4&5 Dynamics,Newton’s Laws and applications
Chapter 4&5
Newtonian Mechanics
1,Newton’s Law
2,Some Particular Forces
3,Applying Newton’s Laws.
4&5 Dynamics,Newton’s Laws and applications
New Words
1 Force (力）
Newton’s First Law — Inertial
（惯性） Law
4&5 Dynamics,Newton’s Laws and applications
Dynamics studies the connection
between force and motion.
4&5 Dynamics,Newton’s Laws and applications
英国物理学家,经典物理学的奠基人,他对力学、光学、
热学、天文学和数学等学科都有重大发现,其代表作,自然哲学的数学原理,是力学的经典著作,牛顿是近代自然科学奠基时期具有集前人之大成的贡献的伟大科学家,
牛顿 Issac Newton
（ 1643－ 1727）
4&5 Dynamics,Newton’s Laws and applications
An interaction（ 相互作用 ） that can cause an
acceleration of a body.
Force is a vector,when two or more forces act
on a body,the net force（ 合力 ） on a body is the
vector sum of all the forces acting on it.
4-1,Force (P77-P78)
1 Force (力）
Unit,N（牛顿）
4&5 Dynamics,Newton’s Laws and applications
4-2&4-3,Newton’s Law on Motion (P78-P79)
Every body continues in its state of rest or of
uniform speed in a straight line as long as no
net force acts on it.
(任何物体都保持静止或沿一条直线作匀速运动状态,
直到作用在它上面的力迫使它改变这种状态为止 ).
1,Newton’s First Law — Inertial（惯性） Law
v?时,恒矢量0?F?
4&5 Dynamics,Newton’s Laws and applications
1 惯性 —— 质点不受力时保持静止或匀速直线运动状态的的性质,其大小用质量量度。
2 力 —— 使质点改变运动状态的原因,
The force is the only reason which makes the states of
body change,It indicates the concept of force,An
interaction —–can cause an acceleration of a body.
Supplementary Explanation:
The concept of Inertia(惯性 ),The mass is an
intrinsic characteristic of a body,it
characterizes the inertia of the body.
Weight is a force and mass is a property of a body itself.
4&5 Dynamics,Newton’s Laws and applications
2 Inertial reference frames（惯性系） P79
In this book we usually assume that the ground is
an inertial frame,（ Neglect Earth’s actual
astronomical（ 天体的 ） motions such as its
rotation.） all frames that moves in uniform linear
motion relative to inertial frame are inertial
frames.
In fact it is a non-inertial frame（ 非惯性系 ）,
An inertial reference frame is one in which
Newton’s laws hold.
4&5 Dynamics,Newton’s Laws and applications
The acceleration of an object is directly
proportional to the net force acting on it and is
inversely proportional to its mass,The direction
of the acceleration is in the direction of the net
force acting on the object.
4-4.Newton’s Second Law of Motion (P79-P82)
1 Newton’s second law
)()( tamtF
4&5 Dynamics,Newton’s Laws and applications
The component forms of N-II Law:
Unit of force
Newton (N) 1N = 1kg · m/s2
zzn e t
yyn e t
xxn e t
maF
maF
maF
,
,
,
4&5 Dynamics,Newton’s Laws and applications
When two bodies interact,the
forces on the bodies from each
other are always equal in
magnitude and opposite in
direction.
m
m
＇T?
T?
P?
＇P?
地球
2112 FF
This two forces
are called third-
law force pair.
4-5.Newton’s Third Law of Motion (P82-P85)
4&5 Dynamics,Newton’s Laws and applications
Hey! The third-law force pair act on different bodies.
Supplementary explanation:
1,Simultaneous同时性 ;
2,Same type of force;
3,Acting on different bodies,do not cancel
each other.
成对性 —— 物体之间的作用是相互的。
同时性 —— 相互作用之间是相互依存，同生同灭。
Example 4-3 on page 83; example 4-5 on page 85
4&5 Dynamics,Newton’s Laws and applications
4-2,Some Particular Forces
1,The Gravitational Force (重力 ) (P 85 &133)
rrMmGF mM?2
Newton’s law of universal gravitation(万有引力定律）,
r
m
M
1F
2F
o
Every particle in the universe attracts
every other particle with a force that is
proportional to the product of their
masses and inversely proportional to the
square of the distance between them.
This force acts along the line joining the
two particles.
