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Slide 1Fig. 15.1, p.453 Active Figure 15.1. Slide 2Fig. 15.2, p.455.

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Presentation on theme: "Slide 1Fig. 15.1, p.453 Active Figure 15.1. Slide 2Fig. 15.2, p.455."— Presentation transcript:

1 Slide 1Fig. 15.1, p.453 Active Figure 15.1

2 Slide 2Fig. 15.2, p.455

3 Slide 3Fig. 15.2a, p.455

4 Slide 4Fig. 15.2b, p.455

5 Slide 5Fig. 15.3, p.456

6 Slide 6Fig. 15.4, p.456

7 Slide 7Fig. 15.5, p.456

8 Slide 8Fig. 15.5a, p.456

9 Slide 9Fig. 15.5b, p.456

10 Slide 10Fig. 15.6, p.458

11 Slide 11Fig. 15.7, p.458 Active Figure 15.1 ActiveFigure 15.7 T does not depend on A

12 Slide 12 Quick Quiz 15.1 A block on the end of a spring is pulled to position x = A and released. In one full cycle of its motion, through what total distance does it travel? (a) A/2 (b) A (c) 2A (d) 4A

13 Slide 13 Answer: (d). From its maximum positive position to the equilibrium position, the block travels a distance A. It then goes an equal distance past the equilibrium position to its maximum negative position. It then repeats these two motions in the reverse direction to return to its original position and complete one cycle. Quick Quiz 15.1

14 Slide 14Fig. 15.8, p.459 Active Figure 15.2 ActiveFigure 15.7ActiveFigure 15.7 Active 15.9Active 15.9

15 Slide 15 Quick Quiz 15.4 Consider the graphical representation below of simple harmonic motion, as described mathematically in Equation 15.6. When the object is at position A on the graph, its (a) velocity and acceleration are both positive (b) velocity and acceleration are both negative (c) velocity is positive and its acceleration is zero (d) velocity is negative and its acceleration is zero (e) velocity is positive and its acceleration is negative (f) velocity is negative and its acceleration is positive

16 Slide 16 Answer: (a). The velocity is positive, as in Quick Quiz 15.2. Because the spring is pulling the object toward equilibrium from the negative x region, the acceleration is also positive. Quick Quiz 15.4

17 Slide 17 Quick Quiz 15.5 An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, the period of the motion is (a) 2T (b) 2T (c) T (d) T/2

18 Slide 18 Answer: (b). According to Equation 15.13, the period is proportional to the square root of the mass. Quick Quiz 15.5

19 Slide 19 Quick Quiz 15.6 The figure shows the position of an object in uniform circular motion at t = 0. A light shines from above and projects a shadow of the object on a screen below the circular motion. The correct values for the amplitude and phase constant of the simple harmonic motion of the shadow are (a) 0.50 m and 0 (b) 1.00 m and 0 (c) 0.50 m and π (d) 1.00 m and π

20 Slide 20 Answer: (c). The amplitude of the simple harmonic motion is the same as the radius of the circular motion. The initial position of the object in its circular motion is π radians from the positive x axis. Quick Quiz 15.6

21 Slide 21 You hang an object onto a vertically hanging spring and measure the stretch length of the spring to be 1 meter. You then pull down on the object and release it so that it oscillates in simple harmonic motion. The period of this oscillation will be a) about half a second, b) about 1 second, c) about 2 seconds, or d) impossible to determine without knowing the mass or spring constant. (end of section 15.2) QUICK QUIZ 15.1

22 Slide 22 (c). This problem illustrates an easy method for determining the properties of a spring-object system. When you hang the object, the spring force, kx, will be equal to the weight, mg, so that kx = mg or x/g = m/k. From Equation 15.13, QUICK QUIZ 15.1 ANSWER

