普通物理 General Physics 5 – Newton's Law of Motion 郭艷光Yen-Kuang Kuo 國立彰化師大物理系暨光電科技研究所 電子郵件: ykuo@cc.ncue.edu.tw 網頁: http://ykuo.ncue.edu.tw

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Outline 5-1 What Is Physics? 5-2 Newtonian Mechanics 5-3 Newton’s First Law 5-4 Force 5-5 Mass 5-6 Newton’s Second Law 5-7 Some Particular Forces 5-8 Newton’s Third Law 5-9 Applying Newton’s Laws 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-1 What Is Physics? In chapters 2 and 4, we have studied “kinematics” i.e. described the motion of objects using parameters such as the position vector, velocity and acceleration without any insights as to what caused the motion. This is the task of chapters 5 and 6 in which the part of mechanics known as “dynamics” will be developed. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-1 What Is Physics? In this chapter, we will introduce Newton’s three laws of motion which is at the heart of classical mechanics. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-2 Newtonian Mechanics The study of that relation, as Newton presented it, is called Newtonian mechanics. If the speeds of the interacting bodies are very large—an appreciable fraction of the speed of light— we must replace Newtonian mechanics with Einstein’s special theory of relativity, which holds at any speed, including those near the speed of light. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-2 Newtonian Mechanics If the interacting bodies are on the scale of atomic structure (for example, they might be electrons in an atom), we must replace Newtonian mechanics with quantum mechanics. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-3 Newton’s First Law Newton’s First Law: If no force acts on a body, the body’s velocity cannot change; that is, the body cannot accelerate. In other words, if the body is at rest, it stays at rest. If it is moving, it continues to move with the same velocity (same magnitude and same direction). If several forces act on a body ( say , , ) the net force is defined as: i.e. is the vector sum of , , . 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-4 Force 1 Newton force: Put a standard body ( mass of 1 kg ) on a horizontal frictionless table and pull it. If it experiences a measured acceleration of 1 m/s2, the force we are exerting on the standard body has a magnitude of 1 Newton (abbreviated N). 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-4 Force Principle of superposition for forces: When two or more forces act on a body, we can find their net force, or resultant force, by adding the individual forces vectorially. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-4 Force Inertial Reference Frames: An inertial reference frame is one in which Newton’s laws hold. Noninertial Reference Frames: An observer in the noninertial frame must invent a fictitious “ inertial force ” to explain the acceleration of the body. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-5 Mass Mass is an intrinsic characteristic of a body that automatically comes with the existence of the body. F a0 m0 aX mX 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-5 Mass The mass of a body is as measure of its inertia, that is, its resistance to change in velocity. Mass is an intrinsic property of a body, independent of its location. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-6 Newton’s Second Law Newton’s Second Law: The net force on a body is equal to the product of the body’s mass and its acceleration. In equation form, must be the vector sum of all the force that act on that body. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-6 Newton’s Second Law Like other vector equations, Newton’s second law is equivalent to three component equations, one for each axis of an xyz coordinate system: Fnet a m 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-6 Newton’s Second Law The acceleration component along a given axis is caused only by the sum of the force components along that same axis, and not by force components along any other axis. To solve problems with Newton’s second law, we often draw a free-body diagram in which the only body shown is the one for which we are summing forces. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-1 In Figs. (a) to (c), show three situations in which one or two forces act on a puck that moves over frictionless ice along an x axis, in one-dimensional motion. The puck’s mass is m = 0.20 kg. Forces and are directed along the axis and have magnitude and . Force is directed at angle and has magnitude . In each situation, what is the acceleration of the puck? 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-1 Solution: Situation A: For Fig. (d), where only one horizontal force acts, 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-1 which, with given data, yields Situation B: In Fig. (e), we have 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-1 Situation C: In Fig. (f), we have from the figure, we see that 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-2 In the overhead view of Fig. (a), a 2.0 kg cookie tin is accelerated at 3.0 m/s2 in the direction shown by , over a frictionless horizontal surface. The acceleration is caused by three horizontal forces, 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-2 only two of which are shown: of magnitude 10 N and of magnitude 20 N. What is the third force in unit-vector notation and in magnitude-angle notation? Key idea: The net force on the tin is the sum of the three forces and is related to the acceleration via Newton’s second law. Thus, which gives us 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-2 Solution: 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-2 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-3 An electron of mass has an initial velocity . It enters a region in which it experiences a force for a period of . What is its velocity as it emerges from the region? Solution: 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-3 the final velocity is . The angle at which it emerges relative to the x axis is found from Which yields . 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-7 Some Particular Forces The Gravitational Force: A force that pulls on a body directly toward the center of Earth. Newton’s second law can be written in the form or 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-7 Some Particular Forces Weight: The weight of an object is the net gravitational force acting on it. or (caution: A body’s weight is not its mass. ) y g W mg 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-7 Some Particular Forces Contact Forces: The contact forces have two components. Normal force and Frictional force. (1) Normal force: When a body presses against a surface, the surface deforms and pushes on the body with a normal force that is perpendicular to the surface. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-7 Some Particular Forces (2) Frictional force : More on friction in chapter 6. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-7 Some Particular Forces Tension: The tension in a rope is the pulling force exerted by one section of the rope on an adjacent section or on an object attached to its end. