Chapter 5 Newton s Laws of Motion

Transcription

1 Chapter 5 Newton s Laws of Motion

2 Newtonian Mechanics

3 Mass Mass is an intrinsic characteristic of a body The mass of a body is the characteristic that relates a force on the body to the resulting acceleration.

4 5-1 Force and Mass Mass is the measure of how hard it is to change an object s velocity. Mass can also be thought of as a measure of the quantity of matter in an object.

5 Force The force that is exerted on a standard mass of 1 kg to produce an acceleration of 1 m/s 2 has a magnitude of 1 newton (abbreviated N)

6 Force: push or pull Understanding Force Force is a vector it has magnitude and direction

7 Effect Of Friction If you stop pushing an object, does it stop moving? Only if there is friction! In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest. This is also known as the law of inertia.

8 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. 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).

9 5-2 Newton s First Law of Motion In order to change the velocity of an object magnitude or direction a net force is required. An inertial reference frame is one in which the first law is true. Accelerating reference frames are not inertial.

10 Force A force is measured by the acceleration it produces. Forces have both magnitudes and directions. When two or more forces act on a body, we can find their net, or resultant force, by adding the individual forces vectorially.

11 Relation Between Force And Mass Two equal weights exert twice the force of one; this can be used for calibration of a spring:

12 Relation Between Force And Acceleration Now that we have a calibrated spring, we can do more experiments. Acceleration is proportional to force:

13 Relation Between Force And Acceleration Acceleration is inversely proportional to mass:

14 5-3 Newton s Second Law of Motion Combining these two observations gives Or, more familiarly,

15 Newton s second law: The net force on a body is equal to the product of the body s mass and its acceleration. In component form, 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.

16 5-3 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: (5-1)

17 Free-body diagrams: Free-body Diagram A free-body diagram shows every force acting on an object. Sketch the forces Isolate the object of interest Choose a convenient coordinate system Resolve the forces into components Apply Newton s second law to each coordinate direction

18 Free-body Diagrams Example of a free-body diagram:

19 Newton s second law; drawing a free-body diagram In a free-body diagram, the only body shown is the one for which we are summing forces. Each force on the body is drawn as a vector arrow with its tail on the body. A coordinate system is usually included, and the acceleration of the body is sometimes shown with a vector arrow (labeled as an acceleration). The figure here shows two horizontal forces acting on a block on a frictionless floor.

20 Some particular forces Gravitational Force: gravitational force on a body is a certain type of pull that is directed toward a second body. The weight, W, of a body is equal to the magnitude F g of the gravitational force on the body. W = mg (weight), uppose a body of mass m is in free fall with the free-fall acceleration of magnitude g. The force that the body feels as a result is: F g = m(g) or F g = mg.

21 5-6 Weight The weight of an object on the Earth s surface is the gravitational force exerted on it by the Earth.

22 Apparent weight: 5-6 Weight Your perception of your weight is based on the contact forces between your body and your surroundings. If your surroundings are accelerating, your apparent weight may be more or less than your actual weight.

23 5-7 Normal Forces The normal force is the force exerted by a surface on an object.

24 5-7 Normal Forces The normal force may be equal to, greater than, or less than the weight.

25 5-7 Normal Forces The normal force is always perpendicular to the surface.

26 Some particular forces Normal Force: hen a body presses against a surface, the surface (even a seemingly rigid one) deforms and pushes on the body with a normal force, F N, that is perpendicular to e surface. the figure, forces F g and F N and are the only two forces on the block and they are both vertical. Thus, for the block we can write Newton s second law for a positive-upward y axis, net, y= ma y ), as: A block resting on a table experiences a normal force perpendicular to the tabletop. (b) The free-body diagram for the block. for any vertical acceleration a y of the table and block

27 Some particular forces Friction f we either slide or attempt to slide a body over a surface, the motion is resisted by a bonding between the body and the surface. he resistance is considered to be single force called the frictional force, f. This force is directed along the surface, opposite the direction of the intended motion.

28 Newton s Third Law of Motion Forces always come in pairs, acting on different objects: If object 1 exerts a force F r on object 2, then object 2 exerts a force F r on object 1. These forces are called action-reaction pairs.

29 Newton s Third Law of Motion Some action-reaction pairs:

30 Newton s Third Law of Motion Although the forces are the same, the accelerations will not be unless the objects have the same mass. Contact forces: The force exerted by one box on the other is different depending on which one you push.

31 Newton s Third Law hen two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction. The minus sign means that these two forces are in opposite directions The forces between two interacting bodies are called a third-law force pair.

32 Special Instructions For Chapter 5 Chapter 5 is very important chapter for Universities and Corporate America. Homework for this chapter is extensive and will be weighed heavily in Exam II. You need to understand this chapter thoroughly before you can understand chapter 6. Exam II will be on Chapter 4, 5 and 6. Try to complete entire homework prior to next class.