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制制 制制制 制制 制制制 Yangtze University Yangtze University Bilingual Bilingual Mechanics Mechanics Chapter 3 Forc Forc e e

制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

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Page 1: 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

BilingualBilingual MechanicsMechanics

BilingualBilingual MechanicsMechanics Chapter 3

ForceForce

Chapter 3

ForceForce

Page 2: 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

Chinese astronauts Jing Haipeng(L), Zhai Zhigang(C) and Liu Boming wave hands during a press conference in Jiuquan Satellite Launch Center (JSLC) in Northwest China's Gansu Province, September 24, 2008. The Shenzhou VII spaceship will blast off Thursday evening from the JSLC to send the three astronauts into space for China's third manned space mission.

Chinese astronauts Jing Haipeng(L), Zhai Zhigang(C) and Liu Boming wave hands during a press conference in Jiuquan Satellite Launch Center (JSLC) in Northwest China's Gansu Province, September 24, 2008. The Shenzhou VII spaceship will blast off Thursday evening from the JSLC to send the three astronauts into space for China's third manned space mission.

Page 3: 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

China´s manned spacecraft Shenzhou-7 blasts offChina´s manned spacecraft Shenzhou-7 blasts off

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China´s manned spacecraft Shenzhou-7 blasts off China´s manned spacecraft Shenzhou-7 blasts off

Page 5: 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

Chinese taikonauts report they feel "physically sound"Chinese taikonauts report they feel "physically sound"

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Astronauts assemble EVA suit for spacewalkAstronauts assemble EVA suit for spacewalk

Page 7: 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

China successfully launched its third manned spacecraft on Thursday with three astronauts on board to attempt the country‘s first-ever space walk.

China successfully launched its third manned spacecraft on Thursday with three astronauts on board to attempt the country‘s first-ever space walk.

The spaceship Shenzhou-7 blasted off on a Long March II-F carrier rocket from the Jiuquan Satellite Launch Center in the northwestern Gansu Province at 9:10 p.m. after a breathtaking countdown to another milestone on China's space

The spaceship Shenzhou-7 blasted off on a Long March II-F carrier rocket from the Jiuquan Satellite Launch Center in the northwestern Gansu Province at 9:10 p.m. after a breathtaking countdown to another milestone on China's space journey.journey.

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Onboard pilots Zhai Zhigang, Liu Boming and Jing Haipeng are expected to orbit the earth for three days, when one of them will float out of the cabin about 343 kilometers above the earth.

Onboard pilots Zhai Zhigang, Liu Boming and Jing Haipeng are expected to orbit the earth for three days, when one of them will float out of the cabin about 343 kilometers above the earth.

When they make it, China will become the third country in the world who is able to conduct extravehicular activity (EVA) in space following the former Soviet Union and the United States.

When they make it, China will become the third country in the world who is able to conduct extravehicular activity (EVA) in space following the former Soviet Union and the United States.

The spaceship is scheduled to land in the central region of north China's Inner Mongolia Autonomous Region after completing the task.

The spaceship is scheduled to land in the central region of north China's Inner Mongolia Autonomous Region after completing the task.

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The fundamental principles of space flight is Mechanics !

The fundamental principles of space flight is Mechanics !

Physics is the cradle of modern science and technology !

Physics is the cradle of modern science and technology !

Congratulations to the successful launching of the Shenzhou-7 !

Congratulations to the successful launching of the Shenzhou-7 !

Page 10: 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

制作 张昆实制作 张昆实

Yangtze UniversityYangtze University

BilingualBilingual MechanicsMechanics

BilingualBilingual MechanicsMechanics Chapter 3

ForceForce

Chapter 3

ForceForce

Page 11: 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University 制作 张昆实 Yangtze University Bilingual Mechanics Chapter 3 Force

Chapter 3 Chapter 3 ForceForce Chapter 3 Chapter 3 ForceForce

3-1 What Is Physics?

3-2 Newtonian Mechanics

3-3 Newton’s First Law

3-4 Force

3-5 Mass

3-6 Newton’s Second Law

3-7 Newton’s Third Law

3-1 What Is Physics?

