Gravity. 10/5 What comes to mind when you hear the word gravity? Convert the following to scientific notation Distance from Sun: 92,960,000 miles ____.

Gravity

10/5

• What comes to mind when you hear the word gravity?

• Convert the following to scientific notation• Distance from Sun: 92,960,000 miles ____• Estimated Age of universe – 14,000,000,000

• Convert the following to standard form• Speed of light = 9.0 * 108 m/s• Gravitational constant = 6.66*10-11

Multiplying in Scientific Notation

Multiplying…

• The general format for multiplying is as follows…

• (N x 10x)(M x 10y) = (N)(M) x 10x+y

• First multiply the N and M numbers together and express an answer.

• Secondly multiply the exponential parts together by adding the exponents together.

Multiplying…

• Finally multiply the two results for the final answer.

• (2.41 x 104)(3.09 x 102)2.41 x 3.09 = 7.454 + 2 = 6

7.45 x 106

Dividing in Scientific Notation

Dividing…

• The general format for dividing is as follows…• (N x 10x)/(M x 10y) = (N/M) x 10x-y

• First divide the N number by the M number and express as an answer.

• Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number.

Dividing…

• Finally multiply the two results together to get the final answer.

• (4.89 x 107)/(2.74 x 104)• 4.89 / 2.74 = 1.78• 7 – 4 = 3• 1.78 x 103

11/22

1. How do you weigh an elephant using only a board, yourself and a fulcrum?

2. Why do you weigh less on a mountain? (universal gravitation)

10/7

• 1. What factors does the force of gravity depend on?

• 2. How did newton change the way we see gravity?

• 3. What is the difference between weight and mass?

Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree—they are both pulled by Earth’s gravity.

13.1 The Falling Apple

3/7

• What comes to mind when you think of newtons laws?

• 1. inertia • 2. F=M*A• 3. Action reaction

Newton understood the concept of inertia developed earlier by Galileo.• He knew that without an outside force, moving objects continue to move at

constant speed in a straight line. • He knew that if an object undergoes a change in speed or direction, then a

force is responsible.

13.1 The Falling Apple

If the moon did not fall, it would follow a straight-line path.

13.2 The Falling Moon

This original drawing by Isaac Newton shows how a projectile fired fast enough would fall around Earth and become an Earth satellite.

13.2 The Falling Moon

Tangential velocity is the “sideways” velocity—the component of velocity perpendicular to the pull of gravity.

13.2 The Falling Moon

If the force that pulls apples off trees also pulls the moon into orbit, the circle of the moon’s orbit should fall 1.4 mm below a point along the straight line where the moon would otherwise be one second later.

13.2 The Falling Moon

Newton’s theory of gravity confirmed the Copernican theory of the solar system.

Earth orbits the sun like the moon orbits the earth, constantly being pulled in, while tangential velocity is keeping the object in orbit.

13.3 The Falling Earth

Universal Gravitation

• Gravity acts everywhere in the universe. The force that causes an apple to fall is the same force that acts on the moon.

• What factors does gravity depend on

1. What are the two things that cause the moon to orbit the earth?

2. What would happen to your weight, if your radius from the center of the Earth doubled?

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.

13.4 Newton’s Law of Universal Gravitation

The force of gravity between objects depends on the distance between their centers of mass.

13.4 Newton’s Law of Universal Gravitation

Your weight is less at the top of a mountain because you are farther from the center of Earth.

13.4 Newton’s Law of Universal Gravitation

The Universal Gravitational Constant, GThe law of universal gravitation can be expressed as an exact equation when a proportionality constant is introduced. The universal gravitational constant, G, in the equation for universal gravitation describes the strength of gravity.

13.4 Newton’s Law of Universal Gravitation

Philipp von Jolly developed a method of measuring the attraction between two masses.

13.4 Newton’s Law of Universal Gravitation

A simpler method was developed by Philipp von Jolly.• He attached a spherical flask of mercury to one arm of a sensitive balance.• A 6-ton lead sphere was rolled beneath the mercury flask. • The flask was pulled slightly downward.• The gravitational force F, between the lead mass and the mercury, was

equal to the weight that had to be placed on the opposite end of the balance to restore equilibrium.

F, m1, m2, and d were all known, so the ratio G was calculated:

13.4 Newton’s Law of Universal Gravitation

Butter spray travels outward from the nozzle in straight lines. Like gravity, the “strength” of the spray obeys an inverse-square law.

13.5 Gravity and Distance: The Inverse-Square Law

This law applies to the weakening of gravity with distance. It also applies to all cases where the effect from a localized source spreads evenly throughout the surrounding space. Examples are light, radiation, and sound.

