Download 6.67 x 10 -11 m 3 /(kg s 2 )

Astronomy 100
Tuesday, Thursday 2:30 - 3:45 pm
Tom Burbine
[email protected]
www.xanga.com/astronomy100
Help Desk
• There is an Astronomy Help Desk in HAS 205. It
will be open from Monday through Thursday
from 7-9 pm.
Another Homework Assignment
(Due Thursday March 3rd)
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Make up a test question
Multiple Choice
A-E possible answers
1 point for handing it in
1 point for me using it on test
Homework assignments
due today (or it is late)
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Two due today
One is from this sheet that I handed out
Two calculations
Worth 1 HW point
I will discuss them next class
2nd HW assignment
due today (or it is late)
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I want you to pick an element
Write its symbol
Is it a solid, metal, or gas?
Atomic Number
Atomic Mass
Its isotopes
What this element is used for?
http://www.webelements.com/
Worth 1 HW point
Next assignment
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Handed out today
More calculations
Due Feb. 24 (Thursday) by 3:45 pm
You need to show work to get credit
PRS
• You need to make sure that you have a clicker
registered
• And your name appears on screen
• If your name does not appear onscreen, I don’t
know you are when you use the clicker
Monkey Drop Experiment
• A hunter shoots at a monkey in the tree
• The monkey drops the second that the hunter
pulls the trigger
• What happens?
Show video
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http://www.ap.stmarys.ca/demos/content/mechanics/monkey_and_hunter/monkey_and_hunter.html
So what is happening
• The monkey and the bullet are accelerating at the
same speed downwards
• g = 9.8 m/s2 = acceleration due to gravity
• Objects fall faster by 9.8 m/s with every second
• Even though the bullet has a velocity in the
horizontal direction, it is also moving downwards
in the vertical direction
Acceleration
• Acceleration is when your velocity is changing
• Velocity not changing, no acceleration
Difference between mass and weight
• Mass is the amount of matter in your body
• Weight is the amount of force acting on your body
• So on the Moon, you would have the same mass
as on Earth but weigh less on the Moon since the
Moon is less massive than Earth
Who came up with the first
understanding of how gravity and
forces really work?
Isaac Newton (1642-1727)
Isaac Newton (1642-1727)
• Supposedly saw an apple fall to the ground
• He then understood that gravity was universal,
meaning it affected both the planets and us on
Earth
• Came up with 3 Laws of Motion
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1
Law
• In the absence of a net (overall) force acting upon
it, an object moves with a constant velocity
• An object at rest remains at rest
• An object in motion tends to remain in motion
unless a force is acting upon it
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Law
Force = mass x acceleration
Units of Force kgm/s2 = newton
So much do you weigh
Say your mass is 100 kg
F = 100 kg x 9.8 m/s2
F = 980 Newtons
Show video
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Law
• For any force, there is an equal and opposite
reaction force
• Gravity is holding you on the ground
• The ground is also pushing back up on you with
the same amount of force
Conservation
of Momentum
Conservation of Angular Momentum
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Angular momentun = m x v x r
M = mass
V = velocity
R = radius
In the absence of a net torque (twisting force), the
angular momentum of a system remains constant
Universal Law of Gravitation
• Every mass attracts every other mass through the
force called gravity
• Newton came up with this formula
F = G M1 M2
d2
M1, M2 are the masses of the two objects
d is the distance between the objects
G = constant = 6.67 x 10-11 m3/(kgs2)
So what should you know
about this formula
F = G M 1 M2
d2
• The force of attraction between any two objects is
directly proportional to the product of their masses
• The force of attraction between two objects decreases
with the square of the distance between their centers
• G is a very small number
What is the attraction of two people in
this room?
F = G M1 M2
d2
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Say their masses are both 100 kg
Their distances are 10 meters apart
F = 6.67 x 10-11 m3/(kgs2) * 100*100 kg2/(10*10 m2)
F = 6.67 x 10-9 N = 0.0000000067 N
Remember the person weighs 980 N
PRS question
F = G M1 M2
d2
• How would the force between the two people
change if they were only 5 meters apart instead of
10 meters?