3-2 Newtonian Mechanics

3-3 Newton’s First Law

3-4 Force

3-5 Mass

3-6 Newton’s Second Law

3-7 Newton’s Third Law

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Chapter 3 Chapter 3 ForceForce Chapter 3 Chapter 3 ForceForce

3-8 Applying Newton’s Laws

3-9 Some Particular Forces

3-10 Friction

3-11 The Drag Force and Terminal Speed

3-12 Uniform Circular Motion

*3-13 Noninertial Reference System and Inertial Forces

3-8 Applying Newton’s Laws

3-9 Some Particular Forces

3-10 Friction

3-11 The Drag Force and Terminal Speed

3-12 Uniform Circular Motion

*3-13 Noninertial Reference System and Inertial Forces

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3-1 What Is Physics 3-1 What Is Physics

★We have discussed how motion is described in terms of velocity and acceleration.

★We have discussed how motion is described in terms of velocity and acceleration.

★ Now we deal with the question of why objects move as they do:

★ Now we deal with the question of why objects move as they do:

★ In this chapter we learn what is physicswhat is physics through investigating the connection between force and motion, which is the subject called dynamics.

★ In this chapter we learn what is physicswhat is physics through investigating the connection between force and motion, which is the subject called dynamics.

What makes an object at rest begin to move?What makes an object at rest begin to move?

What causes a body to accelerate or decelerate?What causes a body to accelerate or decelerate?

What is involved when an object moves in a circle?What is involved when an object moves in a circle?

( Kinematics )( Kinematics )

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.

3-2 Newtonian Mechanics 3-2 Newtonian Mechanics

★ The relationship between a force and the acceleration it causes was first understood by Isaac Newton

★ The relationship between a force and the acceleration it causes was first understood by Isaac Newton

Newton published his book 《 The Mathematical Principles of Natural Philosophy 》 in 1687.

Newton published his book 《 The Mathematical Principles of Natural Philosophy 》 in 1687.

★ The study of that relation is called Newtonian Mechanics★ The study of that relation is called Newtonian Mechanics

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3-2 Newtonian Mechanics 3-2 Newtonian Mechanics

Modifications are necessary: Modifications are necessary:

★★ Quantum mechanicsQuantum mechanics (for the scale of (for the scale of atomic structure)atomic structure)★★ Quantum mechanicsQuantum mechanics (for the scale of (for the scale of atomic structure)atomic structure)

★ ★ Special theory of relativity Special theory of relativity (for very (for very high speed speed of lighhigh speed speed of light)t)

★ ★ Special theory of relativity Special theory of relativity (for very (for very high speed speed of lighhigh speed speed of light)t)Newtonian Mechanics is viewed as a special case of these two more comprehensive theories.

Newtonian Mechanics is viewed as a special case of these two more comprehensive theories.

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3-3 Newton’s First Law3-3 Newton’s First Law

★ Observations: Send a puck sliding over a extremely slippery surface, over which the puck would hardly slow.

★ Observations: Send a puck sliding over a extremely slippery surface, over which the puck would hardly slow.

★Conclusion: a body will keep moving with constant velocityconstant velocity if no forceno force acts on it.

★Conclusion: a body will keep moving with constant velocityconstant velocity if no forceno force acts on it.

★ Newton’s First Law:Newton’s First Law: If no force acts on a body, then the body’s

velocityvelocity cannot changecannot change; that is, the body ccannot accelerateannot accelerate.

★ Newton’s First Law:Newton’s First Law: If no force acts on a body, then the body’s

velocityvelocity cannot changecannot change; that is, the body ccannot accelerateannot accelerate. at rest remain at rest;at rest remain at rest; in motion move with constant in motion move with constant velocity.velocity.

at rest remain at rest;at rest remain at rest; in motion move with constant in motion move with constant velocity.velocity.

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3-4 Force3-4 Force ★ Define the unit of force in terms of the acceleration that a force gives to a standard reference body (a mass of 1 kg).

★ Define the unit of force in terms of the acceleration that a force gives to a standard reference body (a mass of 1 kg). ★ A force (vector)

is measured by acceleration it produces.

★ A force (vector) is measured by acceleration it produces.

mass acceleration force

1kg 1 m/s2 1N

1kg 2 m/s2 2N

1kg a m/s2 aN

★Principle of superposition for forces When two or more forces act on a body, a net force or resultant force can be found. The net force has the same effect on the body as all the individual forces together.