4&5 Dynamics,Newton’s Laws and applications
r
r
MmGF
mM?2
2211 / k gmN1067.6G
where directs away from its origin,The
gravitational constant (universal) (万有引力常数 )
r?
4&5 Dynamics,Newton’s Laws and applications
m
M R
y 226
24
211
2 m / s8.9)m1037.6(
)kg(1098.5)Nm / k g(1067.6?
R
MGg 地
where is also called
gravitational force (重力 ) —— a
special case of gravitation (万有引力 ).
gmF g
,?2 jmgrR mMGF
地
If the second body is earth,the body stay on the
earth,we usually mean a force that pulls on it
directly toward the center of earth,So:
★ 重力 是地球对其表面附近物体万有引力的分力,
4&5 Dynamics,Newton’s Laws and applications
2 The normal force（支持力） p85
When a body presses against a surface,the surface
deforms（变形） and pushes on the body with a
normal force that is perpendicular（垂直） to the
surface.
N N
4&5 Dynamics,Newton’s Laws and applications
3 Tension （张力、拉力）
For a cord（ 绳 ）
For a spring（ mass-less）：
ikxf
★ Hooke law,the elastic force
一般情况下,绳子上各处的张力大小是不相等的,
但在绳子的质量可以忽略不计时,绳子上各处的张力相等 。
4&5 Dynamics,Newton’s Laws and applications
4 Friction（摩擦力） (p105-16)
A frictional force is the force on a body when the
body slides or attempts（ 试图 ） to slide along a
surface,this force is directed along the surface,
opposite the direction of the intended motion.
Direction of attempted
slidef
If the body does not slide,the frictional force is a
static frictional force （ 静摩擦力 ）,If there is
sliding,the frictional force is a kinetic frictional
force (rolling friction).
4&5 Dynamics,Newton’s Laws and applications
4-4,Applying Newton’s Laws
1,Pick a body based on the feature of problem (研究对象 );
2,Draw a free-body diagram (画出隔离体的示力图 p89);
3,Choose coordinate axes (建立较方便的坐标系 );
4,Resolve vectors along chosen axes (沿轴分解矢量 );
5,Apply Newton’s laws of motion (列方程,统一单位,求解 );
6,Decide whether or not the solution makes sense.
Problem Solving Guide (p94 –95)
Note,try to choose one axis in the direction of
the acceleration,It may simplify the algebra.
No e:
4&5 Dynamics,Newton’s Laws and applications
A ring screen of radius R is horizontally fastened
on a frictionless surface,A slippy block of mass m
moves along its inner-wall,The frictional constant
between them is?,Find,(a) when the speed of
block is v,Frictional force f=? and at =? (b) How
long will it take as its(滑块 )speed decreases v? v/3?
N?
v?
tF
R
O
mv?
Using natural coordinate frame
Solution,(a)
4&5 Dynamics,Newton’s Laws and applications
R
vmN 2? R
va
t
2
tt maF?
N
N?
v?
tF
R
O
(b) from
t
va
t d
d
R
v 2
tRv
v dd
2
v
Rt
2
0
t
v
3/v
4&5 Dynamics,Newton’s Laws and applications
Example,Connected Objects(P109:5-5)
Apply Newton’s Laws
separately to each object
The acceleration of both
objects will be the same
The tension is the same in
each diagram
Solve the simultaneous
equations
Two objects m1=4.00 kg and m2=7.00 kg are connected by a
light string that passes over a frictionless pulley,The coefficient
of sliding friction between the 4.00 kg object and the surface is
0.300,Find the acceleration of the two objects and the tension
of the string.
4&5 Dynamics,Newton’s Laws and applications
Given:
mass1,m1=4.00 kg
mass2,m2=7.00 kg
friction,?=0.300
Find:
Tensions T=?
Acceleration a=?
1,Introduce two coordinate frames:
Oy,y’s are directed up
Ox,x’s are directed right
:,kN o t e F m a a n d f n
.0:
,::1
11
11
gmnFOy
amfTFOxM a s s
y
kx
.::2 222 amTgmFOyM a s s y
Solving those
equations:
a = 5.16 m/s2
T = 32.4 N
4&5 Dynamics,Newton’s Laws and applications
Summary for Chapter Two and Three
See P95 and 122
4&5 Dynamics,Newton’s Laws and applications
Homework,
P102:66,p124:20,29,P126:39; P128:76
Chapter 4&5
Newtonian Mechanics
1,Newton’s Law
2,Some Particular Forces
3,Applying Newton’s Laws.