• A) Stay the same
• B) Double (Increase by a Factor of 2)
• C) Quadrupul (Increase by a Factor of 4)
• D) halve (decrease by a factor of 2)
PRS question
F = G M1 M2 = G M1 M2
(d/2)2
d2/4
=4
G M1 M2
d2
• How would the force between the two people
change if they were only 5 meters apart instead of
10 meters?
• A) Stay the same
• B) Double (Increase by a Factor of 2)
• C) Quadrupul (Increase by a Factor of 4)
• D) halve (decrease by a factor of 2)
Can you use this formula to calculate
acceleration of gravity?
• F = M2a = G M1 M2
d2
you are M2
M1 is the Earth’s radius
d is the Earth’s diameter
a = G M1
d2
a = 6.67 x 10-11 m3/(kgs2) * (6.0 x 1024 kg)
(6.4 x 106 m) * (6.4 x 106 m)
a = 9.8 m/s2
Escape velocity
• Velocity above this will allow an object to escape Earth’s
gravity
v = square root[(2 x G x M)/R]
v = square root[(2 x 6.67 x 10-11 m3/(kgs2) x (6.0 x 1024 kg)]
(6.4 x 106 m)
v = square root [1.25 x 108 m2/s2]
v = 11.2 x 103 m/s = 11.2 km/s
Show animation
• Why do we have tides?
Remember
• Rock is stretching too
• However, water is easier to stretch than rock
Force due to Moon on side
closest to Earth
F = G M1 M2
d2
F = 6.67 x 10-11 m3/(kgs2) * (6.0 x 1024 kg) * (7.4 x 1022 kg)
(3.84 x 108 m) * (3.84 x 108 m)
F = 2 x 1020 N
Force due to Moon on side
farthest from Earth
F = G M1 M2
d2
F = 6.67 x 10-11 m3/(kgs2) * (6.0 x 1024 kg) * (7.4 x 1022 kg)
(3.904 x 108 m) * (3.904 x 108 m)
F = 1.94 x 1020 N
Difference is 6 x 1018 N
Is the force due to the Sun stronger or
weaker on the Earth?
F = G M1 M2
d2
F = 6.67 x 10-11 m3/(kgs2) * (6.0 x 1024 kg) * (1.99 x 1030 kg)
(1.5 x 1011 m) * (1.5 x 1011 m)
F = 3.54 x 1022 N
This is approximately 184 times stronger than the force due to
the Moon
PRS Question
• Why aren’t the tides due mainly to the Sun than
the Moon?
• A) they are mainly due to the Sun
• B) the difference in the Sun’s pull on the different
sides of the Earth is smaller than the Moon’s
• C) the forces due to the Moon and Sun contribute
equally to the tides
• D) the tides are not due to forces from either the
Sun or the Moon
PRS Question
• Why aren’t the tides due mainly to the Sun than
the Moon?
• A) they are mainly due to the Sun
• B) the difference in the Sun’s pull on the different
sides of the Earth is smaller than the Moon’s
• C) the forces due to the Moon and Sun contribute
equally to the tides
• D) the tides are not due to forces from either the
Sun or the Moon
What is the difference in forces on the
two sides of the Earth?
F = G M1 M2
d2
F = 6.67 x 10-11 m3/(kgs2) * (6.0 x 1024 kg) * (1.99 x 1030 kg)
(1.50 x 1011 m) * (1.50 x 1011 m)
F = 3.53924 x 1022 N (far side of Earth)
F = 3.53954 x 1022 N (near side of Earth)
Difference due to Sun= 3 x 1018 N
Difference due to Moon = 6 x 1018 N
When Sun and Moon are pulling in same
direction, strongest tides
When Sun and Moon are pulling in
perpendicular directions, weakest tides
Questions?