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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 InformationThis 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.

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

D) It’s not so simple, we need more information.

Clicker Question Room Frequency BA

2r

MMEE

pEGaM

2r

MMpp

pEGaM

2r

ME

pGa

2rM

pEGa

Consider the force of gravity exerted by the Earth’s mass M on a person of mass m on its surface?

RE

mg Fg GmMRE

2 g= ag GMRE

2

Can use this to measure the mass of the Earth if one knows the radius RE.

M gRE

2

G

9.8m/s2 (6.37x106 m)2

6.67x10 11Nm2 /kg2 5.98x1024 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) The force of gravity from the earth is zero on the Space StationB) The force of gravity is much, much weaker on the Space StationC) The Space Station has the “inertial dampers” turned on.D) The Space Station is in circular orbit around the earth.E) The Space Station generates an anti-gravity field.

2E

E

RGM

a

Gravity at the surface of the earth

2/81.9 sm

Gravity at the Space StationOrbit above the earth h ~ 300 km = 3 x 105 meters.

26

242211

1037.6

1098.5/1067.6m

kgkgNm

2)( hRGM

aE

E

256

242211

1031037.6

1098.5/1067.6mm

kgkgNm

2/43.8 sm

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

-mg

NmaFnet mgN 0

mgN If the person were on a scale,

it would read their regular weight.

-a (controlled fall)

-mg

N

“Weightlessness” and “Free Fall”?

maFnet mgN 0

)( agmN If the person were on a scale,

it would read less than their regular weight.

mg

-g (free fall)

-mg

Weightless!If the person were on a scale,

it would read zero.

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

“Weightlessness” and “Free Fall”?

0)( ggm)( agmN

Clicker Question Room Frequency BA

What happens to a person’s “weight” compared to on earth asmeasured on a scale on the shuttle at t=100 seconds?

A) Stays the sameB) IncreasesC) Decreases