43. A mass må undergoes circular motion of radius R on a hori- zontal frictionless table, con- nected by a massless string through a hole in the table to a second mass m² (Fig. 5.33). If m₂ is stationary, find expres- sions for (a) the string tension and (b) the period of the circu- lar motion. m2 R m₁ FIGURE 5.33 Problem 43

CH 70. A block is projected up an incline at angle 0. It returns to its initial position with half its initial speed. Show that the coefficient of ki- netic friction is μk = tano.

Passage Problems A spiral is an ice-skating position in which the skater glides on one foot with the other foot held above hip level. It's a required element in women's singles figure-skating competition and is related to the arabesque performed in ballet. Figure 5.40 shows Canadian skater Kaetlyn Osmond executing a spiral during her medal-winning perfor- mance at the 2018 Winter Olympics in Gangneung, South Korea. 77. From the photo, you can conclude that the skater is a. executing a turn to her left. b. executing a turn to her right. c. moving in a straight line out of the page. 78. The net force on the skater a. points to her left. b. points to her right. c. is zero. 79. If the skater were to execute the same maneuver but at higher speed, the tilt evident in the photo would be a. less. b. greater. c. unchanged. FIGURE 5.40 Passage Problems 77-80 80. The tilt angle 0 that the skater's body makes with the vertical is given ap- proximately by 0 = tan¯¹(0.5). From this you can conclude…

Frictionless surf

71. A 2.1-kg mass is connected to a spring with spring constant 72 k = 150 N/m and unstretched length 18 cm. The two are mounted on a frictionless air table, with the free end of the spring attached to a frictionless pivot. The mass is set into circular mo- tion at 1.4 m/s. Find the radius of its path. cor moving at 77 km/h negotiat CH —what's the minimum icient of frictio

12. Two forces act on a 3.1-kg mass that undergoes acceleration = 0.91 0.27 m/s². If one force is -1.2î – 2.5ĵ N, what's the other?

36. Example 5.7: You whirl a bucket of water around in a vertical circle of radius 1.22 m. What minimum speed at the top of the circle will keep the water in the bucket?

Passage Problems Laptop computers are equipped with accelerometers that sense when the device is dropped and then put the hard drive into a protective mode. Your computer geek friend has written a program that reads the accel- erometer and calculates the laptop's apparent weight. You're amusing yourself with this program on a long plane flight. Your laptop weighs just 5 pounds, and for a long time that's what the program reports. But then the "Fasten Seatbelt" light comes on as the plane encounters turbu- lence. Figure 4.27 shows the readings for the laptop's apparent weight over a 12-second interval that includes the start of the turbulence. 76. At the first sign of turbulence, the plane's acceleration a. is upward. b. is downward. c. is impossible to tell from the graph. 77. The plane's vertical ac- celeration has its greatest magnitude a. during interval B. b. during interval C. c. during interval D. 78. During interval C, you can conclude for certain that the plane is Apparent…

If the metal sphere on the Van de Graff has a charge of 0.14 Coulombs and the person has a mass of 62 kg, how much excess charge would the person need in order to levitate at a distance 25 cm from the center of the charged metal sphere? Assume you can treat both the person and the metal sphere as point charges a distance 25 cm from each other