Chapter 1, Problem 8P

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…