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III. Newton’s Laws of MotionA. Kinematics and MechanicsB. Newton’s Laws of MotionGalileo Galilei (1564-1642)Isaac Newton (1642-1727)PowerPoint PresentationSlide 7Slide 8An important qualification:C. Common Forces in NatureC. Common Forces in Nature, contd.Slide 12D. Problem Solving Using Newton’s LawsProblem Solving Steps (p.97):Example: Two accelerating blocksAnother example: two blocks connected by a stringAn inclined plane problemE. Frictional ForcesIf the force F is increased, the block will remain at rest until F is large enough to cause it to accelerate from rest. At this point the static friction force is a maximum (fs)max. Graphically we can represent this:What does the frictional force depend on?Approximate quantitative relationshipsF. Circular MotionTo find the acceleration:Newton’s Second Law in Circular Motion: an exampleCircular Motion with Frictional Forces: an exampleRemember:III. Newton’s Laws of MotionA. Kinematics and MechanicsB. Newton’s Laws of MotionC. Common Forces in NatureD. Problem Solving Using Newton’s LawsE. Frictional ForcesF. Circular MotionA. Kinematics and MechanicsKinematics is concerned with the relationship between position, velocity, and acceleration of an object without reference to the origin of the motion.Mechanics is the study of the relationship between the forces experienced by an object and the motion resulting from these forces.B. Newton’s Laws of MotionFrom the time of the Greeks until Galileo, the “natural state” of an object was thought to be rest, so it was assumed that there was a direct connection between the force on an object and the object’s velocity:F vA nonzero force was thought to imply a nonzero velocity, and vice-versa.Although this idea seems to be just common sense, Galileo and Newton showed that it is wrong!Galileo Galilei(1564-1642)His genius lie in carrying out “thought experiments”, by which he was able to simplify physical situations and infer the important causal relationships. He realized that a moving object, which seems to slow down as a matter of necessity, would not slow down in the absence of frictional forces.Isaac Newton(1642-1727)A towering genius in both mathematics and physics, he was the co-inventor of differential calculus as well as the discoverer of the inverse square law of universal gravitation.First Law: An object moves with constant velocity (or remains at rest) unless acted upon by a net external force.Also called the law of inertia, this principle assumes that the proper connection is between the force on an object and its change in velocity, or its acceleration: F aThus, if an object moves with a constant velocity, the net external force acting on it isZERO!Second Law: The acceleration of an object is in the direction of the net force it experiences and is inversely proportional to its mass, or inertia.amFjustormFaiiiiThird Law: All forces occur in equal and opposite pairs. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A:A BBAFABFABBAFFThis principle is important in problems involving two or more objects in contact with each other.An important qualification:Newton’s Laws are only valid in inertial (non-accelerating) frames of reference.Thus, the accelerations and forces that we use to write down these laws must be measured by an observer in an inertial reference frame.C. Common Forces in NatureWeight is the force with which a massive object (like the earth) attracts other objects. If an object with mass m is near the surface of the earth, it experiences a force directed toward the center of the earth with magnitudemgW WmC. Common Forces in Nature, contd.Two objects that are touching exert contact forces on each other. The direction of such forces is always normal (perpendicular) to the surface of contact, so they are sometimes called normal forces.Fn = force of table on boxFn' = force of box on tableC. Common Forces in Nature, contd.When a 1-D spring (or similar elastic cord) is elongated or compressed from its equilibrium position by a distance x, it exerts a restoring force (or spring force) Fs which is given approximately byxkFsxFsxwhere k is the spring constant. Note that the force is always opposite to the displacement.D. Problem Solving Using Newton’s LawsWe clearly indicate the forces acting on an object by representing the object as a point particle and drawing arrows from the point in the direction of the force. On such a free-body diagram, be sure you only draw arrows for forces! Velocity and acceleration are not forces!mmgFnfrictionless surfaceProblem Solving Steps (p.97):1. Draw a neat diagram that includes important features.2. Draw separate free-body diagrams for each object of interest.3. Choose a convenient coordinate system for each object.4. Write down Newton’s second law in component form and use Newton’s third law if you have more than one object.5. Solve the resulting equations for desired unknown(s).6. Check your answers for units, plausibility, and familiar limiting cases.Example: Two accelerating blocksTwo blocks, with masses m1 and m2, are in contact on a frictionless horizontal surface. A force F is applied to m1, causing both blocks to accelerate along the surface. Find the force of contact between the two blocks.Note carefully the notation for the normal forces and the weights of the blocks. Also note that force F acts only on m1 and NOT on m2!m1Fm2m2gFn2Fcm1gFn1FFcAnother example: two blocks connected by a stringTwo blocks, with masses m1 and m2, are connected by a string of negligible mass on a frictionless horizontal surface. A force F is applied to m1 at an angle above the horizontal, causing both blocks to accelerate along the surface. Find the acceleration of the two blocks and the tension in the string, in terms of the masses, the angle and the force F.m1Fm2TAn inclined plane problemTwo blocks with mass m and 2m are connected by a string of negligible mass over a pulley as shown. The plane is a frictionless surface inclined at an angle from the horizontal. After the block 2m is released, find the acceleration of the system and the tension in the string, in terms of m and .2mmE. Frictional ForcesThe two basic cases we need to understand are static friction and sliding friction. Consider a block of mass m on a surface and subject to a horizontal force F, but

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