AAST/AEDT NEWTON S LAWS OF MOTION

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1 1 AAST/AEDT AP PHYSICS B: NEWTON S LAWS OF MOTION Newton s laws are fundamental laws of nature. Those laws can not be derived. Newton defined them as the result of a numerous experiments and observations. They are valid, because in all experiments done by scientists nobody and never observed any exclusion of these laws. We can observe several experiments and make the same conclusions as Newton did. Let us assume that we have an object on the table. Two forces are exerted on it. They balance each other. The net force equals to zero. We can make a conclusion. When the net force equals to zero the object can be at rest. Now we assume that the surface is ice (no friction). We push the object and it starts to move. It is easy to imagine that without friction our object will move uniformly and rectilinear. The conclusion is: When the net force equals to zero, the object can move rectilinear and uniformly. If we join our statements we have: When the net force applied to an object is zero, the object can be or at rest or move rectilinearly and uniformly. This is the first Newton s law The same law can be defined in a different way. Every object body continues in its state of rest or of uniform speed in a straight line unless it is compelled to change that state by net force acting on it. This object s ability to continue its motion is called inertia. Inertial and Non inertial Systems of Reference Let us run an experiment. A box is placed on the ground near the tree. At the same time the car accelerates along the road near the box.

2 2 One observer is on the tree (frame of reference-2). From his point of view the forces that applied to the box are balanced and the box is at rest. This completely corresponds with the first Newton s law and we can state that it is valid. If the same observer will be in the car (frame of reference-1) he will state. The forces are balanced but the box accelerates. This contradicts to the first law. Conclusion: The Newton s laws are valid only in a several systems of reference. These systems are called the inertial frames of reference. Systems, where Newton s law are invalid we define as Non inertial systems of reference. Usually we assume that the system of reference attached to the Earth is inertial. However because of the Earth s rotation and spinning it is not exactly so. MASS Let us run an experiment. We measure the accelerations of two different colliding objects. We would discover that any time one object obtained greater acceleration then the another one and that although the absolute values of accelerations are different, their ratio stays the same. Mathematically it can be presented as a 1 a 2 V 1 V o1 t V 2 V o2 t V 1 V o1 V 2 V o2 That means that one object can easier change its velocity. Another one does the same with more difficulties. The ability of the object to change its velocity is defined as inertia. The easier the object alter its velocity the less is its inertia, or the greater the acceleration, the less the inertia. The last statement means, that inertia and acceleration are inversely proportional.

3 3 a 1 inertia 2 a 2 inertia 1 Mass is the physical quantity that measures this property of the objects. The greater the 1 inertia 2 m 2 2 inertia 1 m 1 inertia - the greater the mass. Mathematically it can be written as If we join (1) and (2), the result is a 1 m 2 3 a 2 m 1 The formula allows us to measure the ratio of masses. To obtain the value of mass we need to know at least the mass of one object. Such an object has been introduced and it is defined as standard. Its mass is defined as 1 kg. Thus, to measure any mass we have to take an object of unknown mass and interact it with a standard. If we measure accelerations, than we would be able to estimate the unknown mass. That is the physics that is used by a scale or balances. Mass is the fundamental physical quantity. We can not give exact definition what is the mass. We can only state that mass measures the quantity of the matter. Mass is the scalar quantity. It has no direction. Force Force is the major physical quantity. We use it to define the action of one object on the other. Usually force is a push or pull 2 Newton s law If we run a set of experiments with an air track and measure acceleration with force, we would discover that The acceleration of the object is directly proportional to the net force acting on it and it is inversely proportional to its mass. F a m This is one of the possible ways of how the 2 Newton s law can be defined. In several books you can find another wording of the same law. Because F m a we can state the second law as: Force equals to the product of the mass times acceleration given by this force This formula allows us to define the unit of force.

