1. Newton’s Universal Law of Gravitation

3. Factors Affecting the
Gravitational Force
mass
distance

4. force varies directly with masses
decrease mass 
decreased
force
force varies directly with masses
Fg α m1 m2

5. Distance r
increase r 
force
decreased

6. Force varies
inversely with
distance squared
Fg α 1/r2

7. Fg α m1m2
Fg α 1/r2
m1 m2
Fg α r2 Fg
slope = G
m1 m2/r2

8. G = 6.67 x 10-11
N m2/kg2

9. A 1000 kg car and a 2000 kg truck
are 0.50 m apart.
Gravitational force:
5.3 x 10-4 N

10. Computing mass of Earth
radius of Earth: x 106 m
1.00 kg mass has a weight of 9.81 N
mass of Earth:
5.97 x 1024 kg

11. 2F 4F

12. ¼ F 4F

13. F

14. “g”
gravitational field – weight per mass
wtg Fg
g = =
mass m
G M = r2
M = planet mass

15. Effect of changing variables GM g = ----- r2
if M doubles:
if r doubles:
if M & r doubles:
if r becomes ½: 2g
¼ g
½ g 4g

16. radius: 53% radius of Earth gravitational field for Mars?
mass: 11% mass of Earth
radius: 53% radius of Earth
gravitational field for Mars?
0.39 gE = N/kg

17. Net gravitational force on bottom mass?
√3 GM2/s2

18. G m1 m2 Fg = ---------- = weight r2
What would happen to your weight if:
Earth had twice mass
but the same radius:
Twice weight
Earth had twice radius
but same mass:
¼ weight

19. What is “g” at top of Mt. Everest
(8848 m elevation)?
9.77 N/kg = 9.77 m/s2