Conceptual Physics – Chapter 12

Galileo  Inertia (Newton made it a law later)  Mass does not effect acceleration of gravity  Sun and not the earth was the center of our solar system I discovered it a LONG time ago!

Kepler  Supplemented Galileo’s view of the solar system  Came up with 3 planetary laws I built upon Galileo’s awesome ideas!

THANK YOU! I AM awesome. Tell that to the courts! Was under house arrest for some of my ideas! Small minded creatures!

 Newton  Famous for apple falling on his head- may or may not be true  Made many observations about the world around him  Came up with the Universal Gravitation Law- force of gravity is inversely proportional to the distance between them I make this look good!

He determined that the moon is simply moving in a straight line. But because of gravity it’s path becomes curved. The moon is simply falling with the curvature of the earth.

 It wasn’t until after Newton invented a new branch of mathematics, calculus, to prove his center-of- gravity hypothesis, that he published the law of universal gravitation.  Newton generalized his moon finding to all objects, and stated that all objects in the universe attract each other.

 The tangential velocity of Earth about the sun allows it to fall around the sun rather than directly into it.  All satellites (yes the planets are considered satellites) work this way  Any object without a significant tangential velocity has long ago fallen into the sun.

m is the mass of one of the objects. m is the mass of the other object. r is the radius of separation between the center of masses of each object. F G -----is the force of attraction between the two objects.

 Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object.  Newton deduced that the force decreases as the square of the distance between the centers of mass of the objects increases.

 Consider an imaginary “butter gun” for buttering toast. Melted butter is sprayed through a square opening exactly the size of one piece of square toast The gun deposits a layer of butter 1 mm thick. Twice as far from the butter gun, butter would cover twice as much toast vertically and twice as much toast horizontally. Since the butter has been diluted to cover four times as much area, its thickness will be one quarter as much, or 0.25 mm.

 Twice as far from the gun, the butter is only 1/4 as thick.  Three times as far, it will be 1/9 as thick.  1/9 is the inverse square of 3.  When a quantity varies as the inverse square of its distance from its source, it follows an inverse-square law.

 The greater the distance from Earth’s center, the less an object will weigh. An apple that weighs 1 N at Earth’s surface weighs only 0.25 N when located twice as far from Earth’s center. When it is 3 times as far, it weighs only 1/9 as much. But no matter how great the distance, Earth’s gravity does not drop to zero. The gravitational influence of every object, however small or far, is exerted through all space.

 How does the force of gravity change with distance?  If the distance between 2 objects triples what happens to the force of gravity?  Suppose that an apple at the top of a tree is pulled by Earth’s gravity with a force of 1 N. If the tree were twice as tall, would the force of gravity on the apple be only 1/4 as strong? Explain your answer.

 As distance increases the force of gravity decreases.  If distances triples, the force of gravity would decrease to 1/9 of its original strength (inverse square law)  No, the twice-as-tall apple tree is not twice as far from Earth’s center. The taller tree would have to have a height equal to the radius of Earth (6370 km) before the weight of the apple would reduce to 1/4 N.

Cavendish  Confirmed Newton’s Universal Gravitational Law  determined the mass of the earth  Determined the value of the gravitational constant- G in Newton’s equation I’m the ‘G’ who measured G!

 Cavendish’s first measure of G was called the “Weighing the Earth” experiment. Once the value of G was known, the mass of Earth was easily calculated. G=6.67 x The force that Earth exerts on a mass of 1 kilogram at its surface is 10 newtons. The distance between the 1-kilogram mass and the center of mass of Earth is Earth’s radius, 6.4 × 10 6 meters.   from which the mass of Earth m 1 = 6 × kilograms.

It is 6 × kilograms!!!! What does that look like written out?!?? kg WOW! Not something I have time to do!

Scientific Notation at it’s best! OR you could write When dealing with really big or really small numbers which would you prefer?

1 st -Move the decimal between the first 2 significant digits. So 12,067,800,000 becomes you can’t omit the significant digits. 2 nd - Determine which way and how many place values you moved the decimal. 12,067,800,000. became when we moved the decimal to the left 10 place values. 3 rd It is the number times ten to the number of places you moved the decimal. So it will be x

Move the decimal left it is positive exponent (making a big number manageable) move it to the right (making a small number manageable) give you a negative exponent x x v x x 10 -7

 1. 5,000,089,700,000    4. 4,500   ,400,000

 Must use it to solve for the force of gravity using Newton’s Universal Gravitation Equation

 1. Two basketball players are 30 meters apart during their game. Player one’s mass is 83kg, player two’s mass is 90kg. What is the force of gravity between the two?  2. What would happen to the force if they were half the distance apart?

 Two basketball players are 30 meters apart during their game. Player one’s mass is 83kg, player two’s mass is 90kg. What is the force of gravity between the two?   = 6.67x (83 x90)  30 2  = 5.54 x  Not much force between the two as we would expect!

 2. What would happen to the force if they were half the distance apart?  According to the inverse square law, at half the distance the force should increase by 4 times  If you do the math it works!  At 30 meters f=5.54 x  At 15 meters f=2.22 x  5.54 x x 4 = 2.22 x  So half the distance 4 times the amount of force!!