★Principle of superposition for forces When two or more forces act on a body, a net force or resultant force can be found. The net force has the same effect on the body as all the individual forces together.

magnitude; directionmagnitude; direction

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3-4 Force3-4 Force★ Newton’s First Law (restate): If no net force acts on a body ( ), t

hen the body’s velocity cannot change; that is, the body cannot accelerate.

★ Newton’s First Law (restate): If no net force acts on a body ( ), t

hen the body’s velocity cannot change; that is, the body cannot accelerate.

★ Inertial Reference Frames An inertial reference frame is one in which Newton’s laws hold.

★ Inertial Reference Frames An inertial reference frame is one in which Newton’s laws hold.Example: the ground, any reference frame moving with constant velocity with respect to the ground.

Example: the ground, any reference frame moving with constant velocity with respect to the ground.

★ Noninertial frame: a accelerating frame; a rotational frame.★ Noninertial frame: a accelerating frame; a rotational frame.

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3-5 Mass3-5 Mass

★ What is mass ? the less massive baseball receives a larger acceleration

★ What is mass ? the less massive baseball receives a larger acceleration

0

0

x

x

m a

m a 0

0xx

am m

a

the more massive bowling ball receives a smaller acceleration

the more massive bowling ball receives a smaller acceleration

★ Conjecture: The ratio of the masses of two bodies is equal to the inverse of the ratio of their accelerations when the same force is applied to both.

★ Conjecture: The ratio of the masses of two bodies is equal to the inverse of the ratio of their accelerations when the same force is applied to both.

Equal forceEqual force

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3-5 Mass3-5 Mass

★ What is mass ?

★ What is mass ?

0

0

x

x

m a

m a 0

0xx

am m

a

1.01.0 4.0

0.25xm kg

8.01.0 4.0

2.0xm kg

0 1.0m kg

20.25 /xa m s 20 1.0 /a m s

20 8.0 /a m s

22.0 /xa m s

Equal forceEqual force

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3-5 Mass3-5 Mass

★ Mass is an intrinsic characteristic of a bo

dy a characteristic that automatically co

mes with the existance of the body.

★ Mass is an intrinsic characteristic of a bo

dy a characteristic that automatically co

mes with the existance of the body.

★ The mass of a body is the characteristic

that relates a force on the body to the

resulting acceleration.

★ The mass of a body is the characteristic

that relates a force on the body to the

resulting acceleration.

★ Mass is a measure of the inertia of a body.★ Mass is a measure of the inertia of a body.

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3-6 Newton’s Second Law3-6 Newton’s Second Law

★ Newton's Second Law The net force on a body is equal to the pro

duct of the body’s mass and the acceleration of the body.

(Newton's second law)

★ Newton's Second Law The net force on a body is equal to the pro

duct of the body’s mass and the acceleration of the body.

(Newton's second law)netF ma

, ,net x xF ma , ,net y yF ma ,net z zF ma (3-2)

★ Caution: is the mass of a body, is the vector sum of all the forces act on that body.

★ Caution: is the mass of a body, is the vector sum of all the forces act on that body.

★ Equivalent equations:★ Equivalent equations:

m netF

(3-1)

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★ The acceleration component along a given axis is caused only by the force component along that same axis, and not by force component along any other axis.

★ The acceleration component along a given axis is caused only by the force component along that same axis, and not by force component along any other axis.

3-6 Newton’s Second Law3-6 Newton’s Second Law

, ,net x xF ma , ,net y yF ma ,net z zF ma (5-2)

0netF

v C

0a

IfIf

(a) at rest (a) at rest stays at reststays at rest

(b) In motion(b) In motion move at constant velocitymove at constant velocity

the forces and the body: in equilibriumthe forces and the body: in equilibrium

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3-6 Newton’s Second Law3-6 Newton’s Second Law

★ The SI unit of force: Newton (N)★ The SI unit of force: Newton (N)2 21 (1 )(1 / ) 1 /N kg m s kg m s

★ the free-body diagram ★ the free-body diagram

To solve problems with Newton’s second law, we often draw a free-body diagram in which only one body, represented by a dot, is considered. The external forces on the body are drawn. A coordinate system is usually included.

