Fundamentals of Physics School of Physical Science and Technology Mechanics (Bilingual Teaching) 张昆实 School of Physical Science and Technology Yangtze University

Chapter 5 Force and Motion 5-1 What Causes an Acceleration? 5-2 Newton's First Law 5-3 Force 5-4 Mass 5-5 Newton's Second Law 5-6 Some Particular Forces 5-7 Newton's Third Law 5-8 Applying Newton's Laws 5-9 Ininertial Reference System and Inertial Forces

5-1 What Causes an Acceleration? ★If the velocity of a particle changes in either maglitude or direction (acceleration) an interaction between the body and its surroundings. ★ An interaction that can cause an acceleration of a body is called a force. ★ Newtonian mechanics: The study of the relationship between a force and the acceleration it causes. ★ Quantum mechanics ★ Special theory of relativity Modifications are necessary

5-2 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.

5-3 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. 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. mass acceleration force 1kg 1 m/s 1N 2 m/s 2N a m/s aN

5-3 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. ★ 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. F net =

5-4 Mass ★ What is mass ? the less massive baseball receives a greater 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. a F m a x F m x

5-4 Mass ★ What is mass ? a F m a x F m x F = 1N F = 8N

5-4 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.

5-5 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) ★ Caution: m is the mass of a body, is the vector sum of all the forces act on that body. ★ Equivalent equations: (5-1) (5-2)

5-5 Newton's Second Law If (a) at rest stays at rest ★ 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 (5-2)

5-5 Newton's Second Law ★ 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. ★ external forces: any force on the bodies inside the system (a collection of two or more bodies) from bodies outside the system. (5-3)

5-5 Newton's Second Law ★ Example of a free-body diagram ★ internal forces: forces between two bodies inside the system (a collection of two or more bodies). ★ Example of a free-body diagram Sample Problem 5-3 (P79)

5-6 Some Particular Forces ★ The Gravitational Force on a body is a pull by another body. In most situations the other body is Earth or some other astronomical body. 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.

5-6 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 (5-8) (5-9) Upward force 2N

5-6 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. (5-10) (5-11) (5-12)

5-6 Some Particular Forces Spring scale Measuring the weight of a body: 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 (in mass or force units)

5-6 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 P89 Sample Problem 5-8 apparent weight apparent weight

5-6 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

5-6 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 (5-13) (5-14)

5-6 Some Particular Forces ★ Friction (more in Chapter 6) 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. Exp. A frictional force opposes the attempted slide of a body over a surface. ★ Friction negligible frictionless

5-6 Some Particular Forces ★ Tension: the cord is bing pulled taut The cord is in the state of tension The tension is the maglitude T of the force on the body. ● P83 Checkpoint 5 Sample Problem 5-4

5-7 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. ● A pair of action-reaction forces a third law force pair Book B Crate C B C ● Scalar form: Book B leans against crate C ● Vector form: ●Exp. Cantaloupe-table-earth three bodies

5-8 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. ★ Sample problems: 漆安慎P79 例3

★ 5-9 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 surfice 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

★ 5-9 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

★ 5-9 Noninertial Reference System and Inertial Forces In a lineal 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. interacting force Inertial Force 1.There is a third law force pair; 2. Can be observed in both inertial and noninertial reference frame. 1. There is no reaction force ! 2. Can be observed only in noninertial reference frame !

★ 5-9 Noninertial Reference System and Inertial Forces Dynamical equation in a lineal accelerating reference frame

★ 5-9 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 !

★ 5-9 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

★ 5-9 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

★ 5-9 Noninertial Reference System and Inertial Forces Coriolis force (科里奥利力): Coriolis force Hurricane (typhoon) in north hemisphere