Gravity

Newton rationalized that if the earth puts a force on an apple, then who’s to say that it doesn’t exert a force on the moon?

Contact vs. Non-contact Forces

Newer concept: force

Must be touching acting at a distance (gravity, magnets,

electricity…)

Gravity must be proportional to both masses because of Newton’s 3rd Law (Equal and opposite forces)

F α M m

Newton’s Math ProofForce of gravity must decrease by the inverse square of the distance. F α 1/r2

This is known as the inverse square law! It is repeated in electricity and magnetism!

Combine These!

2

MmF

r

2

GMmF

r

Law of Universal Gravitation

Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distances between them. This force acts along a line joining the 2 particles.

2

GMmF

r

G = gravitational constant (small or large?)G = 6.67 x 10-11 Nm2/kg2

It took 100 years later for this law to be proven. Henry Cavendish performed the experiment. See next slide for a video

Video of Cavendish Experiment

•http://video.google.com/videoplay?docid=7865632513511665648

•This second link will show you the meaning of the Law of Gravitation.

•http://video.google.com/videoplay?docid=3265790422523131277

view 13:00 to 16:05 min.

Click on this link. You do not have to watch the whole video. You can forward the tab to 8:10 and watch up to 11:32 seconds. This will show you where G from F = Gm1m2/r2 comes from.

Sample Problem

A 50 kg girl & a 70 kg boy are 50 cm apart on a park bench. Find the force of attraction…

Field Area around an object that affects other objects.

Gravitational Field

Area around a mass that affects other masses

What represents the gravitational field around the earth?

At Crown Point, the radius of the Earth is 6.37101 x 106 m. If the Earth has a mass of 5.98 x 1024 kg. Then calculate the Earth’s gravitational field in Crown Point.

11 24

2 6 2

2

6.67 10 (5.98 10 )

(6.37101 10 )

9.83 /

GM x xg

r x

g m s