Transcript mechanics

Welcome to
Shandong university
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Chapter 1. Physics and Mechanics
1
Mechanics(力学)
Mechanics
力学
Your first physics lesson in Shandong University
Autumn 2006
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Chapter 1. Physics and Mechanics
2
Mechanics(力学)
Lecturer:
张学尧 Zhang xueyao
Class schedule:
Monday 8:00-9:50
Thursday 8:00 – 9:50
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Chapter 1. Physics and Mechanics
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Mechanics(力学)
Getting the Best Out of us
Speak up! Tell me when something in the class
is not working for you
Ask questions at any time in the lectures
Contact me after the lectures
Office: 新校: 邵逸夫科学馆, 411房间
Phone: 88364516
E-mail:
[email protected]
[email protected]
课程主页：
http://hepg.sdu.edu.cn/~zhangxy
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Chapter 1. Physics and Mechanics
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Mechanics(力学)
Text book
 《力学》，漆安慎、杜婵英，高等教育出版社
 Engineering Mechanics: DYNAMICS,
Andrew Pytel . Jaan Kiusalaas, second Edition
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Chapter 1. Physics and Mechanics
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Mechanics(力学)
Grades
Point of grades is to assess your understanding
of the material.
•Homework: 10%
– will be assigned in class.
•Final Exam: 90%
– Scheduled during final exam period at the end
of term.
– Will cover the entire course
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Chapter 1. Physics and Mechanics
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Mechanics(力学)
Contents of this course
• Kinematics of particles (质点运动学)
• Theorem of momentum and the law of momentum
conservation (动量定理和动量守恒定律)
• Kinetic energy and potential energy (动能和势能)
• Angular momentum (角动量)
• Planar Kinematics of rigid body (刚体平面运动学)
• Planar kinetics of rigid bodies (刚体平面动力学)
• Oscillation (振动)
• Waves and sound (波动和声)
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Chapter 1. Physics and Mechanics
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Mechanics(力学)
Chapter 1
Physics and Mechanics
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Chapter 1. Physics and Mechanics
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Chapter 1: Physics and Mechanics
Physics：
The knowledge or science of natural things.
The basic science that deals
with matter and energy in
terms of motion and force
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Chapter 1. Physics and Mechanics
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Chapter 1: Physics and Mechanics
Mechanics：
A branch of physics that studies the motion of
objects (atoms, blood flow, ice skaters, cars,
planes, galaxies, …)
 Kinematics(运动学): describes the motion of an
object without reference to the cause of the
motion.
 Dynamics(动力学): describes the effects that
forces have on the motion of objects
 Statics(静力学): describes the effects that forces
have on an object which is at rest (bridge,
building, ….)
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Chapter 1. Physics and Mechanics
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Mechanics(力学)
Chapter 1. Physics and Mechanics
1.1 The history of physics development
1.2 The Nature of Physics
1.3 Idealized Models
1.4 Standards For Measurement
1.5 Dimension analysis
1.6 Reference frame,coordinate system and time
1.7 Review and summary
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1.1 The history of physics development
Two broad time periods:
• 1600—1900:
Classical physics developed
• 1890—1930:
Modern physics began developing
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1.1 The history of physics development
Classical physics
Three physicists made great contributions to its
foundation
开普勒Johannes
Kepler(1571-1630)
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牛顿Isaac Newton
伽利略 Galileo
Galilei (1564-1642) (1643-1727)
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1.1 The history of physics development
Johannes Kepler: German astronomer
The first person to describe quantitatively and
accurately the elliptic paths of the planets around
the sun.
The three laws of planetary motion:
1. planets follow elliptical orbits with
the Sun at one focus of the ellipse
2. The radius vector draw from the
sun to a planet sweeps equal areas
in equal times.
3. The square of the orbital period of a
planet is proportional to the cubes
of the semimajor axes of its orbit，
that is, T2/a3=constant
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1.1 The history of physics development
Galileo Galilei:
Italian Astronomer and Physicist. His study includes:
Motion of the body：
Invented the kinematics: quantitative description of motion;
Principle of relativity;
The concept of inertia
Astronomical study with the telescope he
invented
Shown that the Moon's surface is not smooth.
Discovered four moons revolving around Jupiter(木星).
Sunspots
…
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Chapter 1. Physics and Mechanics
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1.1 The history of physics development
Isaac Newton:
English physicist and Mathematician. Based on Galileo
and Kepler’s work, he invented the fundamental laws of
motion:
The three laws of motion  dynamics: a
theory that explained the cause of motion;
The law of universal gravitation.
Published in 1686 as the “Philosophiae Natualis Principia
Methematica” ( Mathematical Principles of natural Philosophy,
Principia)
Established the classical kinematics and dynamics
Newtonian mechanics
The first great physical theory of natural philosophy
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Chapter 1. Physics and Mechanics
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1.1 The history of physics development
Electricity and Magnetism:
Fundamental experiments were performed during 18th
and 19th centuries
Charles Coulomb: the electric force law between
pointlike charges at rest;
Christian Oersted: magnetism
Michael Faraday: the law of electromagnetic
induction
• James Clerk Maxwell: unification of the electrical
and magnetic theories in 1864 The theory of
electromagnetism
The second great physical theory of natural philosophy
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1.1 The history of physics development
Thermodynamics:
Arose during the industrial revolution in 19th century
form a need to understand the parameters associated
with designing better steam engines.
Sadi Carnot: study of engine efficiency
James Prescott Joule: dissipation mechanical
energy and heat transfer;
Rudolf Clausius: entropy
Ludwig Boltzmann: Kinetic theory and statistical
meaning of entrpoy;
J. Willard Gibbs: theoretical work
 The physical laws of thermodynamics
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Chapter 1. Physics and Mechanics
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1.1 The history of physics development
By the end of 19th century, a perfect classical physics
system was formed.
力学：Mechanics(motion)
电磁学：Electromagnetism(charge)
热力学：Thermodynamics(heat)
统计力学：Statistical Mechanics(many bodies)
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Chapter 1. Physics and Mechanics
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1.1 The history of physics development
Modern Physics
A. Einstein(1879-1955): Proposed new view of
space-time and new gravitation theory:
In 1905, he formulated special theory of
relativity( 狭义相对论)
In 1915, he generalized his hypothesis to
formulate the general theory of relativity(广义相对
论)
Relativity:
The “end” of classical physics, as well as the “beginning”
of modern physics.
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Chapter 1. Physics and Mechanics
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1.1 The history of physics development
Modern Physics
Within the last decade of the 19th century, a series
of remarkable discoveries were made, which could
not be explained by classical physics:
In 1895，German physicist
Wilhelm Conrad Röntgen(伦
琴,1845-1923)discovered
the x-ray.
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Chapter 1. Physics and Mechanics
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1.1 The history of physics development
Modern Physics
In 1895, British physicist J.J
Thomoson (J.J.汤姆孙,18561940) discovered the electron.
In 1896, France physicist
A.H.Becquerel(贝可勒尔)
discovered radioactivity(放射性).
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1.1 The history of physics development
These discoveries made the physics studies
extend into the microscopic world.
Quantum mechanics(量子力学)：Describes
the motion and interaction of microscopic
objects
Developed during the 1920s by such giants
of 20th century physics:






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Erwin Schrodinger
Wolfgang Pauli
Werner Heisenberg
P. A. M. Dirac
Niels Bohr
Enrico Fermi
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1.1 The history of physics development
The bases of the modern physics:
 Special relativity
 general relativity
 and quantum mechanics
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1.1 The history of physics development
The scopes of classical and modern physics
c
velocity
相对论
量子力学
相对论力学
Relativistic QM
Relativistic
mechanics
相对论宇宙学
Relativistic
cosmology
量子力学
Quantum
mechanics
经典力学
Classical
mechanics
宇宙学
Cosmology
C/10
10-15m
proton
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10-10 m
atom
1020 m
Chapter 1. Physics and Mechanics
distance
25
Mechanics(力学)
Chapter 1. Physics and Mechanics
1.1 The history of physics development
1.2 The Nature of Physics
1.3 Idealized Models
1.4 Standards For Measurement
1.5 Dimension analysis
1.6 Reference frame,coordinate system and time
1.7 Review and summary
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Chapter 1. Physics and Mechanics
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1.2 The Nature of Physics
Physics is an experimental science
Observation
Experiment to observe the
phenomena of nature
Patterns and principles
that relate the observed
phenomena
Theory
Predictions
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1.2 The Nature of Physics
observation
New
Theory
Disagrees
Agrees
theory
predictions
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1.2 The Nature of Physics
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Chapter 1. Physics and Mechanics
29
Mechanics(力学)
Chapter 1. Physics and Mechanics
1.1 The history of physics development
1.2 The Nature of Physics
1.3 Idealized Models
1.4 Standards For Measurement
1.5 Dimension analysis
1.6 Reference frame,coordinate system and time
1.7 Review and summary
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1.3 Idealized Models
Idealized Model(理想模型)
The physical systems we study are complex. It is
very difficult to describe such a system in detail.
The motion of a baseball thrown through the air:
• Neither perfectly spherical nor perfectly rigid;
• Has raised seams(凸起的接缝）
• Spins as it moves through the air
• Wind and air resistance influence its motion
• The earth rotates beneath it
• The ball’s weight varies a little as its distance
from the center of the earth changes;
• …..
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1.3 Idealized Models
 Idealized model:
Simplified version of a physics system
For example: idealized model for the motion of baseball:
• Neglect the size and shape of the ball by
representing it as a point object, or particle;
• Neglect the air resistance by moving the ball
move in a vacuum;
• Neglect the earth’s rotation;
• Make the weight constant
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1.3 Idealized Models
Particle(质点):
Body whose internal structures or motions can be
ignored and whose parts all move in exactly the
same way.
Particle system(质点系):
A collection of two or more particles
Rigid body(刚体):
A body is said to be rigid if the distance between any
two material points of the body remains constant,
that is, the body does not deform.
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1.3 Idealized Models
Absolute motion
Kinematics
Relative motion
Particles
Classical
mechanics
Force-mass-acceleration
method
Dynamics
Work-energy method
Rigid bodies
Impulse momentum
method
Statics
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Chapter 1. Physics and Mechanics
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Mechanics(力学)
Chapter 1. Physics and Mechanics
1.1 The history of physics development
1.2 The Nature of Physics
1.3 Idealized Models
1.4 Standards For measurement
1.5 Dimension analysis
1.6 Reference frame,coordinate system and time
1.7 Review and summary
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Chapter 1. Physics and Mechanics
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1.4 Standards For Measurement
The laws of physics are expressed in terms of many
different quantities: mass, time, force, speed,
acceleration,…
A physical quantity is the result of measurement
and usually expressed as the product of a numerical
value and a physical unit.
Unit: the standard of the measurement,
kilogram, second,…
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Chapter 1. Physics and Mechanics
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1.4 Standards For Measurement
According to the definition of their units, physical
quantities can be divided into two classes:
1. Base quantities (基本物理量)
2. Derived quantities (导出物理量)
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1.4 Standards For Measurement
Base quantities
• Quantities whose units are directly defined.
• The units of the base quantities are called base units.
• The SI system of units(International System of Units) defines
seven SI base units:
quantity
Time
Length
Mass
Amount of substance
Temperature
Electric current
Luminous intensity
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Name
second
meter
kilogram
mole
SI Units
Symbol
s
m
kg
mol
kelvin
K
ampere
candela
A
cd
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1.4 Standards For Measurement
Length (L)
• Unit: meter (m)
• One meter is defined as the distance light travels in
a vacuum in (1/299,792,458) second.
• This standard was adopted in 1983 when the speed
of light in vacuum was defined to be precisely
(299,792,458)m/s.
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1.4 Standards For Measurement
Mass (m)
• Unit: kilogram (kg)
• One kilogram is defined to
be the mass of a specific
cylinder of platinum-iridium
alloy(铂铱合金）, kept at
the International Bureau of
Weights and Measures near
Paris.
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1.4 Standards For Measurement
Time (t)
• Unit: second (s)
•One second is defined as the time required for
9,192,631,770 periods of the radiation
corresponding to the transition between the two
hyperfine levels of the ground state of cesium
133(铯133).
•This definition was adopted in 1967.
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1.4 Standards For Measurement
Derived quantities
• Quantities whose units are derived from the base units.
• The units of the derived quantities are called the derived
units.
• Using physical laws, derived units can be expressed as
combinations of the base units
For example: force is a derived quantity, its unit can
be determined using Newton’s second law:


