg)(9.8 m/s^2)(0.2 m)/(1 m) = 60 N MA= 5

4. Practice Question 2 You have a meter stick that balances at the 50- cm mark. Is it possible for your meter stick to be inhomogeneous? A)Yes B)No C)Don’t know

5. This Week Newton’s law of Gravity Gravitational Potential Energy Satellites Kepler’s Laws of Planetary Motion – Orbital Shape – Orbital Areas – Orbital Period

6. Gravitational Force

7. Newton’s law of Gravity Gravity – an attractive force between two masses G= gravitational constant = 6.674E-11 Nm 2 /kg 2 Acts at the center of mass http://scienceblogs.com/startswithabang/upload/2009/06/the_last_100_years_1919_einste/300px-NewtonsLawOfUniversalGravitation.svg.png

8. Gravity – in the heavens and on earth The moon and a falling apple behave in the same way… g apple =9.81 m/s 2 g moon =0.00272 m/s 2 =g apple /3600

9. Disputing Gravity There is a force of attraction between all objects across empty space, proportional to m and to M and to 1/r 2. Required given Newton’s system of accelerations being enacted by forces Adapted from Physics for Poets by Robert March Proof: apples, moon, celestial bodies fall towards each other Proof: 130 years later by Cavendish, but at the time seemed nice not to distinguish between an apple and a planet Proof: None at the time. Galileo said there was no dependence of gravity on mass. Later, Cavendish experiment proves. Proof: Comparison of moon’s acceleration to that of an apple, Kepler’s Laws Proof: Cavendish experiment. However, no way to measure mass of the sun or planet independently.

10. Disputing Gravity There is a force of attraction between all objects across empty space, proportional to m and to M and to 1/r 2. Adapted from Physics for Poets by Robert March So called “Spooky action at a distance.” Einstein later shows that gravity leads to curvature in space-time. Is there a gravitational particle? Is gravity just a product of entropy?

11. Example Question: Gravity on Jupiter What is the weight of a 65 kg person on Jupiter? (R J =7.15E7 m, M J =1.9E27 kg)

12. Example Question: Mars and the Earth How big is the gravitational force between Mars and the Earth? (r=1.36E8 km, M M =6.42E23 kg, M E =5.97E24 kg) So why doesn’t Mars revolve around the Earth?

13. Gravitational Potential

14. Gravitational Potential Energy Potential Energy associated with being in a gravitational field

15. Satellites

16. Weightlessness Why do astronauts feel weightless? Isn’t there still a force of gravity on them? Yes, just not a normal force! So why doesn’t Moon fall into earth?

17. Centripetal Force and Gravity For an object (like a satellite) in circular motion due to gravity F c = F G http://qwickstep.com/search/earth-orbit-around-the-sun.html

18. Example Question: Moon Energy If the Moon-Earth distance were to shrink what would happen to the Moon’s kinetic energy? A)Increase B)Stay the same C)Decrease

19. Example Question: Moon Period If the Moon-Earth distance were to shrink what would happen to the period of the moon? A)Increase (Greater than ~28 days) B)Stay the same at ~28 days C)Decrease (Less than ~28 days)

20. Orbital Energy Gravitational potential energy increases as distance increases Kinetic energy decreases as distance increases So, why do higher orbitals have more energy?

21. Example Question: Satellite A Satellite orbiting the Earth wants to go to a lower orbit. What should the satellite do? A) Nothing. It is falling toward the earth. B) Turn on rocket thrusters to accelerate and increase speed, then move to lower orbital. C) Turn on rocket thrusters to decelerate and decrease speed, then move to lower orbital

22. Escape velocity Velocity needed to “escape” the gravitational force Doesn’t depend on mass of object, only depends on the gravitational field…

23. Main Points Gravitational Force = GMm/r 2 Centripetal force = gravitational force for object in orbit Gravitational Potential = GMm/r – To get further from a massive object requires more energy – Gravitational potential = zero at infinity