PROGRAM OF PROGRAM OF “PHYSICS”“PHYSICS”Lecturer: Dr. DO Xuan Hoi

Room 413E-mail : dxhoi@hcmiu.edu.vn

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.