Download - PROGRAM OF “PHYSICS”
PROGRAM OF PROGRAM OF “PHYSICS”“PHYSICS”Lecturer: Dr. DO Xuan Hoi
Room 413E-mail : [email protected]
PHYSICS I PHYSICS I (General Mechanics) (General Mechanics)
02 credits (30 periods)02 credits (30 periods)
Chapter 1 Bases of KinematicsChapter 1 Bases of Kinematics
Motion in One Dimension Motion in One Dimension
Motion in Two DimensionsMotion in Two Dimensions
Chapter 2 The Laws of Motion Chapter 2 The Laws of Motion
Chapter 3 Work and Mechanical EnergyChapter 3 Work and Mechanical Energy
Chapter 4 Linear Momentum and CollisionsChapter 4 Linear Momentum and Collisions
Chapter 5 Rotation of a Rigid Object Chapter 5 Rotation of a Rigid Object About a Fixed Axis About a Fixed Axis
Chapter 6 Static EquilibriumChapter 6 Static Equilibrium
Chapter 7 Universal GravitationChapter 7 Universal Gravitation
References :References :
Halliday D., Resnick R. and Walker, J. Halliday D., Resnick R. and Walker, J. (2005), Fundamentals of Physics, (2005), Fundamentals of Physics, Extended seventh edition. John Willey Extended seventh edition. John Willey and Sons, Inc.and Sons, Inc.
Alonso M. and Finn E.J. (1992). Physics, Alonso M. and Finn E.J. (1992). Physics, Addison-Wesley Publishing CompanyAddison-Wesley Publishing Company
Hecht, E. (2000). Physics. Calculus, Second Hecht, E. (2000). Physics. Calculus, Second Edition. Brooks/Cole.Edition. Brooks/Cole.
Faughn/Serway (2006), Serway’s College Faughn/Serway (2006), Serway’s College Physics, Brooks/Cole.Physics, Brooks/Cole.
Roger Muncaster (1994), A-Level Physics, Roger Muncaster (1994), A-Level Physics, Stanley Thornes.Stanley Thornes.
http://ocw.mit.edu/OcwWeb/Physics/index.htmhttp://www.opensourcephysics.org/index.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.htmlhttp://www.practicalphysics.org/go/Default.htmlhttp://www.msm.cam.ac.uk/http://www.iop.org/index.html...
PHYSICS IPHYSICS I
Chapter 7Chapter 7Universal GravitationUniversal Gravitation
Newton’s Law of Universal GravitationKepler’s LawsGravitational Potential Energy
1. 1. Newton’s Law of Universal Gravitation
1 22g
m mF G
r
The Law: “Every particle in the Universe attracts every other particle with a force that isdirectly proportional to the product of their masses and inversely proportional to the square of the distance between them.”
-11 2 2G = 6.673 10 Nm /kg
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
1 2 1 212 122 3
m m m mF G r G r
r r
Free-Fall Acceleration
The force acting on a freely falling object of mass m near the Earth’s surface. Newton’s second law:
(ME: Earth’s mass; RE: Earth’s radius)
Object of mass m located a distance h above the Earth’s surface or a distance r from the Earth’s center:
22
9.81 /E
E
Mg G m s
R
2
Eg
E
M mF ma mg F G
R
Er R h 2
'( )
E
E
Mg G
R h
EXAMPLE 1EXAMPLE 1Two objects attract each other with a gravitational
forceof magnitude 1.0010-8 N when separated by 20.0
cm. Ifthe total mass of the two objects is 5.00 kg, what is
themass of each? 11 81 2 1 2
2 26.673 10 1.00 10
(0.20)g
m m m mF G
r
1 2 6.00m m
1 2 5.00m m kg
1 22.00 ; 3.00m kg m kg
1 23.00 ; 2.00m kg m kg
2. Kepler’s laws1. All planets move in elliptical orbits with the Sunat one focal point.
2. The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals.
3. The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit.
2 3ST K aT : period of revolution, a : semimajor axis
a
19 2 32.97 10 s /mSK
CIRCULAR ORBIT : A planet of mass Mp moving
around the Sun of mass MS in a circular orbit
EXAMPLE 2EXAMPLE 2Calculate the mass of the Sun using the fact that
the periodof the Earth’s orbit around the Sun is 3.156107 s
and itsdistance from the Sun is 1.4961011 m.
3. Gravitational Potential Energy
dU
Fdr
1 2
2
m mdU Fdr G dr
r
1 21 22 2
ff f
i i i
U r r
fiU r r
m m drU U dU G dr Gm m
r r
1 2
1 1fi
fi
U U Gm mr r
1 2 ;ff
m mU G
r
We put :
1 2i
i
m mU G
r
In general: 1 2m mU G
r
To compare:
F mg Gravitational force near the Earth’s surface:
Gravitational potential near the Earth’s surface:U mgx
F kx Elastic force :
Elastic potential: 212
U kx
Gravitational force :
Gravitational potential :
1 22g
m mF G
r
1 2m mU G
r Coulomb force :
Gravitational potential :
1 22C
q qF K
r
1 2C
q qU K
r
General formula: dU
Fdr
F gradU U
EXAMPLE 3EXAMPLE 3As Mars orbits the sun in its elliptical orbit, its
distance of closest approach to the center of the sun (at
perihelion) is 2.0671011 m, and its maximum distance from the
centerof the sun (at aphelion) is 2.4921011 m. If the
orbitalspeed of Mars at aphelion is 2.198104 m/s, what is
itsorbital speed at perihelion? (You can ignore the
influenceof the other planets.)
Apply conservation of energy:
EXAMPLE 4 EXAMPLE 4 Escape Speed
Escape speed: The minimum speed the object must have
at the Earth’s surface in order to escape from the influence
of the Earth’s gravitational field.
EXAMPLE 4 EXAMPLE 4 Escape Speed
Escape speed: The minimum speed the object must have
at the Earth’s surface in order to escape from the influence
of the Earth’s gravitational field.