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Chapter 6 Lecture

Chapter 6 Lecture. Chapter 6 Dynamics I : Motion Along a Line. Chapter Goal: To learn how to solve linear force-and-motion problems. Slide 6-2. Chapter 6 Preview. Slide 6-4. Chapter 6 Preview. Slide 6-5. Chapter 6 Preview. Slide 6-6. Chapter 6 Preview. Slide 6-7. Reading Question 6.1.

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Chapter 6 Lecture

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  1. Chapter 6 Lecture

  2. Chapter 6 Dynamics I: Motion Along a Line Chapter Goal: To learn how to solve linear force-and-motion problems. Slide 6-2

  3. Chapter 6 Preview Slide 6-4

  4. Chapter 6 Preview Slide 6-5

  5. Chapter 6 Preview Slide 6-6

  6. Chapter 6 Preview Slide 6-7

  7. Reading Question 6.1 Newton’s first law can be applied to • Static equilibrium. • Inertial equilibrium. • Dynamic equilibrium. • Both A and B. • Both A and C. Slide 6-11

  8. Reading Question 6.2 Mass is • An intrinsic property. • A force. • A measurement. Slide 6-12

  9. Reading Question 6.3 Gravity is • An intrinsic property. • A force. • A measurement. Slide 6-14

  10. Reading Question 6.4 Weight is • An intrinsic property. • A force. • A measurement. Slide 6-16

  11. Reading Question 6.5 The coefficient of static friction is • Smaller than the coefficient of kinetic friction. • Equal to the coefficient of kinetic friction. • Larger than the coefficient of kinetic friction. • Not discussed in this chapter. Slide 6-18

  12. Reading Question 6.6 The force of friction is described by • The law of friction. • The theory of friction. • A model of friction. • The friction hypothesis. Slide 6-20

  13. Reading Question 6.7 When an object moves through the air, the magnitude of the drag force on it • Increases as the object’s speed increases. • Decreases as the object’s speed increases. • Does not depend on the object’s speed. Slide 6-22

  14. Reading Question 6.8 Terminal speed is • Equal to the speed of sound. • The minimum speed an object needs to escape the earth’s gravity. • The speed at which the drag force cancels the gravitational force. • The speed at which the drag force reaches a minimum. • Any speed which can result in a person’s death. Slide 6-24

  15. Equilibrium • An object on which the net force is zero is in equilibrium. • If the object is at rest, it is in static equilibrium. • If the object is moving along a straight line with a constant velocity it is in dynamic equilibrium. • The requirement for either type of equilibrium is: The concept of equilibrium is essential for the engineering analysis of stationary objects such as bridges. Slide 6-27

  16. QuickCheck 6.1 The figure shows the view looking down onto a sheet of frictionless ice. A puck, tied with a string to point P, slides on the ice in the circular path shown and has made many revolutions. If the string suddenly breaks with the puck in the position shown, which path best represents the puck’s subsequent motion? Slide 6-28

  17. QuickCheck 6.2 A ring, seen from above, is pulled on by three forces. The ring is not moving. How big is the force F? • 20 N • 10cos N • 10sin N • 20cos N • 20sin N Slide 6-32

  18. Example 6.2 Towing a Car up a Hill Slide 6-34

  19. Example 6.2 Towing a Car up a Hill Slide 6-35

  20. Example 6.2 Towing a Car up a Hill Slide 6-36

  21. Example 6.2 Towing a Car up a Hill Slide 6-37

  22. Example 6.2 Towing a Car up a Hill Slide 6-38

  23. QuickCheck 6.3 A car is parked on a hill. Which is the correct free-body diagram? Slide 6-39

  24. QuickCheck 6.4 A car is towed to the right at constant speed. Which is the correct free-body diagram? Slide 6-41

  25. Using Newton’s Second Law The essence of Newtonian mechanics can be expressed in two steps: • The forces on an object determine its   acceleration , and • The object’s trajectory can be determined by   using in the equations of kinematics. Slide 6-43

  26. Problem-Solving Strategy: Dynamics Problems Slide 6-44

  27. Problem-Solving Strategy: Dynamics Problems Slide 6-45

  28. 1 1 2 4 QuickCheck 6.5 The cart is initially at rest. Force is applied to the cart for time t, after which the car has speed v. Suppose the same force is applied for the same time to a second cart with twice the mass. Friction is negligible. Afterward, the second cart’s speed will be • v • v • v • 2v • 4v Slide 6-46

  29. 1 1 2 4 QuickCheck 6.5 The cart is initially at rest. Force is applied to the cart for time t, after which the car has speed v. Suppose the same force is applied for the same time to a second cart with twice the mass. Friction is negligible. Afterward, the second cart’s speed will be • v • v • v • 2v • 4v Slide 6-47

  30. Example 6.3 Speed of a Towed Car Slide 6-48

  31. Example 6.3 Speed of a Towed Car Slide 6-49

  32. Example 6.3 Speed of a Towed Car Slide 6-50

  33. Example 6.3 Speed of a Towed Car Slide 6-51

  34. QuickCheck 6.6 The box is sitting on the floor of an elevator. The elevator is accelerating upward. The magnitude of the normal force on the box is n > mg. n = mg. n < mg. n = 0. Not enough information to tell. Slide 6-52

