1. Gravitation

2. Universal Law of Gravitation Every mass attracts every mass in universe - F g. F g directly proportional to mass. –Doubling the mass of one object doubles the force of gravity between the two objects. F g decreases with the square of the distance between their centers. –Doubling distance between two objects weakens force of gravity by a factor of 2 2 (or 4).

3. NEWTON’S UNIVERSAL LAW OF GRAVITATION F g = GM 1 m 2 r2r2 G universal constant = 6.67 x 10 -11 N m 2. kg 2. M 1 m 2 are mass of objects - kg. r is distance between ctrs m. When standing on planet surface, r = planet radius.

4. Make a sketch graph of F g (Y axis) vs. distance (X axis). As 2 objects get further apart, what happens to F g ? F g D between objects

5. For any two particular masses, the gravitational force between them depends on their separation as: distance between the masses increasing magnitude of the gravitational force between 2 fixed masses as the separation between the masses is increased, the gravitational force of attraction between them decreases quickly.

6. Gravity and Weight The weight of an object is a measure of the gravitational force the object feels in the presence of another mass. If one mass is large we s/t call it M and the small mass m.

7. Ex 1: Write the equation we use to calculate weight on Earth. F g = mg. Calculate the weight of 1-kg object on Earth. Calculate gravitational attraction between the Earth & the same 1-kg object. Use your tables to find Earth’s mass & radius.

8. Solution F g = GMm/r 2. F g = (6.67 x 10 -11 )(5.98x10 24 kg)(1kg) (6.37 x 10 6 m) 2. 9.8 N THE SAME VALUE!

9. 2. Use the Universal Law of Gravity to find the weight of a 50-kg person in Newtons on Earth? 3. What would be the weight of the 50-kg person on a planet whose radius is 3 x 10 6 m. and whose mass is 6 x 10 22 kg? 4. What is g, the accl of gravity on that planet?

10. For a 50 kg person: W= F g = mg (50 kg) (~10 m/s 2 ) = 500 N.

11. For a 50 kg person on the new planet: W = mg = GMm. r 2. (6.67x10 -11 )(6 x 10 22 kg)(50kg). (3 x 10 6 m) 2 W = 22.2 N

12. 4. Find the distance between a 0.3 kg ball and a 0.4 kg ball if the gravitational force between them is 8.92 x 10 -11 N. 0.3 m

13. Trick for finding F if a variable is doubled, halved etc. Write the equation out. Replace any variable that is not changing with the number 1 (as a place holder). Replace any variable that is doubled with the number 2, any that is halved with the number ½, etc. Solve the equation with the replacements. Your answer is the factor by which to multiply F. Ex: if your answer is 3, then F is tripled, if it is ¼ then it is quartered…etc.

14. 5. What happens to F g between 2 masses A & B if: Mass A is tripled? Mass A is doubled and mass B is halved? The distance between their centers is doubled? Mass A is tripled and the distance between their centers is tripled?

15. Hwk textbook: Read 263 – 265 do pg 265: prac prb’s 2,3

16. Film Clips Mech Universe apple and moon.http://www.youtube.com/watch?v=JCh9uXy8 PHI Isaac Newton 15 min.http://www.youtube.com/watch?v=JCh9uXy8 PHI

17. Concept Check 1: How does a person’s weight differ at 100 km above the Earth’s surface compared with at the surface? 1. The weight is always less than their weight at the surface. 2. Their weight is more than their weight at the surface. 3. Their weight is the same as at the surface.

18. Gravitational Field: A region of space where mass feels F g toward center of planet or star. Each point has a certain degree of pull.

19. Gravitational Field Vectors

20. A region of space where mass feels gravitational force. g the gravitational field measured in N/kg. It is how hard (N) gravity pulls on each kg of mass affected by it. Gravitational field strength (g) Same as accl of grav. g = GM/r 2. g = Fg/m Gravitational Field

21. Ex 1. What is the gravitational field strength at a point where a 10-kg mass has a weight of 25- N? Field strength is the same as accl grav! g = F g m. 25-N/10-kg g = 2.5 N/kg.

22. 2. Calculate the gravitational field strength at a point 9,000 km above the Earth’s surface. Find r. 6.37 x 10 6 m + 9000 x 10 3 m 1.537 x 10 7 m g = GM/r 2. (6.67 x 10 -11 )(5.98x10 24 ) / (1.537 x 10 7 m) 2. 1.69 N/kg.

23. 3. An 50-kg object weighs 22.2 N at a point above the Earth. What is the gravitational field strength at that point? F g = mgg = F g /m = 22.2 N = 0.44 N/kg. 50 kg

24. Ex 4. A 60-kg student has a weight of 50-N on planet X. What is the gravitational field strength on planet X? g = F net m g = 50-N 60-kg g = 0.83 N/kg.

25. Grav Einstein http://www.youtube.com/watch?v =4yyb_RNJWUM http://www.youtube.com/watch?v =4yyb_RNJWUM HWK Rb pg 105 #32-38