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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
© 2012 Pearson Education, Inc. Slide 4-2
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
© 2012 Pearson Education, Inc. Slide 4-3
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
© 2012 Pearson Education, Inc. Slide 4-4
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)
© 2012 Pearson Education, Inc. Slide 4-5
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)
© 2012 Pearson Education, Inc. Slide 4-6
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
© 2012 Pearson Education, Inc. Slide 4-7
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
=
© 2012 Pearson Education, Inc. Slide 4-8
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
© 2012 Pearson Education, Inc. Slide 4-9
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
© 2012 Pearson Education, Inc. Slide 4-10
• 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.
© 2012 Pearson Education, Inc. Slide 4-12
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= + =
© 2012 Pearson Education, Inc. Slide 4-17
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.
© 2012 Pearson Education, Inc. Slide 4-18
• 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.
© 2012 Pearson Education, Inc. Slide 4-20
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
© 2012 Pearson Education, Inc. Slide 4-21
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
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