Force can be exerted by direct contact between bodies: Contact Force.

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Berenice Hamilton
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1 Chapte 4, Newton s Laws of Motion Chapte IV NEWTON S LAWS OF MOTION Study of Dynamics: cause of motion (foces) and the esistance of objects to motion (mass), also called inetia. The fundamental Pinciples of Dynamics ae summaized in Newton s Laws of motion. Kinematics + Dynamics ae the foundation of classical (Newtonian) mechanics. It does not wok all the time: at high speed elativistic mechanics (Einstein) must be used; atomic scale phenomena ae descibed with quantum mechanics. IV-1 Foce and Inteactions A FORCE is the quantitative measue of the inteaction that modifies the MOTION of a body. (Definition also applies to mechanical defomation of bodies). Foce can be exeted by diect contact between bodies: Contact Foce. Physical contact is not necessay: Long- Range Foce, e.g., electo/magnetic foces, gavitation, etc.., The gavitational foce exeted on a body by the Eath is called the weight of the body. Foce is vecto quantity. SI unit is Newton (N). At a single point, the simultaneous effect of seveal diffeent foces is the foce equal to thei vecto sum. Any foce can be eplaced by its component vectos acting at the same point: F y F F x F = F + F x y The vecto sum of all the foces acting on a body is called the Net Foce: R = F1 + F2 + F = F PS 128 Physics/1

2 Chapte 4, Newton s Laws of Motion Newton s Fist Law of Motion: A Body acted on by no net foce moves with constant velocity. Consequences: 1. The net Foce R = 0 2. Thee is no acceleation 3. Body in equilibium (eithe at est o moving with constant velocity) Inetia is the ability of a body at est to emain at est. Newton s Fist Law (o Law of Inetia) is only valid in an inetial fame of efeence. An inetial fame of efeence is eithe at est o moving with constant velocity (with espect to anothe inetial fame), i.e. no acceleation. The Eath is appoximately an Inetial Fame (vey litle acceleation due to its otation). (Read examples on pp.97/98 in Young s book) When a Net Foce F is pesent, the body is acceleated: it is obseved in this case that Σ F / a = constant = m. m is called the inetial mass o mass of the body. Definition of the Newton: The amount of net foce that gives an acceleation of 2 one mete pe second squaed to a body with a one kg mass. 1N = 1kgms.. Neew toonn t ss ss ee ccoonndd LLaaw : ❶ A nnee t ee xxt tee nnaal l foo f ccee pp oodduuccee ss aaccccee lee l aat tioonn.. ❷ TThhee ddi i ee cct tioonn oof f aa iss i thhee t ss aam ee aass thhaat t t oof f thhee t nnee t foo f ccee. ❸ TThhee nnee t foo f ccee vvee cct too iss i ee qquuaal l too t thhee t m aass ss oof f thhee t bbooddyy tit im ee ss iti tss aaccccee lee l aat tioonn.. F = ma Only extenal foces can poduce acceleation: a body cannot change its own motion by exeting a foce on itself Newton s Second Law is only valid in inetial efeence fames. Valid only when m is constant. ma is Not a foce, but the consequence of a foce PS 128 Physics/2

3 Chapte 4, Newton s Laws of Motion IV-2 MASS and WEIGHT Weight is the Eath s gavitational pull on a body, i.e. it s a f oo cc ee. Mass is an inetial popety of a body: elated to the aamoouunnt t oof f maat ttee ( nnuumbbee oof f aat toomss ) it contains. The mass of a body is constant thoughout the Univese. The weight would vay depending on the local value of gavity. Mass and weight ae elated by: w = mg, whee g is the local value of the acceleation due to gavity. PS 128 Physics/3

4 Chapte 4, Newton s Laws of Motion EXAMPLES A mass M moves fom A to B at constant velocity unde the action of seveal foces. What can we say about the foces? Daw a gaph of: 1.The path fom A to B 2. Fom B to C, if an exta constant foce pependicula to v is applied at B 3. Fom C to D, if an exta foce of constant magnitude is applied at C with a diection always pependicula to the path. Pull: Calculate the acceleation when a 20 N hoizontal foce is applied to a box of mass 40 kg esting on a fictionless level suface (1) Choose a coodi-nate system (2) Identify all the foces acting on the system: N 1.The hoizontal pull F 2. The weight w 3.The suppoting foce exeted by the suface N - the nomal foce No vetical acceleation: w = -N Thus, only hoizontal foce acting: a x = F x /m = 20/40 = 0.5 ms -2 PS 128 Physics/4