To solve problems with Newton’s second law, we often draw a free-body diagram in which only one body, represented by a dot, is considered. The external forces on the body are drawn. A coordinate system is usually included.

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3-6 Newton’s Second Law3-6 Newton’s Second Law

★ internal forces: forces between two bodies inside the system (a collection of two or more bodies).

★ internal forces: forces between two bodies inside the system (a collection of two or more bodies).

★ external forces: any force on the bodies inside the system (a collection of two or more bodies) from bodies outside the system.

★ external forces: any force on the bodies inside the system (a collection of two or more bodies) from bodies outside the system.

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3-7 Newton’s Third Law3-7 Newton’s Third Law ★ Newton’s Third Law :

When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.

★ Newton’s Third Law :

When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.

● A pair of action-reaction forces

a third law force pair

● A pair of action-reaction forces

a third law force pair

● Vector form:● Vector form: BC CBF F

BC CBF F● Scalar form:● Scalar form: book B leans against crate Cbook B leans against crate C

BCF

B C CBF

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3-7 Newton’s Third Law3-7 Newton’s Third Law

★ Exp. Cantaloupe-table-earth three bodies★ Exp. Cantaloupe-table-earth three bodies A pair of action-reaction forces ( a third law force pair) A pair of action-reaction forces ( a third law force pair)

CE ECF F

● Cantaloupe-Earth interaction:● Cantaloupe-Earth interaction: Cantaloupe C Cantaloupe C

● Cantaloupe-Table interaction:● Cantaloupe-Table interaction:

CT TCF F

Table T Table T

Earth E Earth E

( gravitational force )( gravitational force )

Note: and Note: and are not !are not !CTF

CEF

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3-8 Applying Newton’s Laws3-8 Applying Newton’s Laws

★ When you read the sample problems, pay attention to:

★ When you read the sample problems, pay attention to:

How to use Newton's Laws to solve problems.

How to use Newton's Laws to solve problems.

Problem solving procedures; Problem solving procedures;

How to draw a free-body diagram with appropriate axes;How to draw a free-body diagram with appropriate axes;

P55 Sample problems 3-1 P55 Sample problems 3-1

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3-8 Applying Newton’s Laws3-8 Applying Newton’s Laws P55 Sample problem 3-1 P55 Sample problem 3-1

frictionless pulleyfrictionless pulley

cord cord

3.3M kg2.1m kg

T

xa

x za a a

za

T

T

Earth is involvedEarth is involved

SolutionSolution Problem descriptionProblem description

Two blocks particles, Earth is also involved ; Two blocks particles, Earth is also involved ;

Cord massless, unstretchable;Cord massless, unstretchable;

Pulley massless, only changes the cord’s orientation.Pulley massless, only changes the cord’s orientation.

equal in all sections of the cord.equal in all sections of the cord.

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3-8 Applying Newton’s Laws3-8 Applying Newton’s Laws

Earth is involvedEarth is involved

draw free-body diagram draw free-body diagram

Block SBlock S

M mx

y

x

y

T a

T Ma

NF

gSF

T

a gHF

apply Newton’s second law apply Newton’s second law0N gSF F

(3-5)

T mg ma Block HBlock H (3-6)

Solving for yieldsSolving for yieldsa

Substituting into Eq.3-5 yieldsSubstituting into Eq.3-5 yields

a

3.3M kg2.1m kg

23.8 /m

a g m sM m

(3-7)

13Mm

T g NM m

(3-8)

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3-8 Applying Newton’s Laws3-8 Applying Newton’s Laws P57 Sample problem 3-2 P57 Sample problem 3-2

In fig.3-8a, a cord holds a 15 kg block stationary on a friction-less plane inclined at angle In fig.3-8a, a cord holds a 15 kg block stationary on a friction-less plane inclined at angle

(a) What are the magnitudes of the force on the block from the cord and the normal force from the plane?(a) What are the magnitudes of the force on the block from the cord and the normal force from the plane?

(b) We now cut the cord. Does the block accelerate as it slides down the inclined plane? If so, what is its acceleration?(b) We now cut the cord. Does the block accelerate as it slides down the inclined plane? If so, what is its acceleration?