F  ma
Newton N: F[N]=m[kg].a[m/s2]
dyn: F[dyn]=m[g].a[cm/s2
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Chapter 1. Physics and Mechanics
42
Mechanics(力学)
Chapter 1. Physics and Mechanics
1.1 The history of physics development
1.2 The Nature of Physics
1.3 Idealized Models
1.4 Standards For Measurement
1.5 Dimension analysis
1.6 Reference frame,coordinate system and time
1.7 Review and summary
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Chapter 1. Physics and Mechanics
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1.5 Dimension Analysis
Dimension analysis(量纲分析）
Dimension: the type of the measurement, regardless
of the units used.
For example, length is a dimension that could be
measured in meters, feet, ..
• The base dimensions in classical mechanics(SI system):
mass[M], length[L], and time[T].
• All the other dimensions can be expressed in terms of
the base dimension:
[ A]  L M T
p
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q
r
Dimensional equation
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1.5 Dimension Analysis
Example:
Force: [F]=LMT-2
Angle(unit:rad)：According the definition of centre
angle
s
L 0 0
   [ ]  M T  L0 M 0T 0  1 dimensionless
r
L
Dimension rule:
• Each term of a equation representing physical
phenomena must have the same dimension.
• The argument of a trigonometric function, and the
exponent in any exponential function are
dimensionless
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1.5 Dimension Analysis
Dimension analysis is a good habit to learn, because
• It can keep you from making errors in writing
equations;
• It can help you to memorize equations
1
L
at 2  L  2 T 2  L
2
T
x
The period of pendulum:
l
g
T  2
T  2
1
T
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L2
 L 
 2
T 
1
T
2
g
l
 L 
 2
T
T   1
L2
1
2
 T 1
Chapter 1. Physics and Mechanics
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1.5 Dimension Analysis
Sample example 4.-1
GIVEN: The acceleration a of a particle is related to its
velocity v, its position coordinate x, and time t by the
equation
a  Ax3t  Bvt 2
Where A and B are constants
FIND: the dimensions and units of A and B
Solution:
According to the dimension rules, each term on the
right-hand side of the equation must be [L/T2]
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1.5 Dimension Analysis
Ax t   Ax t   AL T   TL 
3
3
3

