Physics Chapter 9 - Gravity

Newton and Gravity

So this guy Newton…

Devised three laws of motion.

Realized that all objects accelerate towards the ground at the same rate, g.

Recognized the presence of some force that kept the “heavens” moving in their elliptical paths.

Quick Review of Newton’s discoveries…

Laws 1st Law – The Law of Inertia 2nd Law – acceleration = Force mass 3rd Law – Forces occur in action-reaction pairs

Acceleration due to gravity, g All objects regardless of their mass are accelerated

equally by gravity Since this acceleration is so important to the motion

of all objects on the surface of the earth it is assigned g = 9.8 m/s2 (or 10 m/s2)

Newton & Gravity

Isaac Newton was the first to deduce that the force that makes an apple fall is the same force that keeps the moon in its orbit.

His law of gravitation states that every object pulls on every other object based on their mass and distance between them

But then he asked himself… Does the falling apple exert a force

on the earth? Why doesn’t the moon fall into the

earth?

Answers…

Apple DOES exert a force on the Earth!Does the Earth notice? Why?

The moon IS falling!HUH?!?

Newtonian Mountain

Newton’s Universal Law of Gravitation

What do you think it depends on?

Newton’s Universal Law of Gravitation

Depends on…Mass of the two attracting objects (m1 & m2)

Directly proportionalDistance between the two objects (d)

Inversely proportionalUniversal Gravitation Constant (G)

G = 6.67 x 10-11 Nm2/kg2

1 22

mmF G

d

Example #1

A 10,000 kg asteroid is close to a 20,000 kg asteroid. If their centers are 100 m apart, what is the force of gravity between them?

The Story of 9.8…

From before we know that a 1 kg mass exerts a force of 9.8 N on the Earth because…

Fweight = mass x gravity = (1kg)(9.8 m/s2)

Where did this “9.8” come from in the first place?

The Story of 9.8…

F = mobject x 9.8

1 22 2

becomes... object Earth

Earth

m mmmF G F G

d r

Earth

1 kg mass

distance = radius

26

2411

1038.6

1097.51067.6

objectmF

Acceleration due to Gravity at Different Places on Earth…

g varies slightly due to differences in the distance from the center of the earth (altitude or latitude)North Pole g = 9.832 m/s2

Panama Canal g = 9.782 m/s2

New York City g = 9.803 m/s2

Denver g = 9.796 m/s2

Acceleration due to gravity on Different Planets…

Jupiter 2.54 x gNeptune 1.20 x gSaturn 1.06 x gUranus 0.92 x gEarth 1.00Venus 0.92 x gMercury 0.38 x gMars 0.38 x gPluto uncertainMoon 0.16 x g

These depend on the planet’s mass and radius.

Newton and Gravity Questions

1. When do you weigh more; at the bottom of Death Valley, or atop the high Sierras? Why?

2. What is the magnitude of gravitational force between two 1-kilograms objects that are 1 meter apart?

3. What do we call the gravitational force between the Earth and your body?