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Announcements
• CAPA Set #7 due Friday at 10 pm
• This week in Section 
Assignment 4: Circular Motion & Gravity
• Finish reading all sections of Chapter 5
• Advanced reminder  Exam #2 on Tuesday, October 11
See next slide for details
• Reminder about office hours …
Nagle (Monday 2-3 in office, Wednesday 1:45-3:45 pm help room)
Kinney (Thursday 4-5 pm help room)
Uzdensky (Tuesday 11am-noon help room)
Exam #2 Information
This information also on the course web page under “exam info”.
Tuesday, October 11 starting at 7:30 pm sharp.
Covers all material to date including:
- CAPA Sets 1-7 (emphasis 4-7)
- Textbook Chapters 1-5 (emphasis 3-5)
- Lectures including up to October 5th
- All Labs and Section Assignments including this week
Practice exam and version with solutions available via CULearn.
Equation Sheet (2 pages) posted on web page. Copy will be
included with your exam (no reason to print a copy).
Exam room assignments same as last time,
and posted on “exam info” page.
Room Frequency BA
Clicker Question
You are on the surface of the earth,
and jump up for a second.
The earth exerts a gravitational force
on you Fearth, and you exert a
gravitational force on the earth Fperson.
Which is correct about the accelerations of you and the earth?
A) aearth > aperson
B) aearth < aperson
C) aearth = aperson
M E aE  G
M EM p
M pa p  G
MEM p
r
2
r2
aE  G
Mp
ap  G
ME
D) It’s not so simple, we need more information.
r2
r2
Consider the force of gravity exerted by the Earth’s
mass M on a person of mass m on its surface?
mM
mg  Fg  G 2
RE

M
g= ag  G 2
RE
RE
Can use this to measure the mass of
the Earth if one knows the radius RE.
gRE2 9.8m/s2 (6.37x106 m)2
24
M


5.98x10
kg
11
2
2
G
6.67x10 Nm /kg
Eratosthenes (276–194 BC) estimated Earth’s
circumference around 240 BC.
He had heard that in Syene the Sun was directly
overhead at the summer solstice whereas in
Alexandria it still cast a shadow. Using the differing
angles the shadows made as the basis of his
trigonometric calculations he estimated a
circumference of around 250,000 stades.
Eratosthenes used rough estimates and round
numbers, but depending on the length of the stadion ,
his result is within a margin of between 2% and 20% of
the actual meridional circumference,
40,008 kilometers (24,860 miles).
Radius = Circumference/2p ~ 6300 km.
http://en.wikipedia.org/wiki/Spherical_Earth
International Space Station (ISS)
Circular orbit with altitude between 278 km and 460 km.
Average speed 27,000 km/hour and 15.7 orbits per day.
Astronauts experience “weightlessness”.
Clicker Question
Room Frequency BA
Astronauts aboard the
International Space Station
float around, experiencing
weightlessness.
Why is this?
A)
B)
C)
D)
E)
The force of gravity from the earth is zero on the Space Station
The force of gravity is much, much weaker on the Space Station
The Space Station has the “inertial dampers” turned on.
The Space Station is in circular orbit around the earth.
The Space Station generates an anti-gravity field.
Gravity at the surface of the earth
a
GM E
RE 2

 6.67 10 11 Nm 2

5.98 10 kg
2
 9.81m / s
/ kg 
6.37 10 m
24
2
6
2
Gravity at the Space Station
Orbit above the earth h ~ 300 km = 3 x 105 meters.
a
GM E
( RE  h)
2

 6.67 10
11
2
Nm / kg
 8.43m / s
2

5.98 10
6.37 10
6
24
kg

m  3 10 m
5

2
2
Gravitational acceleration is a little weaker, but not so much.
Satellites and “Weightlessness”
Satellites are routinely put into orbit around the Earth.
The tangential speed must be high enough so that the
satellite does not return to Earth, and not so high that
it escapes Earth’s gravity altogether.
The satellite is kept in orbit by its
speed – it is continually falling,
but the Earth curves from
underneath it.
Because of its continual falling, it
is considered to be “weightless”.
“Weightlessness” and “Free Fall”?
a=0
N
Fnet  ma  N  mg  0
N  mg
-mg
If the person were on a scale,
it would read their regular weight.
“Weightlessness” and “Free Fall”?
-a (controlled fall)
N
-mg
Fnet  ma  N  mg  0
N  m( g  a)  mg
If the person were on a scale,
it would read less than their regular weight.
“Weightlessness” and “Free Fall”?
-g (free fall) Therefore, when gravity alone is operating
unopposed by another force (e.g., normal
force), the object is said to be weightless.
The object is also said to be in free fall.
N  m( g  a)  m( g  g )  0
N
Weightless!
If the person were on a scale,
it would read zero.
-mg
Room Frequency BA
Clicker Question
What happens to a person’s “weight” compared to on earth as
measured on a scale on the shuttle at t=100 seconds?
A) Stays the same
B) Increases
C) Decreases