4&5 Dynamics,Newton’s Laws and applications
New Words
1 Force (力）
Newton’s First Law — Inertial
（惯性） Law
4&5 Dynamics,Newton’s Laws and applications
Dynamics studies the connection
between force and motion.
4&5 Dynamics,Newton’s Laws and applications
英国物理学家,经典物理学的奠基人,他对力学、光学、
热学、天文学和数学等学科都有重大发现,其代表作,自然哲学的数学原理,是力学的经典著作,牛顿是近代自然科学奠基时期具有集前人之大成的贡献的伟大科学家,
牛顿 Issac Newton
（ 1643－ 1727）
4&5 Dynamics,Newton’s Laws and applications
An interaction（ 相互作用 ） that can cause an
acceleration of a body.
Force is a vector,when two or more forces act
on a body,the net force（ 合力 ） on a body is the
vector sum of all the forces acting on it.
4-1,Force (P77-P78)
1 Force (力）
Unit,N（牛顿）
4&5 Dynamics,Newton’s Laws and applications
4-2&4-3,Newton’s Law on Motion (P78-P79)
Every body continues in its state of rest or of
uniform speed in a straight line as long as no
net force acts on it.
(任何物体都保持静止或沿一条直线作匀速运动状态,
直到作用在它上面的力迫使它改变这种状态为止 ).
1,Newton’s First Law — Inertial（惯性） Law
v?时,恒矢量0?F?
4&5 Dynamics,Newton’s Laws and applications
1 惯性 —— 质点不受力时保持静止或匀速直线运动状态的的性质,其大小用质量量度。
2 力 —— 使质点改变运动状态的原因,
The force is the only reason which makes the states of
body change,It indicates the concept of force,An
interaction —–can cause an acceleration of a body.
Supplementary Explanation:
The concept of Inertia(惯性 ),The mass is an
intrinsic characteristic of a body,it
characterizes the inertia of the body.
Weight is a force and mass is a property of a body itself.
4&5 Dynamics,Newton’s Laws and applications
2 Inertial reference frames（惯性系） P79
In this book we usually assume that the ground is
an inertial frame,（ Neglect Earth’s actual
astronomical（ 天体的 ） motions such as its
rotation.） all frames that moves in uniform linear
motion relative to inertial frame are inertial
frames.
In fact it is a non-inertial frame（ 非惯性系 ）,
An inertial reference frame is one in which
Newton’s laws hold.
4&5 Dynamics,Newton’s Laws and applications
The acceleration of an object is directly
proportional to the net force acting on it and is
inversely proportional to its mass,The direction
of the acceleration is in the direction of the net
force acting on the object.
4-4.Newton’s Second Law of Motion (P79-P82)
1 Newton’s second law
)()( tamtF
4&5 Dynamics,Newton’s Laws and applications
The component forms of N-II Law:
Unit of force
Newton (N) 1N = 1kg · m/s2
zzn e t
yyn e t
xxn e t
maF
maF
maF
,
,
,
4&5 Dynamics,Newton’s Laws and applications
When two bodies interact,the
forces on the bodies from each
other are always equal in
magnitude and opposite in
direction.
m
m
＇T?
T?
P?
＇P?
地球
2112 FF
This two forces
are called third-
law force pair.
4-5.Newton’s Third Law of Motion (P82-P85)
4&5 Dynamics,Newton’s Laws and applications
Hey! The third-law force pair act on different bodies.
Supplementary explanation:
1,Simultaneous同时性 ;
2,Same type of force;
3,Acting on different bodies,do not cancel
each other.
成对性 —— 物体之间的作用是相互的。
同时性 —— 相互作用之间是相互依存，同生同灭。
Example 4-3 on page 83; example 4-5 on page 85
4&5 Dynamics,Newton’s Laws and applications
4-2,Some Particular Forces
1,The Gravitational Force (重力 ) (P 85 &133)
rrMmGF mM?2
Newton’s law of universal gravitation(万有引力定律）,
r
m
M
1F
2F
o
Every particle in the universe attracts
every other particle with a force that is
proportional to the product of their
masses and inversely proportional to the
square of the distance between them.
This force acts along the line joining the
two particles.
