Transcript Gravity - South High School

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 = 7.45
4+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?
13.1 The Falling Apple
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.
3/7
• What comes to mind when you think
of newtons laws?
• 1. inertia
• 2. F=M*A
• 3. Action reaction
13.1 The Falling Apple
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.
13.2 The Falling Moon
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.
13.3 The Falling Earth
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.
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?
13.4 Newton’s Law of Universal Gravitation
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, G
The 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:
13.5 Gravity and Distance: The Inverse-Square Law
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.
13.6 Gravitational Field
Field lines represent the gravitational field about Earth.
13.7 Gravitational Field Inside a Planet
As you fall into a hole bored through Earth,
your acceleration diminishes. The pull of
the mass above you partly cancels the pull
below.
13.9 Ocean Tides
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.
13.4 Newton’s Law of Universal Gravitation
The Universal Gravitational Constant, G
What happens to F if
a. One mass is half as much
b. 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.
13.10 Black Holes
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
• 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
• If you were plotting mass and force,
which would be the dependent variable
and which would be the independent
variable?
• Which axis would you place them on?
• http://phet.colorado.edu/en/simulation
/gravity-force-lab
• Gravitational force dependent
variable
• Mass independent variable
Copy the following tables in your science notebook.
After completing the first table,
Mass 1
Mass 2 (kg)
0
30
30
30
30
30
30
30
30
30
30
Force (10-11N)
distance
force
Force vs Mass
y = 5E-11x - 6E-11
R² = 0.9988
6E-09
Force 10^-11 N
5E-09
4E-09
3E-09
force
2E-09
Linear (force)
1E-09
0
-1E-09
0
20
40
60
80
100
Mass in KG
mass 1
• How to create a graph on
microsoft excell
• http://www.youtube.com/watch
?v=Xn7Sd5Uu42A
120
force
0
0
10
3.00E-10
20
1.05E-09
30
1.57E-09
40
2.09E-09
50
2.62E-09
60
3.14E-09
70
3.66E-09
80
4.19E-09
90
4.71E-09
100
5.23E-09
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
• Which direction does a
sun pull on a planet?
13.10 Black Holes
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).
• 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?
13.11 Universal Gravitation
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.
3/13
• What is the relationship between gravitational
force and distance? (is it reduced by, directly
proportional to, independent of)
• What would happen to your weight if the
volume of the earth was smaller but the mass
was the same?
Tomorrow
Gravity quiz
Notebook
check
13.4 Newton’s Law of Universal Gravitation
The Universal Gravitational Constant, G
What happens to F if
a. One mass is half as much
b. 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.
13.11 What is up with Uranus?
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.
• Are you ready for the
quiz?
• Notebook check,
dates from
13.10 Black Holes
The size of the sun is the result of a “tug of war” between two opposing
processes: nuclear fusion and gravitational contraction.
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?
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.
• 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?
13.2 The Falling Moon
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.
13.4 Newton’s Law of Universal Gravitation
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.
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
590 248
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
13.4 Newton’s Law of Universal Gravitation
The force of gravity between objects depends on the distance between their centers of
mass.
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