13.5 Gravity and Distance: The Inverse-Square Law

Gravitational force is plotted versus distance from Earth’s center.

13.5 Gravity and Distance: The Inverse-Square Law

Field lines represent the gravitational field about Earth.

13.6 Gravitational Field

As you fall into a hole bored through Earth, your acceleration diminishes. The pull of the mass above you partly cancels the pull below.

13.7 Gravitational Field Inside a Planet

Newton showed that the ocean tides are caused by differences in the gravitational pull of the moon on opposite sides of Earth.

13.9 Ocean Tides

This difference in pulls across Earth slightly elongates it. The oceans bulge out about 1 meter on average, on opposite sides of Earth. Because Earth spins once per day, a fixed point on Earth passes beneath both of these bulges each day, producing two sets of ocean tides per day—two high tides and two low tides.

13.9 Ocean Tides

The two tidal bulges remain relatively fixed with respect to the moon while Earth spins daily beneath them.

13.9 Ocean Tides

When the attractions of the sun and the moon are at right angles to each other (at the time of a half moon), neap tides occur.

13.9 Ocean Tides

The Universal Gravitational Constant, GWhat happens to F ifa. One mass is half as muchb. Both masses are twice as much.c. The distance is tripled

Hint, substitute a one for every thing then do what the question is asking you to do.

13.4 Newton’s Law of Universal Gravitation

The size of the sun is the result of a “tug of war” between two opposing processes: nuclear fusion and gravitational contraction.

13.10 Black Holes

When a massive star collapses into a black hole, there is no change in the gravitational field at any point beyond the original radius of the star.

You will learn later that our some never becomes a blackhole…sorry

13.10 Black Holes

• What would happen to the earth if the sun collapsed into a black hole?

• Use the gravity equation to explain why a black hole is so powerful.

A black hole is a place in space where gravity pulls so much that even light can not get out. The gravity is so strong because matter has been squeezed into a tiny space. This can happen when a star is dying.

10 / 8 - Today we will be collecting data for the next CER (Claim evidence reasoning)

1. If you were plotting mass and force, which would be the dependent variable and which would be the independent variable?

2. Which axis would you place them on?

• http://phet.colorado.edu/en/simulation/gravity-force-lab

• Gravitational force is the dependent variable.

• Mass is the independent variable

Mass 1 Mass 2 (kg) Force (10-11N)0 30

303030303030303030

distance force

Copy the following tables in your science notebook.

After completing the first table,

• How to create a graph on microsoft excell

• http://www.youtube.com/watch?v=Xn7Sd5Uu42A

mass 1 force0 0

10 3.00E-1020 1.05E-0930 1.57E-0940 2.09E-0950 2.62E-0960 3.14E-0970 3.66E-0980 4.19E-0990 4.71E-09

100 5.23E-09

0 20 40 60 80 100 1200

0.000000001

0.000000002

0.000000003

0.000000004

0.000000005

0.000000006

f(x) = 5.31272727272727E-11 x − 5.99999999999998E-11R² = 0.998762262879643

Force vs Mass

forceLinear (force)

Mass in KG

Forc

e 10

-̂11

N

How to make a line graph on Microsoft excel

• Type the horizontal independent variable values in the left hand column,

• Type the dependent y-values in the right column

• Highlight numbers• Go to insert – scatter – smooth column• Enter in Labels and titles • - left click on line – click add trendline• Click on display equation on chart, and add

r-square value

10/9

• What is the main pattern that you noticed from your data?

• Claim Question: What affect does mass and distance have on the force of gravity?

• What would happen to your weight if the volume of the earth was smaller but the mass was the same?

TomorrowGravity quizNotebook check

10/9

Evidence• Label your graph axis, include title• Graphs should be continuous, can you think of

why. • Include diagrams• Include credits to where you got your data if from

another source

0 20 40 60 80 100 1200

0.000000001

0.000000002

0.000000003

0.000000004

0.000000005

0.000000006

f(x) = 5.31272727272727E-11 x − 5.99999999999998E-11R² = 0.998762262879643

Force vs Mass

forceLinear (force)

Mass in KG

Forc

e 10

-̂11

N

Tips on writing your CER report

• Use all vocabulary on wall

• See gravity article- explain the universal gravitation equation.

• Check to see if graphs are labeled• Give theoretical examples. If I weighed 100 pounds

on earth, if I double the distance my weight would be reduced by……

• Check through rubric

• Sample discussion for reasoning section of your paper

• If an object weighted 400 newtons (about 100 pounds) what would the new weight if the distance between the two spheres is halved?