4&5 Dynamics,Newton’s Laws and applications
r
r
MmGF
mM?2
2211 / k gmN1067.6G
where directs away from its origin,The
gravitational constant (universal) (万有引力常数 )
r?
4&5 Dynamics,Newton’s Laws and applications
m
M R
y 226
24
211
2 m / s8.9)m1037.6(
)kg(1098.5)Nm / k g(1067.6?
R
MGg 地
where is also called
gravitational force (重力 ) —— a
special case of gravitation (万有引力 ).
gmF g
,?2 jmgrR mMGF
地
If the second body is earth,the body stay on the
earth,we usually mean a force that pulls on it
directly toward the center of earth,So:
★ 重力 是地球对其表面附近物体万有引力的分力,
4&5 Dynamics,Newton’s Laws and applications
2 The normal force（支持力） p85
When a body presses against a surface,the surface
deforms（变形） and pushes on the body with a
normal force that is perpendicular（垂直） to the
surface.
N N
4&5 Dynamics,Newton’s Laws and applications
3 Tension （张力、拉力）
For a cord（ 绳 ）
For a spring（ mass-less）：
ikxf
★ Hooke law,the elastic force
一般情况下,绳子上各处的张力大小是不相等的,
但在绳子的质量可以忽略不计时,绳子上各处的张力相等 。
4&5 Dynamics,Newton’s Laws and applications
4 Friction（摩擦力） (p105-16)
A frictional force is the force on a body when the
body slides or attempts（ 试图 ） to slide along a
surface,this force is directed along the surface,
opposite the direction of the intended motion.
Direction of attempted
slidef
If the body does not slide,the frictional force is a
static frictional force （ 静摩擦力 ）,If there is
sliding,the frictional force is a kinetic frictional
force (rolling friction).
4&5 Dynamics,Newton’s Laws and applications
4-4,Applying Newton’s Laws
1,Pick a body based on the feature of problem (研究对象 );
2,Draw a free-body diagram (画出隔离体的示力图 p89);
3,Choose coordinate axes (建立较方便的坐标系 );
4,Resolve vectors along chosen axes (沿轴分解矢量 );
5,Apply Newton’s laws of motion (列方程,统一单位,求解 );
6,Decide whether or not the solution makes sense.
Problem Solving Guide (p94 –95)
Note,try to choose one axis in the direction of
the acceleration,It may simplify the algebra.
No e:
4&5 Dynamics,Newton’s Laws and applications
A ring screen of radius R is horizontally fastened
on a frictionless surface,A slippy block of mass m
moves along its inner-wall,The frictional constant
between them is?,Find,(a) when the speed of
block is v,Frictional force f=? and at =? (b) How
long will it take as its(滑块 )speed decreases v? v/3?
N?
v?
tF
R
O
mv?
Using natural coordinate frame
Solution,(a)
4&5 Dynamics,Newton’s Laws and applications
R
vmN 2? R
va
t
2
tt maF?
N
N?
v?
tF
R
O
(b) from
t
va
t d
d
R
v 2
tRv
v dd
2
v
Rt
2
0
t
v
3/v
4&5 Dynamics,Newton’s Laws and applications
Example,Connected Objects(P109:5-5)
Apply Newton’s Laws
separately to each object
The acceleration of both
objects will be the same
The tension is the same in
each diagram
Solve the simultaneous
equations
Two objects m1=4.00 kg and m2=7.00 kg are connected by a
light string that passes over a frictionless pulley,The coefficient
of sliding friction between the 4.00 kg object and the surface is
0.300,Find the acceleration of the two objects and the tension
of the string.
4&5 Dynamics,Newton’s Laws and applications
Given:
mass1,m1=4.00 kg
mass2,m2=7.00 kg
friction,?=0.300
Find:
Tensions T=?
Acceleration a=?
1,Introduce two coordinate frames:
Oy,y’s are directed up
Ox,x’s are directed right
:,kN o t e F m a a n d f n
.0:
,::1
11
11
gmnFOy
amfTFOxM a s s
y
kx
.::2 222 amTgmFOyM a s s y
Solving those
equations:
a = 5.16 m/s2
T = 32.4 N
4&5 Dynamics,Newton’s Laws and applications
Summary for Chapter Two and Three
See P95 and 122
4&5 Dynamics,Newton’s Laws and applications
Homework,
P102:66,p124:20,29,P126:39; P128:76