15m kg

T27

NF

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3-8 Applying Newton’s Laws3-8 Applying Newton’s Laws

SolutionSolution free-body diagram free-body diagram

0N gT F F

Three forces are in equilibrium Three forces are in equilibrium

Use a coordinate systemUse a coordinate system

sinmg ma (b) Cutting the cord :Cutting the cord :0T

,y axis cos 0NF mg

,x axis sin 0T mg (a)

,x axis

2cos (15 )(9.8 / )(cos 27 ) 131NF mg kg m s N

2sin (15 )(9.8 / )(sin 27 ) 67T mg kg m s N

sina g 2 2(9.8 / )(sin 27 ) 4.4 /m s m s

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3-9 Some Particular Forces3-9 Some Particular Forces

★ The Gravitational Force on a body is a pull by another body (Earth). For Earth, the force is directed down toward the ground, which is assumed to be a inertial frame.

★ The Gravitational Force on a body is a pull by another body (Earth). For Earth, the force is directed down toward the ground, which is assumed to be a inertial frame.

gF

★ A body (mass m) is in free fall with the free- fall acceleration of magnitude g. the only force acting on the body is the gravitational force (neglecting the effects of the air).

★ A body (mass m) is in free fall with the free- fall acceleration of magnitude g. the only force acting on the body is the gravitational force (neglecting the effects of the air).

gF

★ choose a vertical y axis along the body’s path, with the positive direction upward.

★ choose a vertical y axis along the body’s path, with the positive direction upward.

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★ The Gravitational Force

Newton’s second law

the vector form:

★Weight (scalar)

The weight W of a body is the magnitude of the net force required to provent the body from falling freely.

upward force = grivatational forcebalanced keep the ball at rest the weight of the ball is the magnitude of the upward force 2N

★ The Gravitational Force

Newton’s second law

the vector form:

★Weight (scalar)

The weight W of a body is the magnitude of the net force required to provent the body from falling freely.

upward force = grivatational forcebalanced keep the ball at rest the weight of the ball is the magnitude of the upward force 2N

F ma

,net y yF ma( )gF m g gF mg (3-14)

g gF F j mgj mg

(3-15)

Upward force 2N

2gF N

3-9 Some Particular Forces3-9 Some Particular Forces

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In general: a body has relative to the ground (inertial frame), two forces acting on it are balanced. in vertical direction:

(weight, with ground as inertial frame)

Substituting for : (weight)

The weight of a body is equal to the magnitude

of the gravitational force on the body.

In general: a body has relative to the ground (inertial frame), two forces acting on it are balanced. in vertical direction:

(weight, with ground as inertial frame)

Substituting for : (weight)

The weight of a body is equal to the magnitude

of the gravitational force on the body.

(0)gW F m ,net y yF ma

0a

gF

Wy

(3-16)

gW F (3-17)

gFmg W mg (3-18)

( )gF mgW

3-9 Some Particular Forces3-9 Some Particular Forces

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Measuring the weight of a body:

Measuring the weight of a body:

When the device is in balance,The gravitational force on the Body (L) is equal to the gravi-tational force on the reference bodies (R).

When the device is in balance,The gravitational force on the Body (L) is equal to the gravi-tational force on the reference bodies (R).

The body stretches a spring, moving a pointer along a scale (mass or force units)

The body stretches a spring, moving a pointer along a scale (mass or force units)

Equal-arm balanceEqual-arm balance

3-9 Some Particular Forces3-9 Some Particular Forces

Spring scaleSpring scale

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★The weight of a body must be measured when the body is not acceleratingnot accelerating verticallyvertically relative to the grounthe groundd.

● apparent weightapparent weight : elevator (lift) cab

weightapparent

weight apparent weight weight

a a

3-9 Some Particular Forces3-9 Some Particular Forces

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★The weightweight of a body is not the massmass of the b

ody.

★The weightweight of a body is not the massmass of the b

ody.

MassMass WeightWeight

Measurement of inertial

Mass is constant (v<<C speed of light)

Measured in kg

The magnitude of the gravitational force

varies in different places latitude altitudelatitude altitude

Measured in N

3-9 Some Particular Forces3-9 Some Particular Forces

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★The Normal Force

★The Normal Force

gF

Normal forcey

0

gF

NF

gF

NF

When a body presses againsta surface, the surface ( evena seeminly rigid surface ) deforms and pushes on thebody with a normal forcethat is perpendicular to thesurface.

