Download Ch. 13 notes 2017

Physics Teacher Notes - Grothaus
Chapter 13 – Universal Gravitation
Circular Motion (excerpts from chapter 10)
Uniform circular motion is the movement of an object at a constant speed around a
circle with a fixed radius. The position at any moment in time is represented by a vector r
(radius). In a given circle, the length of r stays the same, but the direction changes. (constant
velocity??)
Rotation vs. Revolution:
Rotation: When an object turns about an internal axis
Revolution: When an object turns about an external axis.
Examples: ferris wheel? People in the ferris wheel? Skater? Earth? Record / CD?
Velocity and acceleration vectors for something that is rotating around a circle look like this:
Tangential velocity – why is called this? Look at the picture above.
Centripetal Acceleration
Acceleration changes, but is always pointing towards the center of the circle.
“center seeking”
Remember Newton’s second law: F = ma
If there is acceleration, there must be a net force as well.
There is actually a Newton’s second law for circular motion
Fnet  mac This is called, centripetal force
net force is always in the direction of the accel
When I spin the tennis ball, what is providing the force?
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Physics Teacher Notes - Grothaus
Chapter 13 – Universal Gravitation
The tension in the string.
Car turning a sharp corner?
Centrifugal “Force”? - (book doesn’t do a good job with this)
doesn’t exist
This is actually due to inertia. Things stay in a circular motion because of the balance
between centripetal force and inertia.
“Gravity is an attractive field force that acts between objects with mass”
Usain Bolt vs. gravity – minute physics
https://www.youtube.com/watch?v=9YUtFpLpGfk&list=PLED25F943F8D6081C&i
ndex=76
Title: Universal Gravitation
***Everything pulls on everything else.***
Newton didn’t “discover” gravity, but he discovered that it was a universal force. It’s not
unique to Earth.
Remember Newton’s third law? “For every action, there is an equal and opposite reaction”
Gravity is merely a force! If the Earth has a certain gravitational pull on the moon, how
much is the gravitational force of the moon on the Earth? Less, more or equal?
13.1
The Falling Apple
Newton told at least four people that he got the idea of universal gravitation
by seeing an apple fall out of a tree. Nobody knows if it actually hit him on the
head!
Newton understood the concept of inertia, (what is inertia?) and he knew that things
remained at constant speed in a straight line unless acted upon by a force. If
anything changes speed or direction (acceleration), a force is responsible.
a = F/m Newton’s second law
Apple falling towards Earth: accelerates because of gravity
Moon is pulled by the same force of gravity – why doesn’t it fall as well?
The moon is moving, but doesn’t travel in a straight line path. Newton had the
insight to see that the moon DOES fall towards the Earth just like the apple,
for the same reason. Is this true?
13.2
The Falling Moon
Newton realized that if the moon didn’t fall toward the Earth, inertia would
pull it off in a straight line away from the Earth. (Figure 13.2, p. 233)
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Physics Teacher Notes - Grothaus
Chapter 13 – Universal Gravitation
Tangential velocity: if an object is moving in a circular path, its tangential velocity
is the velocity it would be going if it suddenly began moving in a straight line (“cut the string”
holding it in place)
The moon falls in the sense that it falls beneath the straight line it would follow if no force
acted on it.
The moon is actually falling toward Earth but has great enough tangential velocity to
avoid hitting the Earth.
Side note:
Newton’s Test: Hypothesis to Theory – must be tested.
Remember that it doesn’t matter what mass an object has, it will still
fall at 10m / s 2 (accel. due to gravity).
Newton’s test was to see if the moon would “fall” in the same
proportion to the fall of an apple.
Newton’s Calculation: Using geometry, his value did end up to be about
1.4-mm
He was unsure about a lot of things, so stuck all of this in a drawer for 20
years!
After he developed a new branch of math (Calculus), he was
able to prove his center-of-gravity hypothesis, and then he
was able to publish his Law of Universal Gravitation.
13.3
The Falling Earth
Newton’s theory of gravity confirmed the Copernican theory of the solar system!!
Why don’t the planets fall towards the sun?
13.4
Newton’s Law of Universal Gravitation
Newton did not discover gravity, but he did discover that gravity is universal. Everything
pulls on everything else in the universe in a way that involves only mass and
distance.
Newton’s Law of Universal Gravitation can be stated mathematically as follows:
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Chapter 13 – Universal Gravitation
Physics Teacher Notes - Grothaus
The force of gravity is directly proportional to the masses of the two objects and
inversely proportional to the square of the distances between them.
m1m2
d2
Where m1 is the mass of one object, m2 is the mass of the other
Fg  G
object and d is the distance between their centers.
The Universal Gravitational Constant, G:
G  6.67 1011 Nm2 / kg2 = 0.0000000000667 Nm2 / kg2
Measuring G: G wasn’t measured until about 150 years after Newton’s discovery, by an
English physicist, Henry Cavendish.
