# Lecture4 - Newton’s laws of [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ The concept of...

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Unformatted text preview: Newton’s laws of [email protected] The concept of force What makes things move? What keeps them moving? Which is the right statement? •  Things just move all by themselves whenever they feel like it. •  Things move when a force acts on it. When forces stop they stop moving. •  A force is needed to get a things move. Once it moves, it will keep moving even if no force is [email protected] on it. What is a force ? It is an [email protected] between two bodies that causes a change in [email protected], for example a push or a pull. The concept of force (contd …) Contact forces are not the only forces. There are ﬁeld forces as well. At the microscopic level, however, the sharp [email protected]@on between contact forces and ﬁeld forces disappear. There are four fundamental forces in nature: 1.  [email protected] forces 2.  [email protected] forces 3.  Strong forces (e.g., between nucleons) 4.  Weak forces (responsible for β decay, for example) All other forces are not fundamental. For example [email protected] force originates from [email protected] forces. Newton’s ﬁrst law of [email protected] In the absence of a net external force an object at rest remains at rest and an object in mo+on con+nues in mo+on with a constant velocity. In other words, when no net force acts on an object, its accelera2on is zero. If nothing acts to change the object’s [email protected], then its velocity does not change. Thus, isolated objects is either at rest or moving with constant velocity. The tendency of an object to resist any aSempt to change its velocity is called the iner+a of the object. … and and object [email protected] in its [email protected] with constant velocity. (the wall of the building did not exert enough force to stop it) Newton’s ﬁrst law of [email protected] (contd…) The term net force has been used here to mean the resultant force. A number of forces may be [email protected] on a body at a @me. Since forces are vectors, we add them using a method of vector [email protected] in order to get the net force [email protected] on the body. [email protected] You are driving down the highway at constant speed and in a straight line. What can you say about the net force [email protected] on the car ? 1.  It is the sum of the force on the @res, gravity, and air drag, and it must be [email protected] in the forward [email protected], otherwise the car would not be moving. 2.  It is equal to zero. 3.  You cannot say anything about it without further [email protected] [email protected] and mass [email protected]: Imagine pushing a bike or a car with the same magnitude of force: Which will experience more change in velocity? Ans: The object with less mass  ­ the bike. The body with less mass has less [email protected], which means that it experiences more change in velocity. Similarly more mass means more [email protected] (recall how we introduced [email protected], earlier.) Mass is a measure of iner2a. Mass is a scalar [email protected] and its SI unit is kilogram (kg). Newton’s second law The accelera+on of an object is directly propor+onal to the net force ac+ng on it and inversely propor+onal to its mass. Fnet = ma or ΣF = ma This is a vector [email protected] and can be wriSen in terms of components: ΣFx = max ΣFy = may ΣFz = maz Note that [email protected] is always directed at the [email protected] of the net force. Units of force The SI unit of force is newton (N). It is deﬁned as the force required accelerate a mass of 1kg by 1m/s2. 1 N = 1 kgm/s2 The CGS unit of force is called dyne and 1 dyne force is the force required to accelerate 1g mass by 1 cm/s2. 1 dyne = 10 ­5 N The dimensions of force are [F] = [m][a] = MLT ­2 [email protected] force and weight All masses aSract each other by a force called the gravita2onal force. A mass on the earth, for example, is thus experience an [email protected] force toward the center of the earth. The observed downward [email protected] of free fall, g, is the consequence. If the body has a mass m, the force is Fg = ma = mg. Since weight is a force it is measured in newton. In everyday use a layman may take the term weight synonymously with mass. But we can see the stark diﬀerence – they are simply diﬀerent things. Mass of an object is an invariable [email protected] On the other hand, weight varies whenever g varies. Even on the surface of the earth, the value of g varies with slightly with [email protected]  ­ g increases from 9.789 m s−2 at the equator to 9.832 m s−2 at the poles. [email protected] Which statements are true ? (gmoon= 1.6m/s2) 1.  On the moon you would weigh less than on earth. 2.  On the moon you would have less mass than on earth 3.  