When a body presses againsta surface, the surface ( evena seeminly rigid surface ) deforms and pushes on thebody with a normal forcethat is perpendicular to thesurface.

NF

,net y yF maExp. A block rests on a tabletopExp. A block rests on a tabletop

,net y N yF F mg ma 0ya

3-9 Some Particular Forces3-9 Some Particular Forces

( )N y yF mg ma m g a (3-19)

NF mg(3-20)

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3-9 Some Particular Forces3-9 Some Particular ForcesCord : massless, unstretchable Cord : massless, unstretchable

Pulley : massless, frictionlessPulley : massless, frictionless

The pulls at both ends of the cord have the same maglitude T and are directed along the cord.

The pulls at both ends of the cord have the same maglitude T and are directed along the cord.

Tension: when the cord is bing pulled taut, The cord is under tension, it pulls on a body at each of its ends.

Tension: when the cord is bing pulled taut, The cord is under tension, it pulls on a body at each of its ends.

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★ Friction

★ Friction

● A frictional force is the force on a body when the body slides or attempts to slide along a surface.

● A frictional force is the force on a body when the body slides or attempts to slide along a surface.

f Direction of

attemptedslide

f

★ Frictional forces exist everywhere. ★ Frictional forces exist everywhere.

3-10 Friction3-10 Friction

● The force is always parallel to the surface● The force is always parallel to the surface

● The force is directed so as to oppose the motion of the body.● The force is directed so as to oppose the motion of the body.

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3-10 Friction3-10 Friction

● If the body does not slide, the frictional force is a static frictional force .

● If the body does not slide, the frictional force is a static frictional force .

sf

● If there is sliding, the frictional force is a kinetic frictional force . ● If there is sliding, the frictional force is a kinetic frictional force . kf

F

sf

at restat rest

v

F

kfin motionin motion

F

breakawaybreakaway

,maxsf

kf

breakawaybreakaway

,maxsf

time

Frictio

na

l forc

e

sf

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The frictional force has three properties:The frictional force has three properties:

3-10 Friction3-10 Friction

Property1. If the body does not move, then thestatic frictional force and the component of that is parallel to the surface balance eachother.

Property1. If the body does not move, then thestatic frictional force and the component of that is parallel to the surface balance eachother.

F sf

s is the coefficient of static frictionis the coefficient of static friction

If , the body begins to slide.If , the body begins to slide.,maxsF f

Property2. The magnitude of has a maximum v

elue :

Property2. The magnitude of has a maximum v

elue :

,s maxf

,s max sf N

sf

(3-21)

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Property3. If the body begins to slide along the s

urface, the magnitude of the frictional force rap

idly decreases to a value

Property3. If the body begins to slide along the s

urface, the magnitude of the frictional force rap

idly decreases to a value

kf

k kf N (3-22)

3-10 Friction3-10 Friction

k is the coefficient of kinetic friction.is the coefficient of kinetic friction.

The coefficient and are dimensionless and

must be determined experimentlly.

The coefficient and are dimensionless and

must be determined experimentlly.

ks

P65 Sample problem 3-5 P65 Sample problem 3-5

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When there is a relative motion between air( or some other fluid ) and a body, the bodyexperiences a drag force that opposes the relative motion and points in the direction In which the fluit flows relative to the body. The magnitude of is related to the relative speed by an experimentlly determined drag coefficient C according to

When there is a relative motion between air( or some other fluid ) and a body, the bodyexperiences a drag force that opposes the relative motion and points in the direction In which the fluit flows relative to the body. The magnitude of is related to the relative speed by an experimentlly determined drag coefficient C according to

D

D

(6-14)

v

212D C Av (3-28)

3-11 The Drag Force and Terminal speed3-11 The Drag Force and Terminal speed

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Where is the air density; is the effective cross-sectional area of the body ( the area of a cross section takenperpendicular to the velocity ).

The drag coefficient C can vary with the variation of , For simplicity, take it as a constant.

