Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.

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1 Newton Law Newton firt law: An object will tay at ret or in a tate of uniform motion with contant velocity, in a traight line, unle acted upon by an external force. In other word, the bodie reit any change of their tate of motion. Thi reitance i called inertia, and the meaure of inertia of the body i it ma, a.k.a. the amount of matter in the body. The more ma a body ha, the harder it i to change it motion. Ma i an intrinic property of matter and doe not change a an object i moved from one location to the next. A force i imply a puh or a pull. Force are vector; they have both ize and direction. There are two major type of force. Contact force: Force that arie when two object are in contact (tenion, friction, and elatic force). Action-at-ditance force: Force that do not require the bodie to be in contact (gravitation, electromagnetic force, or the trong nuclear force). Force caue mae to accelerate. Newton econd law relate force acting upon a body to the ma of the body and the acceleration produced by thi force, Fnet = ma or F = ma. The um of the force acting on a body i equal to the object ma multiplied by it acceleration. The igma (Σ) i the ymbol for um. The reult of adding up all the force on an object i called the reultant or net force. Make ure you know that the Force in the problem in thi coure refer to the overall Net force acting on the object in the problem. Remember that force are vector, o we need to ue the rule of vector addition. F 1 + F 2 F 1 F 2

2 However, jut a it wa the cae with two-dimenional motion, we can olve all problem by breaking down the force into component. For example, if there are three force acting on our object, and we know the component of thee three force vector [ F 1x, F 1y, F 1z,] [F 2x, F 2y, F 2z ] [F 3x, F 3y, F 3z ], then the net force in 'x' i F 1x + F 2x + F 3x, in 'y' the net force i F 1y + F 2y + F 3y, and in 'z' F 1z + F 2z + F 3z. If all of thee um are not equal to zero, then by Newton econd law, there will be an acceleration of the object on which the force act: a x = [F 1x + F 2x + F 3x ] /m, a y = [F 1y + F 2y + F 3y ]/m, a z = [F 1z + F 2z + F 3z ]/m where a x, a y, a z are component of the acceleration vector of the object of ma m. The origin of force i alway other object. For example, the force of gravity i exerted by Earth. The force acting on one body and exerted by another body i one ide of interaction between them. According to Newton Third Law of Motion, Whenever one object exert a force on a econd object, the econd exert an equal and oppoite force on the firt. Four force that we uually work with in Newtonian mechanic problem are 1. Gravitational Force 2. Normal Force 3. Tenion Force 4. Friction Force 1. The gravitational force on an object i attractive force. The gravitational force exerted by Earth i what we call weight. By Newton econd law, Weight = ma x acceleration. In thi cae, a i g = 9.8 m/ 2 and, therefore, W = mg. The direction of the weight vector i alway vertically downward. 2. Newton' third law i the reaction force on a body. Thi force reult from the contact between the body and another urface. The direction of normal i perpendicular to the urface with which the body i in contact.

3 Ma and weight are often confued. It i important to realize that ma and weight are different quantitie. Ma i the meaure of inertia of the body; it i meaured in kilogram. Weight i the force of gravity on an object. The amount of matter in an object doe not change; hence, the ma of an object i alway the ame. However, 'g' varie from place to place on the Earth' urface, depending on the ditance from the center of the Earth, o weight doe change. If a body i on a horizontal urface, then a force, exerted by the upport, prevent it from falling down. The net force acting on the body at ret i the um of the weight caued by the force of gravity and the normal force, F + W = 0. Since the force in thi cae all act in a ingle vertical direction, intead of continuing to write thi a vector equation, we will imply write thi equation a F + W = 0 where the normal force will be poitive and acting upward and the weight will be a negative quantity acting downward. Normal force If the peron i not accelerating, then the net force i zero; thu, the normal force mut equal the weight. W = mg Note that an object' apparent weight will change if the upporting urface i accelerating, a i the cae with weight meaurement made in an elevator. In thi cae, the peron i accelerating down, Σ F = ma 0 or mg N = ma; N = mg - ma N < mg, o the peron feel lighter. Σ F = ma N W = mg a

4 3. Tenion force are exerted by tring, cable, cord, etc. when thee tring and cord are ued to apply force or make connection between object in the problem. In an ideal ituation, our tring and cord will be male and inextenible uch that force at one end are tranmitted undiminihed to the other end, keeping the tenion uniform throughout. Tenion i alway a pulling force; it i alway directed along the rope or cable or tring. If a pulling force T i exerted on a rope, thi force i tranmitted all the way along the rope to the other end. 4. Friction i a contact force. It i alway preent when two bodie touch. From an atomic perpective, when two urface are in contact with each other, intermolecular force form contact bond which momentarily bond the urface together. Static friction i friction between any two urface when they are not moving acro each other. Static friction alway reit a force that i trying to lide the urface acro each other. The direction of tatic friction i alway oppoite to that of the applied force. Another important thing about tatic friction i that it doe not have certain magnitude. A you puh on an object with increaing force, the force of tatic friction increae a well. If an object i not moving under an applied force F are equal., then f and the magnitude of the component of F that i parallel to the urface However, tatic friction cannot continue puhing back without limit. At ome point, tatic friction break down. When the component of F that i parallel to the urface exceed f,max, the object tart to move. Up until thi point, the force of tatic friction i equal to whatever the magnitude of the parallel to the urface component of F i, that i inufficient to move the object. Thi point indicate the maximum poible tatic friction force. Thi (maximum) force i proportional to the normal force N between the two urface: f μ N where μ i the coefficient of proportionality, called the coefficient of tatic friction. The tatic friction force i LESS THAN or equal to μ N. When the urface begin to lide acro one another, the force oppoing the motion i called kinetic or liding friction. The direction of liding friction i alway oppoite to that of the

5 velocity. Thi force i alo proportional to the normal force f = μ N, where i the coefficient of kinetic friction. The coefficient of kinetic friction i uually le than that of tatic friction. Thee coefficient depend only on the nature of the material in contact and their condition (roughne, wetne, dut, etc). Neither tatic nor liding friction depend on the total contact area between the urface. k k μ k Drag Force and Terminal Speed: When object are moving through a liquid or ga, a drag force D oppoe the object motion. The magnitude of the drag force motly depend on the object velocity and hape. In the cae of an object falling toward earth, there will be a peed V Terminal = V t for which the magnitude of D i equal to the object weight in kg.

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