PHY 113 A Fall 2012 -- Lecture 24 110/29/2012

PHY 113 A General Physics I9-9:50 AM MWF Olin 101

Plan for Lecture 24:

Chapter 13 – Fundamental force of gravity1. Form of gravitation force law2. Gravitational potential energy3. Conservation of energy4. Energy associated with orbital

motion5. Note: We will not focus attention on elliptical

orbits, black holes, and dark matter

PHY 113 A Fall 2012 -- Lecture 24 210/29/2012

PHY 113 A Fall 2012 -- Lecture 24 310/29/2012

iclicker question:Concerning prepartion for Friday’s exam –

A. I’m good (OK with studying on my own and with the help of the already scheduled tutorials)

B. I would likely attend an extra class reviewing session (probably Tuesday or Thursday)

C. I would like to make an individual appointment to go over my specific questions

D. None of these.

iclicker followup question:Concerning extra review session –

A. I could attend on Tuesday afternoonB. I could attend on Thursday afternoon

PHY 113 A Fall 2012 -- Lecture 24 410/29/2012

Review: Universal law of gravitation Newton (with help from Galileo, Kepler, etc.) 1687

212

122112

ˆ

r

mGm rF

2

211

kg

mN 10674.6

G

PHY 113 A Fall 2012 -- Lecture 24 510/29/2012

Review: Gravitational force of the Earth

RE m

2226

2411

2

2

m/s8.9m/s)1037.6(

1098.51067.6

E

E

E

E

R

GMg

R

mGMF

Note: Earth’s gravity acts as a point mass located at the Earth’s center.

PHY 113 A Fall 2012 -- Lecture 24 610/29/2012

PHY 113 A Fall 2012 -- Lecture 24 710/29/2012

m1

R2

R1

m2

v1

v2

Review: Circular orbital motion about center of mass

CM

21

321

21

2

111

1

2

1

11

1

21

1

2211

2

22

2221

21

1

21

1

2

212

mmG

RRTT

TRm

RT

Rm

R

vm

RmRm

R

vm

RR

mGm

R

vm

2

31

21

321

21

1212

22

then if that Note

Gm

R

mmG

RRTT

RRmm

PHY 113 A Fall 2012 -- Lecture 24 810/29/2012

m1

R1

m2

v1

Review: Circular orbital motion about center of mass

2

31

21

321

21

1212

22

then if that Note

Gm

R

mmG

RRTT

RRmm

PHY 113 A Fall 2012 -- Lecture 24 910/29/2012

Example: Satellite in circular Earth orbit

kgm

kgM

GM

hRT

S

E

E

E

3

24

3

10

1097.5 :Note

2

onous)(geosynchr

11053.8

1083.35 If4

6

daysT

mh

PHY 113 A Fall 2012 -- Lecture 24 1010/29/2012

Work of gravity:

ri

rf

f

i

f

i

f

i

r

r

r

r

fi

r

r

fi

r

mGm dr

r

mGmW

r

mGmdW

212

21

221 ˆ

r

FrF

ifif

fi rUrUr

mGm

r

mGmW

2121

PHY 113 A Fall 2012 -- Lecture 24 1110/29/2012

Gravitational potential energy

r

mGm dr

r

mGmrU

r

mGmdrU

r

gravity

r

r

gravity

ref

212

21

221

''

)(

ˆ )(

rFrF

hR

mGMhRrU

E

SEEgravity

)(

Example:

PHY 113 A Fall 2012 -- Lecture 24 1210/29/2012

hU=mgh

iclicker exercise:We previously have said that the gravitational potential of an object of mass m at a height h isU=mgh. How is this related to

A. No relationB. They are approximately equalC. They are exactly equal

? hR

mGMU

E

SEgravity

PHY 113 A Fall 2012 -- Lecture 24 1310/29/2012

h

hR

mGM

R

mGM

hR

mGMRUhRU

R

h

RRh

RRhRhR

E

E

E

E

E

EEgravityEgravity

EEE

EEEE

2

2

)()(

1/1

1

/1

111

gNear the surface of the Earth U=mgh is a good approximation to the gravitation potential.

PHY 113 A Fall 2012 -- Lecture 24 1410/29/2012

iclicker exercise:How much energy kinetic energy must be provided to an object of mass m=1000kg, initially on the Earth’s surface to outer space?

A. This is rocket science and not a fair question.B. It is not possible to escape the Earth’s

gravitational field.C. We can estimate the energy by simple

conservation of energy concepts.

J

JR

mGMK

KR

mGMU

UKUKE

E

Ei

iE

Ei

ffii

10

6

2411

1025.6

1037.6

10001097.510674.6

0

PHY 113 A Fall 2012 -- Lecture 24 1510/29/2012

Total energy of a satellite in a circular Earth orbit

hR

mGMhRrU

E

SEEgravity

)(

hR

mGMvmK

hR

mGM

hR

vm

vmKUKE

E

SES

E

SE

ES

Sgravity

22

1

:orbitcircular aFor

2

1

2

2

2

2

PHY 113 A Fall 2012 -- Lecture 24 1610/29/2012

Total energy of a satellite in a circular Earth orbit

hR

mGME

hR

mGMU

hR

mGMK

UKE

E

SE

E

SEgravity

E

SE

gravity

2

2

iclicker question:Compared to the energy needed to escape the Earth’s gravitational field does it take

A. moreB. less

energy to launch a satellite to orbit the Earth?

PHY 113 A Fall 2012 -- Lecture 24 1710/29/2012

JJ

JJK

kmh

R

mGM

hR

mGM

R

mGMK

R

mGMU

hR

mGMUKUKE

i

E

E

E

E

E

Ei

E

Ei

E

Effii

1010

6

2411

6

2411

1038.393.62

37.611025.6

1093.62

10001097.510674.6

1037.6

10001097.510674.6

Telescope) Hubble assuch orbit earth (low 560 example,For

2

2

PHY 113 A Fall 2012 -- Lecture 24 1810/29/2012

Energy involved with changing orbits

h’

J

E

kmhkmh

hR

mGM

hR

mGMEEE

E

E

E

E

8

6

2411

1065.1

97.6

1

93.6

1

102

10001097.510674.6

600' and 560 example,For

2'2'

PHY 113 A Fall 2012 -- Lecture 24 1910/29/2012

From Webassign:

PHY 113 A Fall 2012 -- Lecture 24 2010/29/2012

PHY 113 A Fall 2012 -- Lecture 24 2110/29/2012