1. The Law of Universal Gravitation

2. Today you need to know…
The difference between the acceleration of gravity and the force of gravity.
How to calculate the force of gravity between two objects.
Fully understand that forces are not alone – they always act in pairs.
All unbalanced forces are caused by acceleration.

3. LAW OF UNIVERSAL GRAVITATION Gravity is universal – everything is attracted to everything else – forces come in pairs. This attraction can be measured and is based on two things: 1. Mass 2. Distance

4. mass of object one (kg) mass of object two (kg)
G = 6.67 x Nm2/kg2
Gravitational Constant
mass of object one (kg)
The Force of Attraction
(N)
mass of object two (kg)
distance between the centers of the two objects (m)

5. Understanding relationships between variables
DIRECTLY
INVERSELY
The greater the mass the greater the force
The force decreases as the square of the distance increases

6. Understanding relationships between variables
How to solve problems regarding relationships between variables.
1. IGNORE G – it is always the same
2. Set up an original problem where everything is equal to 1
ex. 1= 1 x 1 12
3. Change only what the problem says.
EXAMPLE PROBLEM:
Two objects gravitationally attract each other with a force of 2 N. IF the distance between their centers is tripled, the new force of attraction is _______________ N.
solution
1= 1 x 1 = 1
So the force is reduced by a factor of 9. 2/9 =
The greater the mass the greater the force
The force decreases as the square of the distance increases

8. Rules for Scientific Notation
THE MATH
Rules for Scientific Notation
Final answer has only one digit to the left of the decimal
Use the EE key

9. Constants G = 6.67 x 10-11 Nm2/kg2 This is the Gravitational Constant
me = mass of the Earth
(5.98 x 1024 kg)
re = radius of the Earth
(6.37 x 106 m)

10. EXAMPLE :Find the force between two objects 6371 km apart
EXAMPLE :Find the force between two objects 6371 km apart. The first object has mass 70 kg, the second object has mass 6 x 1024 kg.
F = (6.67 x ) (70) (6 x 1024 ) =
63712
2.8 x1016
4.06 x 10 7
F= 6.90 X 10 8 N
EXAMPLE: Two objects each have a mass of 1x10-3 kg. The force between the objects is 400 N. What is the distance between them?
r = (6.67 x ) (1x10-3) (1x10-3) =
400
6.67 x101-17
400

11. The Falling Apple
Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree—they are both pulled by Earth’s gravity.

12. Newton’s Law of Universal Gravitation
Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance.

13. What is the force between the Earth and a mass of 1200 kg if the mass is meters above the Earth’s surface.

14. The Mass of the Earth https://www.youtube.com/watch?v=9yMQM5AN8mc
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