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 24 310/29/2012
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
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m/s8.9m/s)1037.6(
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mGMF
Note: Earth’s gravity acts as a point mass located at the Earth’s center.
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
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PHY 113 A Fall 2012 -- Lecture 24 810/29/2012
m1
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v1
Review: Circular orbital motion about center of mass
2
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then if that Note
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PHY 113 A Fall 2012 -- Lecture 24 910/29/2012
Example: Satellite in circular Earth orbit
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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
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mGmdW
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21
221 ˆ
r
FrF
ifif
fi rUrUr
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PHY 113 A Fall 2012 -- Lecture 24 1110/29/2012
Gravitational potential energy
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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
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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.
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JR
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ffii
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PHY 113 A Fall 2012 -- Lecture 24 1510/29/2012
Total energy of a satellite in a circular Earth orbit
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mGMhRrU
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mGM
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ES
Sgravity
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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
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mGMK
R
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hR
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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
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600' and 560 example,For
2'2'