Since G is so small, we can see that the force of gravity is a very weak force.
Think about the attraction between you and a classmate. It’s there, but do
you notice it?
The force between you and the Earth, however, is noticeable. This is your
weight!
Gravity depends on the masses AND the distance from the center of the Earth.
You would weigh a little less on the top of the Sears Tower
13.5
Gravity and Distance: The Inverse-Square Law
Look at the formula: Fg  G
m1m2
d2
Q: What happens when you double one of the masses? Triple?
Q: What happens when you double one mass and triple the other mass?
Q: What happens when you double the distance? Careful!!!
Gravity decreases according to what’s called the “inverse square law”
Conceptual Physics
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Chapter 13 – Universal Gravitation
Physics Teacher Notes - Grothaus
Since it’s difficult to measure and see how gravity decreases, we’ll look at an example
using a butter gun:
https://www.youtube.com/watch?v=JW3tT0L2gpc
graphic on inverse square law (gravity, light intensity, electric charge and radiation)
http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/isq.html
Look also at light intensity which also decreases according to the inverse square law - other
examples are electric field, sound, nuclear radiation, electromagnetic radiation, potential
energy in a spring, etc.
It applies whenever something dissipates equally in all directions from a small
source. (point source)
This demonstrates the inverse-square law: if an object is twice as far from the source, the
light will be 1/4th as intense. If the distance is three times as far, the butter will be 1/9th as
intense. How intense will it be if it is four times as far?
Gravity decreases according to the inverse-square law. The force of
gravity weakens as the square of the distance.
One more thing about the inverse square law:
Look at Figure 13.13.
This is a great website with picture representations of everything from this chapter.
(https://kaiserscience.wordpress.com/physics/gravity/ )
(the behavior is asymptotic – never becomes zero, no matter how far away
the objects are from each other!)
Question? If you weigh 300 N. at sea level, you’ll weigh 299 N at the top of Mt. Everest.
Why so little change?
Question: If you were magically transported to the surface of Pluto, would Earth’s
gravitational pull disappear?
Formula work as a class
Work through CD 13.2 – second page as a class Look at the formula once again:
Fg  G
m1m2
d2
What happens if you have a 1 kg mass on the surface of the Earth?
24
Mass of the Earth: 5.9810 kg
6
Radius of the Earth: 6.3810 m
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Physics Teacher Notes - Grothaus
Chapter 13 – Universal Gravitation
What about below Earth’s surface? Is there still gravity?
If you fell into a tunnel through the center of the Earth from the North Pole, you would
pick up speed as you fall towards the center, overshoot and slow down until you reached the
South Pole. Repeat over and over – simple harmonic motion!
Interesting note: Each trip through the Earth would take about 45 minutes, 90 minutes to
return to your original side. It takes a satellite, in close orbit around the Earth 90 minutes to
make one complete rotation and return to its original point. Same time!
https://www.youtube.com/watch?v=jN-FfJKgis8
What if the Earth was hollow – minute physics
Question: What if you were standing on the surface of the Earth, and it suddenly
expanded to twice its size (twice the radius), but remained the same mass. What would
happen to your gravitational attraction to the Earth? What if the mass of the Earth also
doubled? (C.D. 13.2 – back page)
13.8
Weight and Weightlessness
The force of gravity is like any other force. It causes acceleration. Objects under the
influence of gravity are pulled toward each other and accelerate. When we are standing on
the Earth, we think of gravity as something that presses us against the Earth – not as
something that accelerates us!
Force against the Earth is the sensation we interpret as weight! (Support force)
What happens when you are standing on a scale in an elevator during accelerated
motion? Going up? Going down?
What if the cable broke? You would no longer be supported by the floor so you would
feel “weightless”. Are you?
Define weight as the force you and the supporting floor exert on each other. (Newton’s
third law). According to this definition, you are as heavy as you feel.
Weightlessness is not the absence of gravity, it is the absence of a support force.
Veritasium – weightlessness?
https://www.youtube.com/watch?v=iQOHRKKNNLQ
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Physics Teacher Notes - Grothaus
Chapter 13 – Universal Gravitation
In class practice with scientific operations:
(2.1103 )(5.2105 )
(5.3106 )(6.9102 )
(5.8104 )(1.03102 )
(9.1106 )(2.5109 )
Conceptual Physics
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Physics Teacher Notes - Grothaus
Chapter 13 – Universal Gravitation
(3.1102 )(5.8105 )
(8.231012 )(6.171011 )
6.9102
4.3106
8.12108
5.1102
5.32101
1.61105
9.3102
7.23106
(7.3451012 )2
(5.23104 )3
(5.321017 )(6.12102 )
5.1103
(7.39105 )(7.321011 )
6.11018
(3.98104 )(8.3105 )
(8.11012 )2
Conceptual Physics
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