Chapter 4. Newton s Laws of Motion

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The unit of foce in the metic system is the Newton. Foce is a vecto quantity.

1 Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto quantity. Supeposition of Foces Any numbe of extenal foces applied to an object has the same effect as a single foce equal to the vecto sum of the extenal foces. 1

2 4. Newton s Fist Law of Motion Evey body continues in its state of est o of unifom motion in a staight line unless it is compelled by a foce to change that state. That is, a body acted on by NO NET EXTERNAL FORCE moves with constant velocity (which may be zeo) and zeo acceleation. F = 0 " When the net extenal foce acting on an object is zeo, the object is said to be in a state of tanslational equilibium. 4.3 Newton s Second Law of Motion The net foce! F acting on an object of mass m is equal to the poduct of the object s mass with its acceleation a.! F = ma

3 Note that the net foce (o esultant foce)! F is in the same diection as the acceleation vecto a. This is illustated in the following pictue. 4.4 Mass and Weight The mass of an object is that popety that specifies how much esistance the object exhibits to changes in its velocity (a measue of the inetia of the object). Mass is a scala quantity. The unit of mass in the metic system is the kilogam. Weight is a foce exeted on a body by the eath. Weight is thus a vecto quantity. 3

Newton s Law of Univesal Gavitation: Evey paticle (with non-zeo mass) in the univese attacts evey othe paticle (with non-zeo mass) with a foce that is diectly popotional to the poduct of thei masses

4 Newton s Law of Univesal Gavitation: Evey paticle (with non-zeo mass) in the univese attacts evey othe paticle (with non-zeo mass) with a foce that is diectly popotional to the poduct of thei masses and invesely popotional to the squae of the distance between them. That is, F = G m m 1 whee G = 6.67x10-11 Nm /kg = the univesal gavitational constant. = distance fom the cente of mass of one paticle to the cente of mass of the othe paticle. The attactive foce exeted by the Eath on an object is called the gavitational foce F g o W. This foce is called the weight of the object, and its diection is towad the cente of the Eath. The weight of an object of mass m on the Eath has a magnitude equal to: F g = Weight = G M E m R E 4

5 M R E The quantity G appeas so often that it is given the E name g o simply g. This quantity is also called the gavitational field geneated by the Eath at locations nea its suface. The gavitational field g is a vecto quantity with a diection towad the cente of the Eath, and with a magnitude defined as using g = g = G M R E E G = 6.67x10-11 Nm /kg M E = 5.98x10 4 kg (mass of the Eath) R E = 6.37x10 6 m (adius of the Eath) yields a value of g = 9.8 m/s. One can thus say that the weight of an object of mass m on the suface of the Eath is W = m g whee g = the acceleation due to gavity (o the gavitational field), always diected towad the cente of the Eath. 5

6 Mass and weight ae thus elated quantities. The magnitude of a body s weight W is diectly popotional to its mass m. 4.5 Newton s Thid Law (Action-Reaction Law) If body A exets a foce F Aon B on body B, then body B exets an equal (magnitude) and opposite (diection) foce F Bon A on body A. Foces always occu in pais. F Aon B = " F Bon A Essentially, you cannot touch without being touched! 6

7 4.6 Solving Poblems with Newton s Laws: Fee-Body Diagams Objects in Equilibium: An object is said to be in mechanical equilibium when two conditions ae met: (1) The net foce acting on the object is equal to zeo. This ensues tanslational equilibium. Fom! F = ma we see that if! F = 0! a = 0! v = cons tan t, then That is, the object is (i) at est and stays at est o (ii) the object moves in a staight line with constant speed. () The net toque acting on the object is zeo. This ensues otational equilibium. The object is (i) at est and stays at est o (ii) the object spins about a fixed axis with constant angula speed. We will discuss otational equilibium in chapte 10. 7

8 Stategy fo applying Newton s laws of motion: (1) Isolate (conside) a pat of the system o the entie system and daw the foces acting ON it. This is called a fee-body diagam. () Apply Newton s nd law of motion in component fom. That is, solve! F x max! Fy = = may (3) Solve fo any unknown quantities. (4) If the acceleation of the object is constant, then you may also apply the kinematic equations of motion. 8

Chapter 4. Newton s Laws of Motion. Newton s Law of Motion. Sir Isaac Newton ( ) published in 1687

Chapter 4. Newton s Laws of Motion. Newton s Law of Motion. Sir Isaac Newton ( ) published in 1687 Chapte 4 Newton s Laws of Motion 1 Newton s Law of Motion Si Isaac Newton (1642 1727) published in 1687 2 1 Kinematics vs. Dynamics So fa, we discussed kinematics (chaptes 2 and 3) The discussion, was