4 4 The unit of force is 1 Newton. This is the force required to impart acceleration of 1 m/s 2 to the mass of 1 kg. Newton = kg.m/s 2 It is important to notice that if several forces are applied on the object, than the force in the second law is the net force. 3 Newton s Law If we repeat the above mentioned experiment with an air track and measure masses and accelerations, than we can rewrite formula (3) in a shape m 1 a1 m 2 a2 This is a scalar formula that does not take into account the directions of the accelerations. They are obviously opposite. That is why in a vector shape our formula is m 1 a1 m 2 a2 or, if we take into account the second law F = ma, F 1 F2 This is the 3 Newton s law. It states. Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. You can find in a various textbooks different definitions of the third law. But all of them state the same. What is important to realize, is that action and reaction forces are applied to the different objects. Thus, they never balance each other. For example. You walk along the road. The force you push the Earth is applied on the Earth. The reaction of the Earth- the force that pushes you is applied on you. They do not balance one another. FORCES IN MECHANICS There are only three different forces in mechanics: They are: Force of gravity (Weight) Elastic force Friction force All the other forces, such as normal force, resistance force, pulling force etc.-are representative of one of these three. Force of Gravity (Weight) By definition it is the force exerted by the earth on an object. We know that if an object is moving as the result of the earth's attraction its motion is a free fall and its acceleration equals g. We also know from the 2 N law that F=ma. Thus the expression for the gravity force is Fg m g or W m g Elastic force

5 5 Elastic force is the force that appears as the result of the object's deformation. Example: If we compress or stretch the spring the difference in the spring s dimensions is called deformation. Letter x usually defines it British scientist Hooke studied the relationship between the elastic force and deformation. He discovered that they are directly proportional F kx or in a vector shape F k x (Hooke s Law) Coefficient k is a constant, called the spring constant, or elasticity. It is different for different springs. Sign - represents that the direction of the elastic force and the direction of the deformation are opposite. The main property of the elastic force is that it applies always perpendicularly to the deformed surface. An example of the elastic force is the normal force that a table exerts on an object placed on its surface. Friction force It is the force that produces the resistance to the motion of the two objects that are in contact. We know 3 kinds of friction: STATIC FRICTION, SLIDING (KINETIC) FRICTION, ROLLING FRICTION Static friction appears when you try to move an object from rest. This force is an alternating force. It is equal to the applied force by the magnitude but opposite by direction. This force has the limit. Only when the pulling or pushing force exceeds the maximum value of the static friction the object starts to move. The magnitude of the static friction can be expressed by the formula F f s F N where F f - friction force, µ s - coefficient of static friction, F N - normal force (the force with which the object presses on the surface) You have to realize that the formula above is the formula for the maximum possible static friction (limit static friction). If the pushing or pulling force is below that value, the static friction is also below its limit value

6 6 Kinetic (Sliding) friction This is the resistance force that appears when one object is sliding along the surface of another. The force can be expressed by formula F f k F N where µ k -is the coefficient of the kinetic friction. Usually the kinetic friction coefficient is less then the static one. It depends on the quality of the adjacent surfaces. Bellow you can observe several examples Surface Coef. of static friction Coef. of kinetic friction Wood on wood Metal on metal It is important to realize that friction coefficients do not depend on the surface area or on the force of the Normal pressure. F N is equal to the weight only for horizontal surfaces. If we deal with an inclined plane or vertical wall F N differs from Weight. There are two reasons for the existence of friction: a) Roughness of the contacting surfaces. If we observe the surface through the magnifying glass we can see a lot of roughness. When one object slides along another these roughnesses catch one another and create a resistance to a motion b) Mutual attraction between the molecules. If we were able to create an ideal surface, i.e. a surface without any roughness, the friction will increase many times, because the molecules of the contacting surfaces start to attract each other. There are two widely used methods of reducing friction. a) Lubricating the surfaces. The interval between the surfaces filled with a lubricant prevents roughness interaction. b) Substituting the sliding friction with the rolling friction. (Bearings) Home assignment: Cutnell: page 119 Conceptual questions #1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12 (oral) Problems page 121 #3, 5, 8, 11, 12, 16, 20, 39, 41, 44

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