1. The Universal Law of Gravitation
Mr.Rockensies
Regents Physics

2. Gravity r A remote force of mutual attraction between any two masses
Magnitude of the force depends on the distance between the masses and their size m1 m2 r
Gravity
Distance between the centers

3. Newton’s Law of Universal Gravitation
Fg = Gm1m2/r2
Works everywhere for all masses
Fg = The force due to gravity
m1 and m2 = The masses
r = the distance between the center of the two masses
G = The Universal gravitation constant = 6.67x10-11N·m2/kg2
G can be found on the front of the reference table
Newton’s Law of Universal Gravitation

4. The forces due to gravity are small for ordinary objects
The forces due to gravity are small for ordinary objects. In order to see a large noticeable force, there needs to be large scale masses – planets, moons, stars, etc.
G was measured in a Cavendish Experiment a century after Newton
Newton’s Universal Law of Gravitation

5. F F r2 r
Inverse Relationship Inverse Square Relationship
Relationships

6. Weight Revisited 100 kg box Fg = (GmEmbox)/rE2 mE = 5.98 x 1024 kg rE
rE = 6.37x106 m
both on reference table rE
Earth
Fg = (6.67 x 10-11N•m2/kg2)(5.98 x 1024 kg)(100 kg)
(6.37x106 m)2
Fg = 983 N – same as Fg = mg = 100(9.81) = 981 N
Weight Revisited

7. Weight off of Earth 2rE Gravity is an inverse-square law Fg α 1 r2
100 kg
Earth
Fg α 1 r2
Weight off of Earth

8. What do we do when a question asks…
A question asks you what will happen to the Force of Gravity when the radius between two objects is doubled. How do you find out what will happen?
If we multiply r by… We multiply Fg by…
/22 = ¼
/32 = 1/9
/102 = 1/100
½ /(½)2 = 1/¼ = 4
So in the example from the previous slide, a 100 kg box 2rE from Earth’s center weighs 981/22 = 245N
What do we do when a question asks…

9. The Explanations of Gravity
Newton’s (what we will use)
Space around a mass is altered to be a gravitational field. The field exerts a force on a second mass.
Einstein
Space is warped by mass. Traveling in a straight line is impossible. Objects orbit by the following curves in space.
Modern
Masses exchange particles (called Bosons) which bind them together. M Fg m1 m2 m
The Explanations of Gravity

10. How does our weight change when we ride in an elevator?
Apparent Weight on an Elevator
How does our weight change when we ride in an elevator?

11. Apparent Weight
Scales will read normal force, which is the “apparent weight”
Free-Body Diagram
Elevator
FN = Fscale m
scale Fg

12. 4 cases:
Standing still; v = 0, a = 0,
FNET = 0 FN = Fg
2) Moving at a constant speed (up or down) a = 0
FNET = 0 FN = Fg
Accelerating up, FNET is up therefore FN > Fg
scale reads above true weight – you feel heavier
Accelerating down, FNET is down therefore Fg>FN
scale reads below true weight – you feel lighter
If the elevator is in free fall, FN = 0!

14. Apparent Weight on InclineFN
F||
scale
F | θ Fg
Scale reads: FN = F
FN = Fgcosθ always less than Fg |