Essential University Physics - hsiao-scu / FrontPagehsiaoscu.pbworks.com/w/file/fetch/69365742/lecture-4.pdf · Essential University Physics ... • Forces come in pairs. ... 1 with

Chapter 4 Lecture

Essential University Physics Richard Wolfson

2nd Edition

© 2012 Pearson Education, Inc. Slide 4-1

第4章Force and Motion力與運動


In this lecture you’ll learn 簡介 •  The concept of force and its role

in causing changes in motion力之觀念, 力與運動的關係

•  The fundamental forces of physics自然界的基本力

•  Newton’s three laws of motion 牛頓三定律

•  About the force of gravity 重力 –  Including the distinction

between mass and weight質量與重量之差

•  How to apply Newton’s laws in one-dimensional motion一維運動---牛頓三定律的應用


What Causes Motion? ???引起運動? •  That’s the wrong question! 把問題問錯了！！！

–  The ancient Greek philosopher Aristotle believed that forces—pushes and pulls—caused motion.2000年前希臘亞里斯多德相信力（推與拉）是造成運動的原因 •  The Aristotelian view prevailed for some 2000 years.

–  Galileo and Newton discovered the correct relation between force and motion.發現正確的關係---運動的改變 •  Force causes not motion itself but change in motion.

The Aristotelian view The Newtonian view


Newton’s Laws of Motion 牛頓的運動定律

•  Newton’s first law of motion: A body in uniform motion remains in uniform motion, and a body at rest remains at rest, unless acted on by a nonzero net force.

•  Newton’s second law of motion: The rate at which a body’s momentum changes is equal to the net force acting on the body:

•  Newton’s third law of motion: If object A exerts a force on object B, then object B exerts an oppositely directed force of equal magnitude on A.

Fnet =

dpdt

(Newton’s 2nd Law)


The First Law 討論第一定律

•  The first law is a special case of the second law, when there’s no net force acting on an object.特別的情形之下, 第一定律是第二定律的特例

–  In that case the object’s motion doesn’t change.物體的運動維持不變

–  If at rest it remains at rest. 靜止, 一直靜止 –  If in motion, it remains in uniform motion.運動, 一直均勻的

運動 •  Uniform motion is motion at constant speed in a straight line.

均勻運動時, 速率不變, 沿直線運動 •  Thus the first law shows that uniform motion is a natural

state, requiring no explanation.均勻地運動是可以持續的, 不需用外力來維持（例如：摩擦力, 這是亞里斯多德以為的）


The Second Law 討論第二定律 •  The second law tells quantitatively how force causes

changes in an object’s “quantity of motion.”量化地敘述如何改變運動

–  Newton defined “quantity of motion,” now called momentum, as the product of an object’s mass and velocity:

–  Newton’s second law equates the rate of change of momentum to the net force on an object:

–  When mass is constant, Newton’s second law becomes

–  The force required to accelerate a 1-kg mass at the rate of 1 m/s2 is defined to be 1 newton (N).

p =mv

F = d

pdt

F =

d mv( )dt

=mdvdt=ma


Mass, Inertia and Force 質量慣性力 •  If we solve the second law for the acceleration we find that

showing that a given force is less effective in changing the motion of a more massive object.

a =F /m

–  The mass m that appears in Newton’s laws is thus a measure of an object’s inertia and determines the object’s response to a given force.

•  From Newton’s second law for a force of magnitude F,

we get

known known unknown unknown,F m a F m a= =

unknown known

known unknown

m am a

=


The Fundamental Forces 自然界之作用力 •  Physicists now recognize three fundamental forces:有三種

–  Gravity重力 –  The strong force 強力 –  The electroweak force 電弱力

•  All common forces fall under these three categories. –  Nearly all everyday forces, except gravity, are

electromagnetic forces — one aspect of the electroweak force.最常見的有重力與電磁力（電屬於電弱力）

•  Historically, more forces were once regarded as fundamental, but were later understood to be related.之前不同之各力,如今皆相關

