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

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.

China´s manned spacecraft Shenzhou-7 blasts off

China´s manned spacecraft Shenzhou-7 blasts off

Chinese taikonauts report they feel "physically sound"

Astronauts assemble EVA suit for spacewalk

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 journey.

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

Congratulations to the successful launching of the Shenzhou-7 ! The fundamental principles of space flight is Mechanics ! Physics is the cradle of modern science and technology !

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

Chapter 3 Force 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

Chapter 3 Force 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

3-1 What Is Physics ★ We have discussed how motion is described in terms of velocity and acceleration. （Kinematics） ★ Now we deal with the question of why objects move as they do: What makes an object at rest begin to move? What causes a body to accelerate or decelerate? What is involved when an object moves in a circle? ★ In this chapter we learn what is physics through investigating the connection between force and motion, which is the subject called dynamics.

Newton published his book 《The Mathematical Principles of Natural 3-2 Newtonian Mechanics . ★ 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. ★ The study of that relation is called Newtonian Mechanics

Modifications are necessary: 3-2 Newtonian Mechanics Modifications are necessary: ★ Quantum mechanics (for the scale of atomic structure) ★ Special theory of relativity (for very high speed speed of light) Newtonian Mechanics is viewed as a special case of these two more comprehensive theories.

3-3 Newton’s First Law ★ 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 velocity if no force acts on it. ★ Newton’s First Law: If no force acts on a body, then the body’s velocity cannot change; that is, the body cannot accelerate. at rest remain at rest; in motion move with constant velocity.

3-4 Force is measured by acceleration it produces. ★ 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. mass acceleration force 1kg 1 m/s2 1N 2 m/s2 2N a m/s2 aN magnitude; direction ★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.

3-4 Force ★ Newton’s First Law (restate): If no net force acts on a body ( ), then the body’s velocity cannot change; that is, the body cannot accelerate. F net = ★ 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. ★ Noninertial frame: a accelerating frame; a rotational frame.

3-5 Mass ★ What is mass ? the less massive baseball receives a larger acceleration F a m x Equal force 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.

3-5 Mass ★ What is mass ? F a m x Equal force F = 1N F = 8N

3-5 Mass ★ Mass is an intrinsic characteristic of a body a characteristic that automatically comes 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. ★ Mass is a measure of the inertia of a body.

3-6 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 the acceleration of the body. (Newton's second law) (3-1) ★ Caution: is the mass of a body, is the vector sum of all the forces act on that body. ★ Equivalent equations: (3-2)

3-6 Newton’s Second Law If (a) at rest stays at rest (b) In motion (5-2) ★ 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. If (a) at rest stays at rest (b) In motion move at constant velocity the forces and the body: in equilibrium

3-6 Newton’s Second Law ★ the free-body diagram ★ The SI unit of force: Newton (N) ★ 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.

3-6 Newton’s Second Law inside the system (a collection of two or ★ external forces: any force on the bodies inside the system (a collection of two or more bodies) from bodies outside the system. ★ internal forces: forces between two bodies inside the system (a collection of two or more bodies).

3-7 Newton’s Third Law forces ★ 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 B C ● Scalar form: book B leans against crate C ● Vector form:

3-7 Newton’s Third Law ( a third law force pair) ★ Exp. Cantaloupe-table-earth three bodies A pair of action-reaction forces ( a third law force pair) ● Cantaloupe-Earth interaction: Cantaloupe C ( gravitational force ) Table T Earth E ● Cantaloupe-Table interaction: Note: and are not !

3-8 Applying Newton’s Laws ★ When you read the sample problems, pay attention to: Problem solving procedures; How to draw a free-body diagram with appropriate axes; How to use Newton's Laws to solve problems. P55 Sample problems 3-1

3-8 Applying Newton’s Laws P55 Sample problem 3-1 cord frictionless pulley Earth is involved Solution Problem description Two blocks particles, Earth is also involved ; Cord massless, unstretchable; Pulley massless, only changes the cord’s orientation. equal in all sections of the cord.

3-8 Applying Newton’s Laws draw free-body diagram Earth is involved apply Newton’s second law Block S (3-7) (3-5) Substituting into Eq. 3-5 yields Block H (3-6) Solving for yields (3-8)

3-8 Applying Newton’s Laws 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 (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?

3-8 Applying Newton’s Laws Solution free-body diagram Three forces are in equilibrium Use a coordinate system (a) (b) Cutting the cord :

3-9 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. ★ 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). ★ choose a vertical y axis along the body’s path, with the positive direction upward.

