Law of Universal Gravitation

Gravity Sucks!

The acceleration due to gravity on the International space station is 8.7 m/s2. If an 50 kg astronaut stood on a scale what would it read?

A. 435 N

B. 5.7 N

C. .17 N

D. 0 N

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The “Discovery” of Gravity We’ve all heard the story…

an apple fell on Newton’s head and he discovered gravity.

Most scholars believe that Newton did see an apple fall and it got him wondering about the rules for falling objects.

He wondered if the force that pulled the apple down also affected the Moon.

Remember Newton’s 1st Law He had already explained that straight-line

motion was perfectly natural and moving in a circle required a force

Johannes Kepler had shown that planets and moons moved in an ellipse.

Newton wanted to understand what made them move that way.

His breakthrough was to explain how the same rules apply to little things like apples and big things like the moon.

Making sense of one force and two very different results

We already learned that the apple will accelerate at about 9.8 m/s2 downward

Newton also knew that the moon accelerates toward the Earth at 0.00272 m/s2

Distance is only part of the story Distance has a large effect on the force of gravity

(we’ll explore this more in a minute) Remember, though F = m • a

The force of gravity is also affected by the massor more correctly, both masses

Gravitational Force Gravitational Force is the mutual force of

attraction between particles of matter This force always exists between two masses,

regardless of the medium that separates them It is not just between large masses, like the

sun and the Earth. The chair you are sitting on is attracted to the

person next to you. However, the force of friction between the

chair and the carpet is so great that you don’t move.

Newton’s Law of Universal Gravitation is an example of an inverse-square law

This is because the force decreases the further the two objects get from each other.

The distance is measured from the center of each mass.

221

r

mmGFg

Remember, the Force of gravity (Fgrav) that acts on an object is the same as that object’s weight (in Newtons)

Inverse Square Law

4

1/49

1/9161/16

Inverse Square LawInverse Square Law

At 2d apple weighs

1/4 N

At 3d apple weighs

1/9 N

At 4d apple weighs

1/16 N

At 5d apple weighs

1/25 N

If a large meteor hits the moon, causing it to get closer to the earth. If the moon’s orbits the earth at half of its original radius, would its force be?

A. Double the original force

B. Half the original force

C. Four times the original force

D. One fourth the original force

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Connecting the two formulas

Example #1Find the force of gravity between a 30 kg girl and her 10 kg cat if they are 2 meters apart.

m1 = 30 kg

m2 = 10 kg

G = 6.67 x 10-11 N·m2/kg2

r = 2m

NxF

m

kgkgxF

r

mmGF

g

g

g

9

211

221

100025.5

)2(

10301067.6

Example #2Find the distance between a 0.300 kg billiard ball and a 0.400 kg billiard ball if the magnitude of the gravitational force is 8.92 x 10-11 N.

m1 = 0.3 kg

m2 = 0.4 kg

Fg = 8.92 x 10-11 N

r = ?

cmaboutmr

x

x

F

mmGr

F

mmGr

mmGFr

r

mmGF

g

g

g

g

302996.0

1092.8

400.0300.01067.611

1121

212

212

221

Determine the magnitude of the gravitational force between a baseball player with a mass of 100 kg and Earth (5.98 X 1024 kg), if they are separated by a distance of 5.38 X 106 m.

A. [Option 1]

B. [Option 2]

C. [Option 3]

D. [Option 4]

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Tides Newton also used the inverse square

law to explain the tides. People had known for centuries that the

moon affects the tides. No one until Newton knew how it did

this.

dd-R

d+R

Which of the two forces: moon on left mass (m) or moon on right mass (m) is stronger and why? Fd-R

Tidal Bulges

Ocean tides are the alternate rising and falling of the surface of the ocean that usually occurs in two intervals everyday, between the hours of 7a.m. to 7p.m.

It is caused by the gravitational attraction of the moon occurring unequally on different parts of the earth.