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

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1 Chapter 4 Lecture Essential University Physics Richard Wolfson 2 nd Edition 第 4 章 Force and Motion 力與運動 2012 Pearson Education, Inc. Slide 4-1

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 4-2

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.

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 4-3

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: F net = d p (Newton s 2 dt nd Law) 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 Pearson Education, Inc. Slide 4-4

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 4-5

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: p = mv Newton s second law equates the rate of change of momentum to the net force on an object: F = d p dt When mass is constant, Newton s second law becomes F = d ( m v) = m d v dt dt = m a The force required to accelerate a 1-kg mass at the rate of 1 m/s 2 is defined to be 1 newton (N) Pearson Education, Inc. Slide 4-6

7 Mass, Inertia and Force 質量慣性力 If we solve the second law for the acceleration we find that a = F / m showing that a given force is less effective in changing the motion of a more massive object. 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 F = m a, F = m a known known unknown unknown m m unknown known = a a known unknown 2012 Pearson Education, Inc. Slide 4-7

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.

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 4-8

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 w = mg 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/ s 2 or 9.8 N/kg, and is directed downward. g r 2012 Pearson Education, Inc. Slide 4-9

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 Pearson Education, Inc. Slide 4-10

11 Solving Problems with Newton s Second Law 2012 Pearson Education, Inc. Slide 4-11

12 Example 例題 A 740-kg elevator accelerates upward at 1.1 m/s 2, 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 F net = T + F g = ma EVALUATE In a coordinate system with y-axis upward, Newton s law reads T y + F gy = ma y. Solving gives ( ) 8.1 kn T = m a + g = 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. y 2012 Pearson Education, Inc. Slide 4-12

13 Draw a Free-Body Diagram is important 畫力圖很重要 2012 Pearson Education, Inc. Slide 4-13

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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 Pearson Education, Inc. Slide 4-17

18 Example: 舉例 Push on book of mass m 1 with force Note third-law pair F 21 and F 12. Third law is necessary for a consistent description of motion in Newtonian physics. F Pearson Education, Inc. Slide 4-18

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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: F sp = 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 4-20

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: F = d p dt ; for constant mass, F = ma 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 Pearson Education, Inc. Slide 4-21

22 Homework: 12, 18, 27, 31, 33, 45, 58, (68,69,70,71) 2012 Pearson Education, Inc. Slide 4-22

运动 Prepared by Jiang Xiao

顿运动 Prepared by Jiang Xiao 运动 Prepared by Jiang Xiao 运动运动运动 Aristotle 384BC - 322BC 变运动维运动 Galileo 1564-1642 Newton 1642-1727 线运动态变这态顿 - 惯顿线运动态变这态满惯满满转 0.034 m/s 2 转 0.006 m/s 2 银转动