Gravity & Motion (Newton's Law of Gravitation):

Objectives:

1. Given a vector, resolve it into vertical and vertical components.

2. For a projectile, describe the changes in the horizontal and vertical components of its velocity, when air resistance is negligible.

3. Explain projectile motion.

Key Terms:

component resolution projectile

Web Resources:

Notes:

Nearly every living person realizes that the force of gravity (weight) is responsible for holding things on earth. It keeps your coffee in your cup, helps create the friction necessary for us to walk and drive, and contributes to the saying "what goes up must come down". Sir Isaac Newton also realized this that day he saw the apple fall. He reasoned that since the apple falls to the ground the moon must also be falling toward the Earth. To figure out this problem Newton made these assumptions:

- The falling apple and the moon are both accelerating, therefore, require a force.
- Since the moon did not fall into the earth it had to be a projectile.
- The apple and the moon were being acted on by the same force, the difference was that the the moon had forward velocity.

Newton called this collective force gravity. Newton theorized that an object with enough sideways (tangential) velocity will orbit the Earth much like the moon. Newton's proof of his gravitational system came with the following measurements.

- Newton reasoned that all things fall at the same speed toward the Earth (already proven by Galileo) so the moon should fall at the same speed as the apple.
- Reasoned that the rates of fall would be affected inversely by the distances between their masses.
- Reasoned that the force of attraction between the two objects would also be affected directly by the size of their masses.

Based on these assumptions, Newton estimated that
since the moon was 60 time farther from the Earth's center than the apple.
Applying his formula (1/(60)^{2}) he calculated that the moon should
fall 1.4mm to the apple's 4.9m. Upon measurement of the moon he was almost
exactly right. Because of criticism and rejection of his ideas, Newton's
work on gravitation was not published for nearly 20 years. Many good
things came from the discovery.

- Acceptance of the Copernican sun centered solar system
- The advent of the branch of mathematics called calculus

Newton's Law of Universal Gravitation

F ~ (M_{1} m_{2})/ d^{2
}or^{ }F = G(M_{1} m_{2})/ d^{2 }(G =
m to the gravitational constant on Earth)

Newton's Law states that there is a gravitational force present between any two objects containing mass. The reason we don't feel the gravitational attraction toward objects around us is that the Earth is so massive compared to everything else that we come in contact with.

- The size of the force is directly related to the masses of the two objects
- The size of the force is indirectly related to the square of the distance between them

The Inverse Square Law

According to Newton's equation (F
~ (M_{1} m_{2})/ d^{2})
as distance increases the force decreases by the inverse of the distance
squared.

(www.achilles.net/~jtalbot/glossary/ inversesquare.gif)

1m F = 1

2m F = 1/4

3m F = 1/9