Where is the air density; is the effective cross-sectional area of the body ( the area of a cross section takenperpendicular to the velocity ).

The drag coefficient C can vary with the variation of , For simplicity, take it as a constant.

A

v

v

212D C Av (3-28)

3-11 The Drag Force and Terminal speed3-11 The Drag Force and Terminal speed

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D

gF

gF

D

gF

D

(3-28)21

2D C Av

,net yF ,net yF

gF

Falling body

v D v

D v D

During the falling, Newton’s second law for a vertical y axis:

If the body falls long enough, eventually equals the body falls at the terminal speed ( constant ).

During the falling, Newton’s second law for a vertical y axis:

If the body falls long enough, eventually equals the body falls at the terminal speed ( constant ).

, ,net y yF ma gD F ma (3-29)

DgF 0a

, 0net yF

gF

D

tv c

gD F

0a

3-11 The Drag Force and Terminal speed3-11 The Drag Force and Terminal speed

tv

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If the body falls long enough, eventually equals the body’s speed no longer increases. The body then falls at a constant speed, called the

terminal speed

If the body falls long enough, eventually equals the body’s speed no longer increases. The body then falls at a constant speed, called the

terminal speed(3-29)

D

gF 0a

tv

, 0net yF

gF

D

tv c

gD F

0a

Find :Find :tv 0gD F ma

(3-30)2 g

t

Fv

C A

212 0t gC Av F

terminal speedterminal speed

3-11 The Drag Force and Terminal speed3-11 The Drag Force and Terminal speed

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Skydiving

3-11 The Drag Force and Terminal speed3-11 The Drag Force and Terminal speed

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Group Skydiving

3-11 The Drag Force and Terminal speed3-11 The Drag Force and Terminal speed

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★ Uniform circular Motion : ( Section 2-12 )

A particle travel around a circle or a circular arc at constant (uniform) speed , it is said to be in Uniform circular Motion. The body has a centripetal acceleration.direction: toward the center of the circle; magnitude:

3-12 Uniform Circular Motion3-12 Uniform Circular Motion

2va

R (2-70)

Example: P70 Fig.3-21 ,

A centripetal force accelerates a body by changing the direction of the body’s velocity without changing the body’s speed.

v

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★ From Newton’s second law and ★ From Newton’s second law and

3-12 Uniform Circular Motion3-12 Uniform Circular Motion

Sample problem 3-9 : P73

2a v R2v

F mR

(4-32)(magnitude of centripetal force)(magnitude of centripetal force)

The directions of the centripetal acceleration and force are not constant, they vary continuously so as to always point toword the center of the circlealong a radial axis . The positive direction of the axis is radially outward, but the acceleration and force vectors point radially inward.

The directions of the centripetal acceleration and force are not constant, they vary continuously so as to always point toword the center of the circlealong a radial axis . The positive direction of the axis is radially outward, but the acceleration and force vectors point radially inward.

r

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3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

1. Lineal accelerating reference frame 1. Lineal accelerating reference frame A car is moving with acceleration from rest. A steel ball is put on a frictionless surface of a table in the car

A car is moving with acceleration from rest. A steel ball is put on a frictionless surface of a table in the car

No net force on the ball,The ball accelerats with relative to the car !Newton’s laws don’t hold !Suppose: a acting on it, then: hold !

No net force on the ball,The ball accelerats with relative to the car !Newton’s laws don’t hold !Suppose: a acting on it, then: hold !

No net force acts on the ball,The ball rests related to the ground.Newton’s laws hold

No net force acts on the ball,The ball rests related to the ground.Newton’s laws hold

observer on ground observer on ground observer in the car observer in the car

F ma

a

a

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3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

1. Lineal accelerating reference frame 1. Lineal accelerating reference frame A steel ball is connectedto a spring As the car moves with a acceleration from rest,the spring is stretched

A steel ball is connectedto a spring As the car moves with a acceleration from rest,the spring is stretched

a

A elastic force acts on the ball, But the ball rests relative to the car !Newton’s laws don’t hold !Suppose: a acting on it, then: hold !

A elastic force acts on the ball, But the ball rests relative to the car !Newton’s laws don’t hold !Suppose: a acting on it, then: hold !