Dimension of A: A 
2

L  1 
 2 3
3
2

L T   T   L T 
1
 
Unit: m-2s-3
Bvt   Bvt   BTL  T   TL 
2
2
2
 

2

T   1   L   1 
Dimension of B: B     2   2    3 
 L  T  T  T 
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Chapter 1. Physics and Mechanics
Unit: s-3
48
Mechanics(力学)
Chapter 1. Physics and Mechanics
1.1 The history of physics development
1.2 The Nature of Physics
1.3 Idealized Models
1.4 Standards For Measurement
1.5 Dimension analysis
1.6 Reference frame,coordinate system and time
1.7 Review and summary
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Chapter 1. Physics and Mechanics
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1.6 Reference frame,coordinate system and time
Every physics process is related to time and space: we
need to know when and where the process occurs.
In classical mechanics, the space and time are “absolute”:
• Space and time are
unaffected by the presence
or absence of objects.
• Time is continuous,
uniform, and flows for ever.
• Space is continuous,
uniform, and isotropic.
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1.6 Reference frame,coordinate system and time
• Reference frame and coordinate system
Motion is absolute:
Everything in the universe is in motion;
Motion is relative:
To describe a body’s motion, you need to have an
another body as reference.
Reference frame(参考系):
The reference body or system of bodies without
relative internal motion;
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1.6 Reference frame,coordinate system and time
Note:
In kinematics, the choice of the reference
frame is arbitrary.
In kinetics, the representation of the law of motion
depends on the choice of reference frame:
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
Inertial reference frame(惯性参考系)

Non-inertial reference frame(非惯性参考系)
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1.6 Reference frame,coordinate system and time
Coordinate system:
Mathematical abstraction of the reference frame, used
to give quantitatively the spatial position of a body
relative to a point on the reference frame.
A coordinate system consists of:
• a fixed reference point called the origin
• a set of axes
• a definition of the coordinate variables
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1.6 Reference frame,coordinate system and time
Three kind of coordinate systems:
p
z
r
z
o
X
p
x
y
Rectangular
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y
o

Polar
Chapter 1. Physics and Mechanics
s
p
O
Path(自然坐标系）
54
1.6 Reference frame,coordinate system and time
Time coordinate
Quantitatively determines when a physical process
happened.
Origin
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t1
duration
t2
t
Chapter 1. Physics and Mechanics
55
Mechanics(力学)
Chapter 1. Physics and Mechanics
1.1 The history of physics development
1.2 The Nature of Physics
1.3 Idealized Models
1.4 Standards For Measurement
1.5 Dimension analysis
1.6 Reference frame,coordinate system and time
1.7 Review and summary
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1.7 Review and summary
1. The brief history of the physics development
• Classical physics
• Modern Physics
2. Characteristics of physics study
• Physics is an experimental science
• Ideal model: particle and rigid body
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1.7 Review and summary
3. Unit and dimension
• Base unit, derived unit
• Dimension and dimensional equation
• Dimension rules
4. Reference frame and coordinate system
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