On the moon it would require the same force to accelerate an object than on earth. 4.  On the moon it would require the same force to keep an object moving in a circle as it does on earth. Newton’s Third Law If I pull on an object, what is the force I feel in my ﬁngers, i.e. the force with which the object pulls back ? 1 2 If two objects interact, the force F21 exerted on object 2 by object 1 is equal in magnitude to and opposite in direc+on to the force F12 exerted on object 1 by object 2*. F21 F12 F21 = − F12 Newton’s third law may be stated as ‘the ac2on force is equal in magnitude to the reac2on force and opposite in direc2on’. In our example, F21 might be called [email protected] and F12 its [email protected] It is very important to note that the [email protected] and [email protected] forces act on diﬀerent bodies * Note that my indexing in the subscript is opposite to the one used in the textbook. A force on body A by body B in my [email protected] is FAB whereas in the book it is FBA. [email protected] How can a [email protected] pull a wagon if the wagon pulls back at the [email protected] with the same force as the [email protected] pulls forward ? In order to ﬁgure out if an object is moving, we need to look at the net force on that object. Example II The Normal Force Consider a TV on a table. If the [email protected] force (weight) is pulling the TV down, what keeps it from falling through the surface of the table? Normal force The normal force is a contact force that, for example, prevents the TV from falling through the table and can have any magnitude needed to balance the downward force Fg , up to the point of breaking the table. [email protected] When objects slide on a surface, there is a force [email protected] the [email protected] (i.e. [email protected] in the opposite [email protected] of [email protected]). Experiment: Pulling on a block sipng on a surface. What happened ? Up to a [email protected] force the block does not move. Then it will suddenly break free and accelerate and then [email protected] to move. [email protected]: [email protected] to pull: “Pull” F is opposed by a [email protected] force of equal magnitude, fs. [email protected] [email protected] = unmoving [email protected] As the pulling force increases, [email protected] [email protected] [email protected] to oppose it up to a maximum value. Then the object begins to slide. At this point, the [email protected] force is reduced to the [email protected] [email protected], fk. [email protected] (contd…) •  Experiments have shown that for dry, sliding [email protected], the [email protected] force •  depends on the normal force, FN, with which the sliding body presses against the surface. •  depends on the nature of the surfaces in contact. •  does NOT depend on the contact area! •  does NOT depend on the sliding speed. [email protected] [email protected] The maximum sustainable [email protected] [email protected] (before sliding occurs) is given by: [email protected] [email protected] [email protected] [email protected] is (to ﬁrst order) independent of the sliding speed and is given by: µ s is called the coeﬃcient of [email protected] [email protected] and depends on the nature of surfaces. fs , max = µ s FN fk = µ k FN µ k is called the coeﬃcient of [email protected] [email protected] and depends on the nature of surfaces. [email protected] of Newton’s laws of [email protected] We will do some problems. Most chalk board stuﬀs. Take notes. Example 1 ( the traﬃc light problem, example 5.4, done in the book) A traﬃc light weighing 122 N hangs from a cable @ed to two other cables fastened to a support. The upper cables make angles of 37.0° and 53.0° with the horizontal. Find the tension in the three cables. y Example 2 A shuMle of mass M slides on a fric+onless track. A rope is aMached to the shuMle, which passes over a pulley and is aMached to a block of mass m, hanging from the rope. Assuming the rope and M: the pulley are massless, what is the accelera+on of the shuMle ? M m y M x FN m : T x y m T x FgM Look at each object separately and draw a free ­body diagram: (1) M a = T (2) T - m g = - m a a= m g M +m Fgm a) What are the magnitudes of T and FN ? b) If I cut the rope, what’s the accelera+on of the block (assume no fric+on)? Free ­body diagram: Note special choice of coordinate system & [email protected] of FN. a) Block is in equilibrium: b) If I cut the rope, the y component of the weight will [email protected] be balanced by the normal force. But the tension will be removed. − mg sin θ = ma ⇒ a = − g sin θ Compare with Example 5.10 ...
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## This note was uploaded on 11/16/2010 for the course PHY 2170 taught by Professor Blank during the Spring '08 term at Wayne State University.

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