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# v1chap5(4) - Chapter 5 Forces and Motion II 5.1 5.1.1 The...

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Chapter 5 Forces and Motion II 5.1 The Important Stuff 5.1.1 Friction Forces Forces which are known collectively as “friction forces” are all around us in daily life. In elementary physics we discuss the friction force as it occurs between two objects whose surfaces are in contact and which slide against one another. If in such a situation, a body is not moving while an applied force F acts on it, then static friction forces are opposing the applied force, resulting in zero net force. Empirically, one finds that this force can have a maximum value given by: f max s = μ s N (5.1) where μ s is the coefficient of static friction for the two surfaces and N is the normal (perpendicular) force between the two surfaces. If one object is in motion relative to the other one (i.e. it is sliding on the surface) then there is a force of kinetic friction between the two objects. The direction of this force is such as to oppose the sliding motion and its magnitude is given by f k = μ k N (5.2) where again N is the normal force between the two objects and μ k is the coefficient of kinetic friction for the two surfaces. 5.1.2 Uniform Circular Motion Revisited Recall the result given in Chapter 3: When an object is in uniform circular motion, moving in a circle of radius r with speed v , the acceleration is directed toward the center of the circle and has magnitude a cent = v 2 r . 99

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100 CHAPTER 5. FORCES AND MOTION II Therefore, by Newton’s Second Law of Motion, the net force on this object must also be directed toward the center of the circle and have magnitude F cent = mv 2 r . (5.3) Such a force is called a centripetal force , as indicated in this equation. 5.1.3 Newton’s Law of Gravity (Optional for Calculus–Based) The force of gravity is one of the fundamental forces in nature. Although in our first physics examples we only dealt with the fact that the earth pulls downward on all masses, in fact all masses exert an attractive gravitational force on each other, but for most objects the force is so small that we can ignore it. Newton’s Law of Gravity says that for two masses m 1 and m 2 separated by a distance r , the magnitude of the (attractive) gravitational force is F = G m 1 m 2 r 2 where G = 6 . 67 × 10 - 11 N · m 2 kg 2 (5.4) While the law as given really applies to point (i.e. small) masses, it can be used for spherical masses as long as we take r to be the distance between the centers of the two masses. 5.2 Worked Examples 5.2.1 Friction Forces 1. An ice skater moving at 12 m s coasts to a halt in 95 m on an ice surface. What is the coefficient of (kinetic) friction between ice and skates? [Ser4 5-51] The information which we are given about the skater’s (one-dimensional) motion is shown in Fig. 5.1(a). We know that the skater’s notion is one of constant acceleration so we can use the results in Chapter 2. In particular we know the initial and final velocities of the skater: v 0 = 12 m s v = 0 and we know the displacement for this interval: x - x 0 = 95 m we can use 2.8 to find the (constant) acceleration a . We find: v 2 x = v 2 0 x + 2 a x ( x - x 0 ) = a x = ( v 2 x - v 2 0 x )
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v1chap5(4) - Chapter 5 Forces and Motion II 5.1 5.1.1 The...

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