1. Inverse Squared Laws

2. Newton and his apple…
You’ve probably heard the story of Isaac Newton and his falling apple.
Pondering this event (maybe) led Newton to discover the theory of gravity.

3. If Newton lived today…
The apple is accelerated from 0 as it hangs on the tree to moving rapidly as it hits the ground.
Thus, by the 2nd law, there must be an unbalanced force acting on this apple to cause the acceleration.

4. Newton’s reasoning – 2 things affect gravitation
Newton reasoned that the more massive two objects were, the bigger the attractive force between them.
He also reasoned that the smaller the distance between the centers of the two objects, the greater the attractive force between them.

5. Newton’s apple math
Written as a math equation:

7. Newton’s UNIVERSAL law…
Could the orbit of the moon around the earth be a result of the centripetal force supplied by Earth’s gravity?
YES! All objects in the universe have gravity (if they have mass)

8. Big G vs. little g… Big G is the universal gravitational constant
G = 6.67 x Nm2
kg2
(Find this on your equations page - write it down, but no need to memorize)
This number is the same for the WHOLE UNIVERSE
Little g is the acceleration due to gravity at Earth’s surface. g = 9.8 m s2

9. Gravity gets weaker with distance
When two objects are moved 3 times farther apart, the force is not 1/3 weaker, it is 1/9 weaker!

10. Visualizing the inverse square law…
Sprayed from 1 meter away
1 square unit
Sprayed from 2 meters away
4 square units

11. Thought experiment… Which spray would be “thicker”?
Sprayed from 1 meter away
Sprayed from 2 meters away
So which spray “force” would be stronger?

12. Try creating a graph of gravitation…
Gravitational force
Distance between objects

14. Sample Problem 1
Calculate the gravitational attractive force between two identical 5 kg spheres with centers 0.8 meters apart.

15. Sample Answer 1
Find the gravitational attractive force between two identical 5 kg spheres with centers 0.8 meters apart?
G = 6.67x10-11 N m2/kg2
So you use the equation
Fg = G*m1*m2 r2
Fg = 6.67x10-11*5*5/0.82
Fg = 2.61x10-9 N

16. Sample Problem 2
Apply logic and Newton’s Law of Universal Gravitation to think this through…
Down in a cave below the surface of Earth, there is…
a. more gravity than at Earth’s surface
b. less gravity than at Earth’s surface
c. the same gravity as at Earth’s surface

17. Sample Answer 2
Apply logic and Newton’s Law of Universal Gravitation to think this through…
Down in a cave below the surface of Earth, there is…
a. more gravity than at Earth’s surface
(since the objects’ centers are closer together, their gravitational attraction will be stronger.)

18. Sample Problem 4
The moon and Earth are attracted to each other by gravitational force. Does the more massive Earth attract the moon with a greater force than the moon attracts Earth? Explain?

19. Sample Answer 4
The force of attraction between Earth and the moon is the same both ways. The Earth’s much larger mass makes the mass of the moon move toward the Earth, but the force between them is the same.

20. Sample Problem 5
If Earth were twice as massive, but remained the same size, what would happen to the value of G and g?

21. Sample Answer 5
If Earth were twice as massive, but remained the same size, G would not change because it is UNIVERSAL.
If Earth were twice as massive but had the same radius, it would accelerate objects toward its center with twice the force, so g would double.
g = G*m/r2

22. The relationship between two charged particles is the same as gravitation it’s an Inverse Squared Law But electrical attractive force can be positive or negative

23. Notice the similarities between the
Law for Gravitational Force
and the
Law for Electrical Force

24. The guy who wrote this law was Charles Augustin de Coulomb
Born in 1736 in France Used a sensitive torsion balance to investigate the forces between charged pith balls.

25. Sample Problem 6
Two charged spheres are hanging from the ceiling, and they separate from each other. What can you say for sure about their charges?
One is positive, one is negative
Both are positive
Both are negative
Both have the same charge

26. Answer 6
Two charged spheres are hanging from the ceiling, and they separate from each other. What can you say for sure about their charges?
Both have the same charge

27. Sample Problem 7
Calculate the resulting electric force between particles A and B if particle A has a charge of -2 C, particle B has a charge of +0.5 C, and the distance between them is 1 m.

28. Answer 7

29. Sample Problem 8
How will the electric force between A and B make them behave?

30. Answer 8
Since A and B have opposite charges, they will move toward each other.

31. Sample Problem 9
If particle A has a charge which is quadrupled, how will this affect the electric force between A and B?

32. Answer 9
Since electric charge is in the numerator of the Coulomb’s Law equation, the resulting force will also be quadrupled.

33. Sample Problem 10
Charged glass rods are placed near a neutral conducting sphere, causing a redistribution of charge on the spheres. Which of the diagram(s) depict the proper distribution of charge of the spheres?

34. Answer 10
Charged glass rods are placed near a neutral conducting sphere, causing a redistribution of charge on the spheres. Which of the diagrams depict the proper distribution of charge of the spheres? A and D