•  A goal of physics is to unify all forces in a “Theory of Everything.”終極目標：要整合


Mass, Weight, and Gravity 質量重量重力

•  Weight is the force of gravity on an object: 一物受重力, 方有重量 –  Mass doesn’t depend on the presence or strength

of gravity.質量與重力無關 –  Weight depends on gravity, so varies with location. Weight is different on different planets. 而重量與重力有關, 因此與地點有關

•  Near Earth’s surface, has magnitude 9.8 m/s2 or 9.8 N/kg, and is directed downward.

w =mg

gr


•  All objects experience the same gravitational acceleration, regardless of mass.重力加速度與質量無關

–  Therefore objects in free fall—under the influence of gravity alone—appear “weightless” because they share a common accelerated motion.一自由落體與另一自由落體相對靜止, 互相觀察都是無重狀態.

–  This effect is noticeable in orbiting spacecrafty在繞地衛星上, 特別明顯: •  because the absence of air resistance means gravity

is the only force acting. 因為大氣稀薄, 重力為唯一之力

•  because the apparent weightlessness continues indefinitely, as the orbit never intersects Earth. 而且衛星軌道不通過地球, 可維持無重力狀態很久很久.

注意：這樣的狀況是和衛星的高度無關的.


Solving Problems with Newton’s Second Law


Example 例題 •  A 740-kg elevator accelerates upward at 1.1 m/s2, pulled by a

cable of negligible mass. Find the tension force in the cable. •  張力

–  INTERPRET The object of interest is the elevator; the forces are gravity and the cable tension.

–  DEVELOP Newton’s law reads

–  EVALUATE In a coordinate system with y-axis upward, Newton’s law reads

Solving gives

–  ASSESS Makes sense; look at some special cases. •  When a = 0, T = mg and the cable tension balances gravity. •  When T = 0, a = –g, and the elevator falls freely.

Fnet =

T +Fg =m

a

Ty + Fgy = may .

( ) 8.1 kNyT m a g= + =


Draw a Free-Body Diagram is important 畫力圖很重要





Newton’s Third Law 討論第三定律 •  Forces come in pairs.力是成對出現

–  If object A exerts a force on object B, then object B exerts an oppositely directed force of equal magnitude on .

A物體施一力給B物體, 則B物體亦施一力給A物體; 此二力之大小相等但方向相反. –  Obsolete language: “For every action there is an equal but

opposite reaction.”作用力與反作用力不再是好的說法 –  Important point: The two forces

always act on different objects; therefore they can’t cancel each other.

重點是兩力作用在不同的物體, 因此不會相消.


•  Example: 舉例 –  Push on book of mass m1 with force –  Note third-law pair –  Third law is necessary for

a consistent description of motion in Newtonian physics.

F21 and

F12.

F.



Spring Forces 彈簧力（一維之力） •  A stretched or compressed spring produces a force

proportional to the stretch or compression from its equilibrium configuration: Fsp = –kx.

•  The spring force is a restoring force because its direction is opposite that of the stretch or compression.是回復力, 方向與伸或縮的方向相反.

•  Springs provide convenient devices for measuring force.

方便用來測量力


Summary •  In Newtonian physics, force—a push or pull—causes not

motion itself but change in motion.

•  Newton’s three laws are –  First law: A body in motion remains in uniform motion, and a body at

rest remains at rest, unless acted on by a nonzero net force.

–  Second law: The rate at which a body’s momentum changes is equal to the net force acting on the body:

–  Third law: If object A exerts a force on object B, then object B exerts an oppositely directed force of equal magnitude on A.

•  Physicists recognize three fundamental forces. •  An object’s weight is the force that gravity exerts on it.

F = d

pdt

; for constant mass, F =ma


•  Homework: 12, 18, 27, 31, 33, 45, 58, (68,69,70,71)

Essential University Physics - hsiao-scu / FrontPagehsiaoscu.pbworks.com/w/file/fetch/69365742/lecture-4.pdf · Essential University Physics ... • Forces come in pairs. ... 1 with

Documents