Yangtze University

Yangtze UniversityBilingual Mechanics Chapter 3 Force

Chinese astronautsJing Haipeng(L), Zhai Zhigang(C) and Liu Boming wave hands during a press conference in Jiuquan Satellite Launch Center (JSLC)inNorthwest China'sGansu 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.

Chinas manned spacecraft Shenzhou-7 blasts off

Chinas 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 countrys 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.

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

Yangtze University

Yangtze UniversityBilingual Mechanics Chapter 3 Force

Chapter 3 Force3-1 What Is Physics?3-2 Newtonian Mechanics3-3 Newtons First Law3-4 Force3-5 Mass3-6 Newtons Second Law3-7 Newtons Third Law

Chapter 3 Force3-8 Applying Newtons Laws3-9 Some Particular Forces3-10 Friction3-11 The Drag Force and Terminal Speed3-12 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. Now we deal with the question of why objects move as they do: In this chapter we learn what is physics through investigating the connection between force and motion, which is the subject called dynamics.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?Kinematics

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 Philosophyin 1687. The study of that relation is called Newtonian Mechanics

3-2 Newtonian MechanicsModifications are necessary: Quantum mechanics (for the scale of atomic structure)Newtonian Mechanics is viewed as a special case of these two more comprehensive theories.

3-3 Newtons 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.

Newtons First Law: If no force acts on a body, then the bodys velocity cannot change; that is, the body cannot accelerate.

at rest remain at rest; in motion move with constant velocity.

3-4 Force 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.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.magnitude; direction

3-4 Force Newtons First Law (restate): If no net force acts on a body ( ), then the bodys velocity cannot change; that is, the body cannot accelerate.

Inertial Reference Frames An inertial reference frame is one in which Newtons 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 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.Equal force

3-5 Mass What is mass ?

Equal force

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 Newtons Second Law Newton's Second Law The net force on a body is equal to the product of the bodys mass and the acceleration of the body. (Newton's second law) Caution: is the mass of a body, is the vector sum of all the forces act on that body.

Equivalent equations:(3-1)

3-6 Newtons Second Law 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.

(a) at rest(b) In motionthe forces and the body: in equilibrium

3-6 Newtons Second Law The SI unit of force: Newton (N)

the free-body diagramTo solve problems with Newtons 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 Newtons Second Law internal forces: forces between two bodies inside the system (a collection of two or more bodies). external forces: any force on the bodies inside the system (a collection of two or more bodies) from bodies outside the system.

3-7 Newtons Third Law Newtons 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 pairbook B leans against crate C

3-7 Newtons Third Law Exp. Cantaloupe-table-earth three bodies A pair of action-reaction forces ( a third law force pair) Cantaloupe-Earth interaction: Cantaloupe C Cantaloupe-Table interaction:( gravitational force )

3-8 Applying Newtons Laws When you read the sample problems, pay attention to: How to use Newton's Laws to solve problems.

Problem solving procedures;How to draw a free-body diagram with appropriate axes; P55 Sample problems 3-1

3-8 Applying Newtons Laws P55 Sample problem 3-1frictionless pulley cordEarth is involvedSolutionProblem descriptionequal in all sections of the cord.

3-8 Applying Newtons LawsEarth is involved draw free-body diagram Block S apply Newtons second law(3-5)(3-7)(3-8)

3-8 Applying Newtons Laws P57 Sample problem 3-2In 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 Newtons LawsSolutionThree forces are in equilibrium Use a coordinate system

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. choose a vertical y axis along the bodys path, with the positive direction upward.

3-9 Some Particular Forces The Gravitational Force Newtons 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 forcebalanced keep the ball at rest the weight of the ball is the magnitude of the upward force 2NUpward 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:

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 ForcesThe weight of a body must be measured when the body is not accelerating vertically relative to the ground. apparent weight : elevator (lift) cab

3-9 Some Particular ForcesThe weight of a body is not the mass of the body.

3-9 Some Particular ForcesThe Normal Force

Normal forceWhen a body presses againsta surface, the surface ( evena seeminly rigid surface ) deforms and pushes on thebody with a normal forcethat is perpendicular to thesurface.

Exp. A block rests on a tabletop

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

3-10 Friction Friction

A frictional force is the force on a body when the body slides or attempts to slide along a surface. Frictional forces exist everywhere. The force is always parallel to the surface The force is directed so as to oppose the motion of the body.

3-10 Friction

3-10 FrictionThe frictional force has three properties:

3-10 FrictionProperty3. If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value

(3-22) 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 bodyexperiences 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

(6-14)

3-11 The Drag Force and Terminal speed

Where is the air density; is the effective cross-sectional area of the body ( the area of a cross section takenperpendicular 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 speedDuring the falling, Newtons 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 speedIf the body falls long enough, eventually equals the bodys speed no longer increases. The body then falls at a constant speed, called the terminal speed(3-29)Find :(3-30)terminal speed

3-11 The Drag Force and Terminal speedSkydiving

3-11 The Drag Force and Terminal speedGroup 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:

Example: P70 Fig.3-21 , A centripetal force accelerates a body by changing the direction of the bodys velocity without changing the bodys speed.

3-12 Uniform Circular Motion From Newtons second law and

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

3-13 Noninertial Reference System and Inertial Forces 1. Lineal accelerating reference frame A steel ball is connectedto a spring As the car moves with a acceleration from rest,the spring is stretched

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.

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

3-13 Noninertial Reference System and Inertial Forces

2. Rotating noninertial reference frame A circular plate is rotating about axis with a angularspeed , a ball is fixed bya rope with its other end fixed at the vertical axis.

A centripetal force acts on the ball, the ball rests on the plate!Newtons laws dont hold !Suppose: a acting on it, then: hold !A centripetal force acts on the ball,The ball is in uniformcircular motion. Newtons laws hold

observer on ground observer on the plate

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 () If a body rests on a rotating noninertial frame , then

3-13 Noninertial Reference System and Inertial Forces Coriolis force ():If a body has motion relative to a rotating noninertial reference frame, the body mayexperience the Coriolis force

Coriolis acceleration

Coriolis force

The examples of Coriolis force

3-13 Noninertial Reference System and Inertial Forces Coriolis force ():Coriolis force

Hurricane (typhoon) in north hemisphere