Chapter 6. Dynamics I: Motion Along a Line
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1 Chapter 6. Dynamics I: Motion Along a Line This chapter focuses on objects that move in a straight line, such as runners, bicycles, cars, planes, and rockets. Gravitational, tension, thrust, friction, and drag forces will be essential to our understanding. Chapter Goal: To learn how to solve problems about motion in a straight line.
2 Chapter 6. Dynamics I: Motion Along a Line Topics: Equilibrium Using Newton s Second Law Mass, Weight, and Gravity Friction Drag More Examples of Newton s Second Law
3 Chapter 6. Reading Quizzes
4 Newton s first law can be applied to A. static equilibrium. B. inertial equilibrium. C. dynamic equilibrium. D. both A and B. E. both A and C.
5 Newton s first law can be applied to A. static equilibrium. B. inertial equilibrium. C. dynamic equilibrium. D. both A and B. E. both A and C.
6 The coefficient of static friction is A. smaller than the coefficient of kinetic friction. B. equal to the coefficient of kinetic friction. C. larger than the coefficient of kinetic friction. D. not discussed in this chapter.
7 The coefficient of static friction is A. smaller than the coefficient of kinetic friction. B. equal to the coefficient of kinetic friction. C. larger than the coefficient of kinetic friction. D. not discussed in this chapter.
8 The force of friction is described by A. the law of friction. B. the theory of friction. C. a model of friction. D. the friction hypothesis.
9 The force of friction is described by A. the law of friction. B. the theory of friction. C. a model of friction. D. the friction hypothesis.
10 Chapter 6. Basic Content and Examples
11 Equilibrium An object on which the net force is zero is said to be in equilibrium. The object might be at rest in static equilibrium, or it might be moving along a straight line with constant velocity in dynamic equilibrium. Both are identical from a Newtonian perspective because the net force and the acceleration are zero.
12 Problem-Solving Strategy: Equilibrium Problems
13 Problem-Solving Strategy: Equilibrium Problems
14 Problem-Solving Strategy: Equilibrium Problems
15 Problem-Solving Strategy: Equilibrium Problems
16 EXAMPLE 6.2 Towing a car up a hill QUESTION:
17 EXAMPLE 6.2 Towing a car up a hill
18 EXAMPLE 6.2 Towing a car up a hill
19 EXAMPLE 6.2 Towing a car up a hill
20 EXAMPLE 6.2 Towing a car up a hill
21 EXAMPLE 6.2 Towing a car up a hill
22 EXAMPLE 6.2 Towing a car up a hill
23 Using Newton s Second Law The essence of Newtonian mechanics can be expressed in two steps. The forces on an object determine its acceleration a = Fnet/m, and The object s trajectory can be determined by using the equations of kinematics.
24 Problem-Solving Strategy: Dynamics problems
25 Problem-Solving Strategy: Dynamics problems
26 Problem-Solving Strategy: Dynamics problems
27 Problem-Solving Strategy: Dynamics problems
28 EXAMPLE 6.3 Speed of a towed car QUESTION:
29 EXAMPLE 6.3 Speed of a towed car
30 EXAMPLE 6.3 Speed of a towed car
31 EXAMPLE 6.3 Speed of a towed car
32 EXAMPLE 6.3 Speed of a towed car
33 EXAMPLE 6.3 Speed of a towed car
34 EXAMPLE 6.3 Speed of a towed car
35 Mass Mass is a scalar quantity that describes an object s inertia. Loosely speaking, it also describes the amount of matter in an object. Mass is an intrinsic property of an object. It tells us something about the object, regardless of where the object is, what it s doing, or whatever forces may be acting on it.