5 Chapte 4, Newton s Laws of Motion Push with Fiction: an object (m = 0.45 kg) is shoved towad the ight along a smooth level suface. It comes to est afte sliding ove 1m and stated with an initial velocity of 2.8 m/s. Calculate the diection and magnitude of the acting foce(s)? f The fiction foce f is constant, theefoe the acceleation is constant Diection of motion v v0 a = ( x x = ) ( = 39. ms ) f = ma = 045. ( 39. ) = 18. N -2 Fom eveyday expeience, we know that foces always come in pais: kicking a ball, pulling a weight, etc...thus, the ball, the weight also exets a foce on you. Newton s Thid Law: the foces that two bodies (say A and B) exet on each othe ae equal in magnitude and opposite in diection: F = F AonB BonA These two foces act on diffeent bodies! Action - Reaction Case of opes, etc... Pulling foces ae applied at its ends and the ope is in tension. The tension at any point of the ope is the magnitude of the foce acting at that point. If in equilibium, the tension is the same at both ends and thoughout the ope. IV-3 USING NEWTON S LAWS The laws ae simple but the specific situation in which they can be applied can be complex. PS 128 Physics/5

6 Chapte 4, Newton s Laws of Motion Whethe, R = 0, i.e. (Fist Law) o R = ma, (Second Law), iti t m uuss t bbee aappppl liee dd too t oonnee ss ppee cci ificc bbooddyy. One should daw a FREE-BODY DIAGRAM (FBD). It is the body itself fee fom its suoundings with vectos dawn to show the diection and the magnitude of ALL the foces applied. Action-eaction pai of foces should neve appea. They do not act on the same body. In cases whee a body is in equilibium, Newton s Fist Law: ΣF = 0 will usually be used in its component fom, i.e. ΣF x = 0, ΣF y = 0 N T W = mg α Along 0x: T+(-wsinα)=0 T= wsinα Along 0y N+(-wcosα)=0 N= wcosα Same technique applies to dynamics poblems. In which case, Newton s second Law applies and will be used in its component fom: ΣF x = ma x, ΣF y = ma y N Solid of mass m sliding on a fictionless suface α W = mg Along 0x: PS 128 Physics/6

7 Chapte 4, Newton s Laws of Motion (-wsinα)=ma x a x = -gsinα Along 0y N+(-wcosα)=0 N= mgcosα IV-4 FRICTIONAL FORCES Fiction is vey impotant in many aspects of eveyday life: lubication of engines, ubbe tyes, ai dag, etc... The contact foce exeted by a suface on a body can always be epesented as the vecto sum of the nomal foce N (pependicula to the suface) and the fiction foce f (paallel to the suface). The kinetic fiction foce f k acts when a body slides ove a suface. Its magnitude inceases when the nomal foce inceases. In many cases, one can wite: f k = µ k N (magnitude of kinetic fiction foce) µ k is the coefficient of kinetic fiction The moe slippey the suface, the smalle the coefficient of kinetic fiction. **Table 5-1, p.133** The static fiction foce f s acts when thee is no elative motion between the two sufaces. In ode to move a body the static fiction foce must be ovecome fist, then the kinetic fiction foce acts. Example PS 128 Physics/7

8 Chapte 4, Newton s Laws of Motion N Solid of mass m sliding on a ough suface f k α W = mg Along 0x: (-wsinα) +f k = ma x a x = g(µ k cosα-sinα) Along 0y N+(-wcosα)=0 N= mgcosα When the body has wheels, one defines a coefficient of olling fiction. A fluid (wate, ai) exets a esistance (Thid Law) on a body which moves though it. In a diection opposite that of the body s velocity elative to the fluid. The magnitude of the fluid esistance (f) is: - popotional to v fo low v s: f = kv - popotional to v 2 fo high v s (e.g. ai dag): f = Dv 2 In case of unifom cicula motion (UCM), the acceleation is constant and always diected towad the cente of the cicle (adial acceleation, see Chap. III) UCM is govened by Newton s Second Law: a ad v R Fext = ma 2 F ma m v net = ad = R PS 128 Physics/8

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights