1. How do we explain Newton’s Law of Gravitation
Ch 12 Notes
How do we explain Newton’s Law of Gravitation

2. Ch 12 Notes
The Apple & the Moon
Isaac Newton realized that the motion of a falling apple and the motion of the Moon were both actually the same motion, caused by the same force - the gravitational force.

3. Universal Gravitation
Ch 12 Notes
Universal Gravitation
Newton’s idea was that gravity was a universal force acting between any two objects.

4. At the Earth’s Surface W = mg
Ch 12 Notes
At the Earth’s Surface
Newton knew that the gravitational force on the apple equals the apple’s weight, mg, where g = 9.8 m/s2.
W = mg

5. Universal Gravitation
Ch 12 Notes
Universal Gravitation
From this, Newton reasoned that the strength of the gravitational force is not constant, in fact, the magnitude of the force is inversely proportional to the square of the distance between the objects.

6. Universal Gravitation
Ch 12 Notes
Universal Gravitation
Newton concluded that the gravitational force is:
Directly proportional to the masses of both objects.
Inversely proportional to the distance between the objects.

7. Law of Universal Gravitation
Ch 12 Notes
Law of Universal Gravitation
In symbols, Newton’s Law of Universal Gravitation is:
Fgrav = G
Where G is a constant of proportionality.
G = 6.67 x N m2/kg2 Mm
r 2

8. Calculate the following
Calculate the gravitational force between two 2 kg objects which are separated by a distance of .5 m.
Calculate the gravitational force of attraction between the earth and the moon. (Look up values in the reference table)
Fg=Gm1m2/r2
Fg=(6.67x10-11 Nm2/kg2)(2 kg)(2 kg)/(0.5m)2
Fg=1.06 x 10-9 N
2) Fg=Gm1m2/r2
Fg=(6.67 x N m2 /kg2 )(5.98 x 1024 kg)(7.35 x 1022 kg)/(3.84 x 108 m)2
Fg=2 x 1020 N

9. Earth and Moon
Compare the force that the Earth exerts on the moon with the force that the moon exerts on the Earth. Draw the gravitational force acting on each object.

10. Turn and Talk: State what happens to the gravitational force of attraction between two objects when you do the following:
Double the mass of object 1.
Double Fg (2Fg )
2. Double the mass of both objects.
Quadruples Fg (4Fg)
3.Double the distance between both objects.
Quarters Fg (1/4 Fg )
4.Triple the distance between both objects.
Ninths Fg (1/9 Fg )
5.Double the mass of both of objects and double the distance between both objects.
Same Fg (Fg)

11. Where does Fg = mg come from?
Calculate the following:
GME/RE2 = (6.67 x N m2/kg2 )(5.98 x 1024 kg)/(6.37 x 106 m)2
=9.8 m/s2

12. Review Book Questions
104) 3
105) 1/9 F
106) 4
107) 3
108) B