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

MmFr

2

GMmFr

Keeping Relationships Simple

• Proportions: Compare two quantities while their outcome remains constant. Symbol:

• Inverse relationship means you are comparing two quantities and as one quantity gets larger the other gets smaller.

• F = ma • When the F is kept constant the m is inversely

proportional to the a.

Still Keeping it Simple

Inverse Square relationship means that as one quantity gets larger the other gets smaller by the square of the smaller quantity. F 1/r2

When r goes up, F goes down.

Keep is Simple Direct

• Direct Relationship means that as one quantity gets larger the other gets larger as well.

• F a

• As F increases so does the a.• F = ma, mass will be kept constant.

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

GMmFr

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.

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 xgr x

g m s