36 Gravity It was Newton who first recognized that gravity is an attractive, long-range force between any two objects. Somewhat more loosely, gravity is a force that acts on mass. When two objects with masses m1 and m2 are separated by distance r, each object pulls on the other with a force given by Newton s law of gravity, as follows:
37 Gravity We can write the gravitational force even more simply as where the quantity g is defined to be
38 Weight When you weigh yourself, you stand on a spring scale and compress a spring. With that in mind, let s define the weight of an object as the reading Fsp of a calibrated spring scale on which the object is stationary. Because Fsp is a force, weight is measured in newtons. If the scale is at rest relative to the earth, then the object being weighed is in static equilibrium. The upward spring force exactly balances the downward gravitational force, so that Fsp = FG = mg. Because we defined weight as the reading Fsp of a spring scale, the weight of a stationary object is
39 EXAMPLE 6.5 Mass and weight on Jupiter QUESTION:
40 EXAMPLE 6.5 Mass and weight on Jupiter
41 Friction
42 Static Friction The box is in static equilibrium, so the static friction must exactly balance the pushing force:
43 Static Friction There s clearly a limit to how big fs can get. If you push hard enough, the object slips and starts to move. In other words, the static friction force has a maximum possible size fs max. An object remains at rest as long as fs < fs max. The object slips when fs = fs max. A static friction force fs > fs max is not physically possible. where the proportionality constant μs is called the coefficient of static friction.
44 Kinetic Friction The kinetic friction force is proportional to the magnitude of the normal force. where the proportionality constant μk is called the coefficient of kinetic friction.
45
46 EXAMPLE 6.10 A dog sled race QUESTION:
47 EXAMPLE 6.10 A dog sled race
48 EXAMPLE 6.10 A dog sled race
49 EXAMPLE 6.10 A dog sled race
50 EXAMPLE 6.10 A dog sled race
51 EXAMPLE 6.10 A dog sled race
52 EXAMPLE 6.10 A dog sled race
53 EXAMPLE 6.10 A dog sled race
54 EXAMPLE 6.11 Make sure the cargo doesn t slide QUESTION:
55 EXAMPLE 6.11 Make sure the cargo doesn t slide
56 EXAMPLE 6.11 Make sure the cargo doesn t slide
57 EXAMPLE 6.11 Make sure the cargo doesn t slide
58 EXAMPLE 6.11 Make sure the cargo doesn t slide
59 EXAMPLE 6.11 Make sure the cargo doesn t slide
60 Chapter 6. Summary Slides
61 General Strategy
62 General Strategy
63 Important Concepts
64 Important Concepts
65 Applications
66 Applications
67 Chapter 6. Clicker Questions
68 A Martian lander is approaching the surface. It is slowing its descent by firing its rocket motor. Which is the correct freebody diagram for the lander?
69 A Martian lander is approaching the surface. It is slowing its descent by firing its rocket motor. Which is the correct freebody diagram for the lander?
70 An elevator that has descended from the 50th floor is coming to a halt at the 1st floor. As it does, your apparent weight is A. less than your true weight. B. equal to your true weight. C. more than your true weight. D. zero.
71 An elevator that has descended from the 50th floor is coming to a halt at the 1st floor. As it does, your apparent weight is A. less than your true weight. B. equal to your true weight. C. more than your true weight. D. zero.
72 Rank order, from largest to smallest, the size r r of the friction forces fa to fe in these five different situations. The box and the floor are made of the same materials in all situations. A. fc > fd > fe > fb > fa. B. fb > fc = fd = fe > fa. C. fb > fc > fd > fe > fa. D. fa > fc = fd = fe > fb. E. fa = fb > fc = fd = fe.
73 Rank order, from largest to smallest, the size r r of the friction forces fa to fe in these five different situations. The box and the floor are made of the same materials in all situations. A. fc > fd > fe > fb > fa. B. fb > fc = fd = fe > fa. C. fb > fc > fd > fe > fa. D. fa > fc = fd = fe > fb. E. fa = fb > fc = fd = fe.
74 The terminal speed of a Styrofoam ball is 15 m/s. Suppose a Styrofoam ball is shot straight down with an initial speed of 30 m/s. Which velocity graph is correct?
75 The terminal speed of a Styrofoam ball is 15 m/s. Suppose a Styrofoam ball is shot straight down with an initial speed of 30 m/s. Which velocity graph is correct?
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