Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.

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1 Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a mass? Perhaps suggest a history google project here Newton s First Law of Motion An object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force. Net force is crucial. It means the vector sum of all of them - demonstration. A state of rest (zero velocity) and a state of constant velocity are equivalent under Newton s law. Interia and Mass Inertia is the natural tendency of an object to remain at rest or in motion at a constant speed along a straight line. The mass of an object is a quantitative measure of inertia. SI unit of inertia and mass is the kilogram (kg). An inertial reference frame is on ein which Newton s law of inertia is valid. Inertial Reference Frames? Newton s Second Law of Motion When a net external force F acts on an object of mass m, the acceleration a that results is directly proportional to the mass. The direction of the acceleration is the same as the direction of the net force. SI unit of Force is kg.m/s 2 = newton(n), or a = F m, F = ma. This is for external forces. Internal forces are forces that one part of an object exerts on another part and are not included in the above. 1

2 Go over example 1, p. 84. Vector Nature of the Second Law The net force F has components F x and F y and by analogy with kinematics in 2D, can write, Fx = ma x, Fy = ma y. Go over Example 2,3 p. 85/86. Newton s third law of Motion Whenever one body exerts a force on a second body, the second body exerts an opposite directed force of equal magnitude on the first body. Action-reaction law. Pressing on desk, walking example. Go over example 4, p. 92. Forces play a central role in determining the motion of an object. Types of Forces: Gravitational, Normal, Frictional, Tension - all obey Newton s laws. The Gravitational Force Newton s universal law of gravitation: every particle in the universe exerts an attractive force on every other particle. For two particles that have masses m 1, m 2 and are separated by a distance r, the force that each exerts on the other is directed along the line joining the particles and has a magnitude given by F = G m 1m 2 r 2, where G denotes the universal gravitational constant and is found to be N.m 2 /kg 2. The unit of the gravitational force is Newtons. Go over figure 4.9, 4.10 p. 94. What happens when r increases?, r decreases? Go over example 5, p. 94. Weight 2

3 The weight of an object on or above the Earth is the gravitational force that the Earth exerts on the object. The weight always acts downward, toward the center of the earth. SI unit is Newtons (N). Using W for the magnitude of the weight, m for the mass of the object, M E for the mass of the Earth, W = G M Em r 2. Difference between mass and weight, weight on different planets etc. Go over Example 6, p. 95. The Normal Force The normal force F N is one component of the force that a surface exerts on an object with which it is in contact - namely, the component that is perpendicular to the surface. Newtons third law plays an important role in connection with the normal force. If an object is resting on a horizontal table and there are no other forces acting, then F N = W, that is the magnitude of the object s weight and normal force are equal but directed in opposite direction - connection to Newton s second law. If other forces, in addition ot W F N, act in the vertical direction then the magnitudes of the weight and normal force are no longer equal. Go over Figure 4.15,a)b), p. 93. Go over Exampe 8, p. 97. F N = mg + ma, Apparent weight = True Weight + force due to other accelerations Presentation on Apparent weight? Go over Fig. 4.16, p.99 Staic and Kinetic Frictional forces When an object is in contact with a surface, there is a force acting on the object. Previous section discussed the component of this force that acts perpendicular to the surface - the normal force. When an object moves or attempts to move along the surface, there is a component of the force that is parallel to the surface - frictional force or friction. 3

4 Static friction The magnitude f s of the static frictional force can have any value from zero up to a maximum value fs MAX, depending on the applied force. That is f s fs MAX. The equality holds when f s attains its maximum value when fs MAX = µ s F N. Here µ s is the coefficient of static friction and F N is the magnitude of the normal force. Does the coefficient of static friction have any units? No. Why not? Example 9, p. 102 Kinetic friction Once two surfaces begin sliding over each other, we have kinetc friction and static friction is no longer present. The magnitude of the kinetic frictional force ise f k = µ k F N, where µ k is the coefficient of kinetic friction and F N is the magnitude of the normal force. What direction does friction act in? Exampe 10, p. 104 The Tension force Go over figure 4.25, 4.26, p. 106 or ask some to do this. Equilibrium applications of Newton s Laws of Motion An object is in equilibrium when it has zero acceleration. Since the acceleration is zero, F x = 0, F y = 0. Go over reasoning stratgey, p Go over example 11, p Someone go over example 12, p Groups go over example 13, p Nonequilibrium Applications of Newton s Laws of Motion When an object is accelerating, it is not in equilibrium. Thus the bf net force is not zero in Newton s second law. Then we have Fx = ma x, and Fy = ma y. 4

5 Go over example 14, p Groups go over example 15, p Go over example 16, p Groups go over examples 17,18, p. 115/116. Go over example 19, p Review Concept Summary, p. 120/121. Do questions: 1,2,3,4,5,6, p Questions 3,4,5,7,p Questions 10,12,14, p Questions 19, 24, p Questions 36,37,38, p Questions 46, 47, p Questions 63, 66,67,70, p

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