Mass 1 (Kg) Force (10-11N)0 010 3020 10530 15740 20950 26260 31470 36680 41990 471

Distance (m) Force (10-11 N)

2.5 8983 5793.5 4354 3394.5 2615 2305.5 1826 1516.5 129

Claim Question: What affect does mass and distance have on the force of gravity?

Copy the following tables in your science notebook.If you have not collected all the data from yesterday

• Which direction does a sun pull on a planet?

The gravitational field strength near a giant star that collapses to become a black hole is the same before collapse (left) and after collapse (right).

13.10 Black Holes

• Force and distance will be two of the variables we will be looking at today. Which one would be considered the independent variable and which would be the dependent variable?

Recent evidence suggests the universe is not only expanding, but accelerating outward. It is pushed by an anti-gravity dark energy that makes up an estimated 73 percent of the universe.

Twenty-three percent of the universe is composed of the yet-to-be discovered particles of exotic dark matter.

The concepts of dark matter and dark energy will continue to inspire exciting research throughout this century.

13.11 Universal Gravitation

The Universal Gravitational Constant, GWhat happens to F ifa. One mass is half as muchb. Both masses are twice as much.c. The distance is tripled

Hint, substitute a one for every thing then do what the question is asking you to do.

13.4 Newton’s Law of Universal Gravitation

Until the middle of the last century astronomers were puzzled by unexplained perturbations (path changes) of the planet Uranus.

The source of Uranus’s perturbation was uncovered in 1845 and 1846 by two astronomers, John Adams in England and Urbain Leverrier in France.

Applying Newton’s law of gravitation, both astronomers concluded that there was a body beyond the orbit of Uranus.

The planet Neptune was discovered.

13.11 What is up with Uranus?

• Are you ready for the quiz?

• Notebook check, dates from

The size of the sun is the result of a “tug of war” between two opposing processes: nuclear fusion and gravitational contraction.

13.10 Black Holes

Blackholes

• Gravity always wins! • Future questions• Do black holes have

mass?

• Finish gravity post test. Use evidence from your computer simulation to support your reasoning in the last question. What comes to mind when you think of universal gravitation?

Keep variable a one and everything a

• Could you survive a plane crash? Why or why not? How could you test this?

• If you dropped a penny from a tall building could it kill a person?

• What did you think of the final?• How do you think you did on the forbidden

kingdom final?• Discuss number five• Introduce astronomy presentations part two:

gravity

• What are some characteristics of a strong presentation?

• Which topic did you decide?

• Today• Study your topic and generate two questions

• What comes to mind when you think of gravity?

This original drawing by Isaac Newton shows how a projectile fired fast enough would fall around Earth and become an Earth satellite.

13.2 The Falling Moon

• What is the main idea behind your presentation?

• What is a future question you can ask based on your presentation?

• If you weight 160 pounds on the Earth’s surface what would be your weight if you climbed a ladder that was as long as the earths radius?

The moon was already known to be 60 times farther from the center of Earth than an apple at Earth’s surface.

• The apple will fall 5 m in its first second of fall.• Newton reasoned that gravitational attraction to Earth must be “diluted” by

distance. • The influence of gravity should be diluted to 1/60 of 1/60.• In one second the moon should fall 1/(60)2 of 5 m, which is 1.4 millimeters.

13.2 The Falling Moon

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.

13.4 Newton’s Law of Universal Gravitation

The magnitude of G is given by the magnitude of the force between two masses of 1 kilogram each, 1 meter apart: 0.0000000000667 newton. (In scientific notation: G = 6.67 × 10−11 N·m2/kg2)

• Planet Semimajor axis (1010m)PeriodT (y)T2/a3(10-34y2/m3)

• Mercury 5.79 0.241 2.99• Venus 10.8 0.615 3.00• Earth 15.0 1 2.96• Mars 22.8 1.88 2.98

• Jupiter 77.8 11.9 3.01• Saturn 143 29.5 2.98• Uranus 287 84 2.98• Neptune 450 165 2.99• Pluto 590248 2.99

• Kepler’s third law • T2/ a3 period

squared = axis cubed

3/14

• Are you ready for the quiz?

• What are two ways of reducing your weight without exercise or dieting?

• Notebook check # of days since 3/3

• Hints• Weight is the same thing as force

• What topic did you choose?

• What are some strong communication skills?

• What are some strong listening skills

The force of gravity between objects depends on the distance between their centers of mass.

13.4 Newton’s Law of Universal Gravitation

12/1/10

• Think of two questions that your presentation will answer.

12/2 warm up

• Is your presentation ready?

• What is one part that could use work?

• Take about 10 minutes to practice your explanations with your group members