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-7 Some Particular Forces It is always directed along the rope. It is always pulling the object. It has the same value along the rope. Assumptions: a. The rope has negligible mass. b. The rope does not stretch. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-4 Takeoff illusion. A jet plane taking off from an aircraft carrier is propelled by its powerful engines while being thrown forward by a catapult mechanism installed in the carrier deck. The resulting high acceleration allows the plane to reach takeoff speed in a short distance on the deck. However, that high acceleration also compels the pilot to angle the plane sharply nose-down as it leaves the deck. Pilots are 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-4 trained to ignore this compulsion, but occasionally a plane is flown straight into the ocean. Let’s explore the physics behind the compulsion. Your sense of vertical depends on visual clues and on the vestibular system located in your inner ear. That system contains tiny hair cells in a fluid. When you hold your head upright, the hairs are vertically in line with the gravitational force on you and the system signals your brain that your 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-4 head is upright. When you tilt your head backward by some angle , the hairs are bent and the system signals your brain about the tilt. The hairs are also bent when you are accelerated forward by an applied horizontal force . The signal sent to your brain then indicates, erroneously, that your head is tilted back, to be in line with an extension through the vector sum (Fig. (a)). However, the erroneous signal is ignored when visual clues clearly indicate 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-4 no tilt, such as when you are accelerated in a car. A pilot being hurled along the deck of an aircraft carrier at night has almost no visual clues. The illusion of tilt is strong and very convincing, with the result that the pilot feels as though the plane leaves the deck headed sharply upward. Without proper training, a pilot will attempt to level the plane by bringing its nose sharply down, sending the 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-4 plane into the ocean. Suppose that, starting from rest, a pilot undergoes constant horizontal acceleration to reach a takeoff speed of 85 m/s in 90 m. What is the angle of the illusionary tilt experienced by the pilot? 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-4 Solution: 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-4 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 5-8 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. For the book and crate, we can write this law as the scalar relation or as the vector relation 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-9 Applying Newton’s Laws System (a) = block A + block B. The only horizontal force is System (b) = block A. There are now two horizontal forces: and System (c) = block B. The only horizontal force 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

5-9 Applying Newton’s Laws Recipe for the application of Newton’s law’s of motion: (1) Choose the system to be studied. (2) Make a simple sketch of the system. (3) Choose a convenient coordinate system. (4) Identify all the forces that act on the system. Label them on the diagram. (5) Apply Newton’s laws of motion to the system. 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-5 Figure shows a block S ( the sliding block ) with mass M = 3.3 kg. the block is free to move along a horizontal frictionless surface and connected, by a cord that wraps over a frictionless pulley, to a second block H ( the hanging block ), with mass m = 2.1 kg. the cord and pulley have negligible masses compared to the blocks 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-5 ( they are “massless” ). The hanging block H falls as the sliding block S accelerates to the right. Find (a) the acceleration of block S, (b) the acceleration of block H, and (c) the tension in the cord. Solution: 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-6 In Fig. (a), a cord pulls on a box of sea biscuits up along a frictionless plane inclined at . The box has mass m = 5.00 kg, and the force from the cord has magnitude T = 25.0 N. what is the box’s acceleration component a along the inclined plane? 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-6 Solution: 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-7 Let’s return to the chapter opening question: What produces the fear factor in the last car of a traditional gravity-driven roller coaster? Let’s consider a coaster having 10 identical cars with total mass M and massless interconnections. Figure. (a) shows the coaster just after the first car has begun its descent along a frictionless slop with an angle . Figure. (b) shows the coaster just before the last car begins its descent. What is 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-7 the acceleration of the coaster in these two situations? Solution: 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-8 Figure. (a) shows the general arrangement in which two forces are applied to a 4.00 kg block on a frictionless floor, but only force is indicated. That force has a fixed magnitude but can be applied at angle to the positive direction of the x axis. Force is horizontal and fixed in both magnitude and angle. Figure. (b) gives the horizontal acceleration of the block for any given value of from 0°to 90°. What is the value 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-8 of for ? Solution: 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-9 In Figure. (a), a passenger of mass m = 72.2 kg stands on a platform scale in an elevator cab. We are concerned with the scale readings when the cab is stationary and when it is moving up or down. (a) Find a general solution for the scale reading, whatever the vertical motion of the cab. (b) What does the scale read if the cab is 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-9 stationary or moving upward at a constant 0.50 m/s? (c) What does the scale read if the cab accelerates upward at 3.20 m/s2 and downward at 3.20 m/s2? (d) During the upward acceleration in part (c), what is the magnitude of the net force on the passenger, and what is the magnitude of his acceleration as 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-9 measured in the frame of the cab? Does ? Solution: (a) (b) (c) (d) 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-10 In the Fig. (a), a constant horizontal force of magnitude 20 N is applied to block A of mass mA = 4.0 kg, which pushes against block B of mass mB = 6.0 kg. The blocks slide over a frictionless surface, along an x axis. (a) What is the acceleration of the blocks? (b) What is the force on block B from block B from block A ( Fig. (c) )? 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 Example 5-10 Solution: (a) (b) 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授 End of chapter 5! 2018/9/16 普通物理講義-5 / 國立彰化師範大學物理系/ 郭艷光教授