3-9 Some Particular Forces ★ 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 force balanced keep the ball at rest the weight of the ball is the magnitude of the upward force 2N (3-14) (3-15) Upward force 2N

3-9 Some Particular Forces 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. (3-16) (3-17) (3-18)

3-9 Some Particular Forces Measuring the weight of a body: Spring scale Equal-arm balance 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)

3-9 Some Particular Forces ★The weight of a body must be measured when the body is not accelerating vertically relative to the ground. ● apparent weight : elevator (lift) cab apparent weight apparent weight

3-9 Some Particular Forces ★The weight of a body is not the mass of the body. Mass Weight 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 altitude Measured in N

3-9 Some Particular Forces ★The Normal Force y Normal force When a body presses against a surface, the surface ( even a seeminly rigid surface ) deforms and pushes on the body with a normal force that is perpendicular to the surface. Exp. A block rests on a tabletop (3-19) (3-20)

3-9 Some Particular Forces Cord : massless, unstretchable Pulley ：massless, frictionless Tension: when the cord is bing pulled taut, The cord is under tension, it pulls on a body at each of its ends. The pulls at both ends of the cord have the same maglitude T and are directed along the cord.

3-10 Friction ★ Friction to the surface Direction of attempted slide ● A frictional force is the force on a body when the body slides or attempts to slide along a surface. ● The force is always parallel to the surface ● The force is directed so as to oppose the motion of the body. ★ Frictional forces exist everywhere.

3-10 Friction force is a static frictional force . at rest breakaway ,max s f r breakaway ,max s f r time Frictional force in motion ● If the body does not slide, the frictional force is a static frictional force . ● If there is sliding, the frictional force is a kinetic frictional force .

3-10 Friction The frictional force has three properties: Property1. If the body does not move, then the static frictional force and the component of that is parallel to the surface balance each other. Property2. The magnitude of has a maximum velue : (3-21) is the coefficient of static friction If , the body begins to slide.

3-10 Friction P65 Sample problem 3-5 Property3. If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value (3-22) is the coefficient of kinetic friction. The coefficient and are dimensionless and must be determined experimentlly. P65 Sample problem 3-5

3-11 The Drag Force and Terminal speed When there is a relative motion between air ( or some other fluid ) and a body, the body experiences 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 (3-28) (6-14)

3-11 The Drag Force and Terminal speed (3-28) Where is the air density; is the effective cross-sectional area of the body ( the area of a cross section taken perpendicular to the velocity ). The drag coefficient C can vary with the variation of , For simplicity, take it as a constant.

3-11 The Drag Force and Terminal speed (3-28) Falling body 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 ). (3-29)

3-11 The Drag Force and 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 Find : (3-29) terminal speed (3-30)

3-11 The Drag Force and Terminal speed Skydiving

3-11 The Drag Force and Terminal speed Group Skydiving

3-12 Uniform Circular Motion ★ 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: (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.

3-12 Uniform Circular Motion ★ From Newton’s second law and (4-32) (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 circle along a radial axis . The positive direction of the axis is radially outward, but the acceleration and force vectors point radially inward. Sample problem 3-9 : P73

3-13 Noninertial Reference System and Inertial Forces 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 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 observer on ground observer in the car

3-13 Noninertial Reference System and Inertial Forces 1. Lineal accelerating reference frame A steel ball is connected to a spring As the car moves with a acceleration from rest, the spring is stretched * 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 ball moves with , Newton’s laws hold observer on ground observer in the car

3-13 Noninertial Reference System and Inertial Forces In 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 force ! 2. Can be observed only in noninertial reference frame ! 1.There is a third law force pair; 2. Can be observed in both inertial and noninertial reference frame. interacting force Inertial Force

3-13 Noninertial Reference System and Inertial Forces Dynamical equation in a linear accelerating reference frame In a linear accelerating reference frame the Inertial Force acting on a body is In a linear accelerating reference frame, Newton’s second law still hold if the inertial force is considered

3-13 Noninertial Reference System and Inertial Forces 2. Rotating noninertial reference frame * A circular plate is rotating about axis with a angular speed , a ball is fixed by a rope with its other end fixed at the vertical axis. observer on ground observer on the plate A centripetal force acts on the ball, The ball is in uniform circular motion. Newton’s laws hold 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 !

3-13 Noninertial Reference System and Inertial Forces In a rotating noninertial reference frame the Inertial Force acting on a body in the radial direction is It is called the inertial centrifugal force (离心惯性力) If a body rests on a rotating noninertial frame , then

3-13 Noninertial Reference System and Inertial Forces Coriolis force (科里奥利力): If a body has motion relative to a rotating noninertial reference frame, the body may experience the Coriolis force Coriolis acceleration Coriolis force The examples of Coriolis force

3-13 Noninertial Reference System and Inertial Forces Coriolis force (科里奥利力): Coriolis force Hurricane (typhoon) in north hemisphere