23 Slide 23Fig. 15.9, p.459

24 Slide 24Fig. 15.10, p.462 Active 15.10

25 Slide 25Fig. 15.10a, p.462

26 Slide 26Fig. 15.10b, p.462

27 Slide 27Fig. 15.11, p.463

28 Slide 28Fig. 15.12, p.464

29 Slide 29Fig. 15.14, p.465 Af 15.14

30 Slide 30Fig. 15.15, p.466

31 Slide 31Fig. 15.15a, p.466

32 Slide 32Fig. 15.15b, p.466

33 Slide 33Fig. 15.15c, p.466

34 Slide 34Fig. 15.15d, p.466

35 Slide 35Fig. 15.16, p.467

36 Slide 36Fig. 15.17, p.468 AF 15.11 AF 15.17

37 Slide 37 Quick Quiz 15.7 A grandfather clock depends on the period of a pendulum to keep correct time. Suppose a grandfather clock is calibrated correctly and then a mischievous child slides the bob of the pendulum downward on the oscillating rod. Does the grandfather clock run (a) slow (b) fast (c) correctly

38 Slide 38 Answer: (a). With a longer length, the period of the pendulum will increase. Thus, it will take longer to execute each swing, so that each second according to the clock will take longer than an actual second – the clock will run slow. Quick Quiz 15.7

39 Slide 39 Quick Quiz 15.8 Suppose a grandfather clock is calibrated correctly at sea level and is then taken to the top of a very tall mountain. Does the grandfather clock run (a) slow (b) fast (c) correctly

40 Slide 40 Answer: (a). At the top of the mountain, the value of g is less than that at sea level. As a result, the period of the pendulum will increase and the clock will run slow. Quick Quiz 15.8

41 Slide 41Fig. 15.18, p.469

42 Slide 42Fig. 15.19, p.470

43 Slide 43Fig. 15.20, p.470

44 Slide 44Fig. 15.21, p.471 AF 15.22

45 Slide 45Fig. 15.22, p.471

46 Slide 46Fig. 15.23, p.471

47 Slide 47Fig. 15.24a, p.472

48 Slide 48Fig. 15.24b, p.472

49 Slide 49 Quick Quiz 15.9 An automotive suspension system consists of a combination of springs and shock absorbers, as shown in the figure below. If you were an automotive engineer, would you design a suspension system that was (a) underdamped (b) critically damped (c) overdamped

50 Slide 50 Answer: (a). If your goal is simply to stop the bounce from an absorbed shock as rapidly as possible, you should critically damp the suspension. Unfortunately, the stiffness of this design makes for an uncomfortable ride. If you underdamp the suspension, the ride is more comfortable but the car bounces. If you overdamp the suspension, the wheel is displaced from its equilibrium position longer than it should be. (For example, after hitting a bump, the spring stays compressed for a short time and the wheel does not quickly drop back down into contact with the road after the wheel is past the bump – a dangerous situation.) Because of all these considerations, automotive engineers usually design suspensions to be slightly underdamped. This allows the suspension to absorb a shock rapidly (minimizing the roughness of the ride) and then return to equilibrium after only one or two noticeable oscillations. Quick Quiz 15.9

51 Slide 51Fig. 15.25, p.473

52 Slide 52Fig. P15.25, p.478

53 Slide 53Fig. P15.26, p.478

54 Slide 54Fig. P15.39, p.479

55 Slide 55Fig. P15.51, p.480

56 Slide 56Fig. P15.52, p.481

57 Slide 57Fig. P15.53, p.481

58 Slide 58Fig. P15.56, p.481

59 Slide 59Fig. P15.59, p.481

60 Slide 60Fig. P15.61, p.482

61 Slide 61Fig. P15.66, p.482

62 Slide 62Fig. P15.67, p.482

63 Slide 63Fig. P15.68, p.483

64 Slide 64Fig. P15.69, p.483

65 Slide 65Fig. P15.71, p.483

66 Slide 66Fig. P15.71a, p.483

67 Slide 67Fig. P15.71b, p.483

68 Slide 68Fig. P15.74, p.484

69 Slide 69Fig. P15.75, p.484

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