A elastic force acts on the ball, The ballmoves with ,

Newton’s laws hold

A elastic force acts on the ball, The ballmoves with ,

Newton’s laws hold

observer on groundobserver on ground observer on groundobserver on ground observer in the carobserver in the car observer in the carobserver in the car

*f ma

a

*

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*F ma

3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

In a linear accelerating reference frameIn a linear accelerating reference frame the Inertial Force acting on a body is equal to the product of and ( the acceleration of the noninertial reference system ), in opposite direction.

In a linear accelerating reference frameIn a linear accelerating reference frame the Inertial Force acting on a body is equal to the product of and ( the acceleration of the noninertial reference system ), in opposite direction.

1. There is no reaction 1. There is no reaction force !force ! 2. Can be observed 2. Can be observed onlyonly in in noninertial referencenoninertial reference frame ! frame !

1. There is no reaction 1. There is no reaction force !force ! 2. Can be observed 2. Can be observed onlyonly in in noninertial referencenoninertial reference frame ! frame !

1.There is 1.There is a third law fa third law force pair;orce pair; 2. Can be 2. Can be observed in both observed in both inertiinertialal and and noninertial refernoninertial reference frame.ence frame.

1.There is 1.There is a third law fa third law force pair;orce pair; 2. Can be 2. Can be observed in both observed in both inertiinertialal and and noninertial refernoninertial reference frame.ence frame.

interacting forceinteracting force interacting forceinteracting force Inertial ForceInertial Force Inertial ForceInertial Force

*F

am

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3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

Dynamical equation in a linear

accelerating reference frame

Dynamical equation in a linear

accelerating reference frame

*i c RelF F ma

*AbsF ma

In a linear accelerating reference frameframe,,Newton’s second law still hold Newton’s second law still hold if if the the inertial force is considered

In a linear accelerating reference frameframe,,Newton’s second law still hold Newton’s second law still hold if if the the inertial force is considered

In a linear accelerating reference frameIn a linear accelerating reference frame the Inertial Force acting on a body isIn a linear accelerating reference frameIn a linear accelerating reference frame the Inertial Force acting on a body is

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3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

2. Rotating noninertial reference frame A circular plate is rotating about axis with a angularspeed , a ball is fixed bya rope with its other end fixed at the vertical axis.

A centripetal force acts on the ball, the ball rests on the plate!Newton’s laws don’t hold !Suppose: a acting on it, then: hold !

A centripetal force acts on the ball,The ball is in uniformcircular motion. Newton’s laws hold

observer on groundobserver on ground observer on the plateobserver on the plate

* 2cF m r

z

*

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3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

In a rotating noninertial reference frameIn a rotating noninertial reference frame

the Inertial Force acting on a body in the radial

direction is

It is called the inertial centrifugalinertial centrifugal forceforce ( 离心惯性力 )

If a body rests on a rotatingrotating noninertial framenoninertial frame ,

then

In a rotating noninertial reference frameIn a rotating noninertial reference frame

the Inertial Force acting on a body in the radial

direction is

It is called the inertial centrifugalinertial centrifugal forceforce ( 离心惯性力 )

If a body rests on a rotatingrotating noninertial framenoninertial frame ,

then* 0cF F

* 2cF m r

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3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

Coriolis forceCoriolis force (( 科里奥利力科里奥利力 ):):

If a body has motion relative to a rotating noninertial reference frame, the body mayexperience the Coriolis force

Coriolis acceleration

Coriolis force

The examples of Coriolis forceCoriolis force

Coriolis forceCoriolis force (( 科里奥利力科里奥利力 ):):

If a body has motion relative to a rotating noninertial reference frame, the body mayexperience the Coriolis force

Coriolis acceleration

Coriolis force

The examples of Coriolis forceCoriolis force

* 2k rF mv

2k ra v

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3-13 Noninertial Reference System and Inertial Forces

3-13 Noninertial Reference System and Inertial Forces

Coriolis forceCoriolis force ( ( 科里奥利力科里奥利力 ):):

Coriolis force

Coriolis forceCoriolis force ( ( 科里奥利力科里奥利力 ):):

Coriolis force * 2k rF mv

Hurricane (typhoon) in north hemisphereHurricane (typhoon) in north hemisphere