  35. Mass: An Intrinsic Property • A pan balance, shown in the figure, is a device for measuring mass. • The measurement does not depend on the strength of gravity. • Mass is a scalar quantity that describes an object’s inertia. • Mass describes the amount of matter in an object. • Mass is an intrinsic property of an object. Slide 6-54

  36. Gravity: A Force • Gravity is an attractive, long-range force between any two objects. • The figure shows two objects with masses m1and m2 whose centers are separated by distance r. • Each object pulls on the other with a force: where G = 6.67 × 10−11 N m2/kg2 is the gravitational constant. Slide 6-55

  37. Gravity: A Force • The gravitational force between two human-sized objects is very small. • Only when one of the objects is planet-sized or larger does gravity become an important force. • For objects near the surface of the planet earth: where M and R are the mass and radius of the earth, and g = 9.80 m/s2. Slide 6-56

  38. Gravity: A Force • The magnitude of the gravitational force is FG = mg, where: • The figure shows the free-body diagram of an object in free fall near the surface of a planet. • With , Newton’s second law predicts the acceleration to be: • All objects on the same planet, regardless of mass, have the same free-fall acceleration! Slide 6-57

  39. Weight: A Measurement • You weigh apples in the grocery store by placing them in a spring scale and stretching a spring. • The reading of the spring scale is the magnitude of Fsp. • We 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. Slide 6-58

  40. Weight: A Measurement • A bathroom scale uses compressed springs which push up. • When any spring scale measures an object at rest, . • The upward spring force exactly balances the downward gravitational force of magnitude mg: • Weight is defined as the magnitude of Fspwhen the object is at rest relative to the stationary scale: Slide 6-59

  41. QuickCheck 6.7 An astronaut takes her bathroom scales to the moon, where g = 1.6 m/s2. On the moon, compared to at home on earth: Her weight is the same and her mass is less. Her weight is less and her mass is less. Her weight is less and her mass is the same. Her weight is the same and her mass is the same. Her weight is zero and her mass is the same. Slide 6-60

  42. QuickCheck 6.7 An astronaut takes her bathroom scales to the moon, where g = 1.6 m/s2. On the moon, compared to at home on earth: Her weight is the same and her mass is less. Her weight is less and her mass is less. Her weight is less and her mass is the same. Her weight is the same and her mass is the same. Her weight is zero and her mass is the same. Slide 6-61

  43. Weight: A Measurement • The figure shows a man weighing himself in an accelerating elevator. • Looking at the free-body diagram, the y-component of Newton’s second law is: • The man’s weight as he accelerates vertically is: • You weigh more as an elevator accelerates upward! Slide 6-62

  44. QuickCheck 6.8 A 50-kg student (mg = 490 N) gets in a 1000-kg elevator at rest and stands on a metric bathroom scale. As the elevator accelerates upward, the scale reads > 490 N. 490 N. < 490 N but not 0 N. 0 N. Slide 6-63

  45. QuickCheck 6.8 A 50-kg student (mg = 490 N) gets in a 1000-kg elevator at rest and stands on a metric bathroom scale. As the elevator accelerates upward, the scale reads > 490 N. 490 N. < 490 N but not 0 N. 0 N. Slide 6-64

  46. QuickCheck 6.9 A 50-kg student (mg = 490 N) gets in a 1000-kg elevator at rest and stands on a metric bathroom scale. As the elevator accelerates upward, the student’s weight is > 490 N. 490 N. < 490 N but not 0 N. 0 N. Slide 6-65

  47. Weightlessness • The weight of an object which accelerates vertically is • If an object is accelerating downward with ay = –g, thenw = 0. • An object in free fall has no weight! • Astronauts while orbiting the earth are also weightless. • Does this mean that they are in free fall? Astronauts are weightless as they orbit the earth. Slide 6-67

  48. QuickCheck 6.10 A 50-kg student (mg = 490 N) gets in a 1000-kg elevator at rest and stands on a metric bathroom scale. Sadly, the elevator cable breaks. What is the student’s weight during the few second it takes the student to plunge to his doom? > 490 N. 490 N. < 490 N but not 0 N. 0 N. Slide 6-68

  49. QuickCheck 6.11 A 50-kg astronaut (mg = 490 N) is orbiting the earth in the space shuttle. Compared to on earth: His weight is the same and his mass is less. His weight is less and his mass is less. His weight is less and his mass is the same. His weight is the same and his mass is the same. His weight is zero and his mass is the same. Slide 6-70

  50. Static Friction • A shoe pushes on a wooden floor but does not slip. • On a microscopic scale, both surfaces are “rough” and high features on the two surfaces form molecular bonds. • These bonds can produce a force tangent to the surface, called the static friction force. • Static friction is a result of many molecular springs being compressed or stretched ever so slightly. Slide 6-72

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