10-1. A ball is attached to the end of a 1.5 m string and it swings in a circle with a constant speed of 8 m/s. What is the centripetal acceleration?
[pic] ac = 42.7 m/s2
10-2. What are the period and frequency of rotation for the ball in Problem 10-1?
[pic]; T = 1.18 s
[pic]; f = 0.849 rev/s
10-3. Adrive pulley 6-cm in diameter is set to rotate at 9 rev/s. What is the centripetal acceleration of a point on the edge of the pulley? What would be the linear speed of a belt around the pulley? [ R = (0.06 m/2) = 0.03 m ]
[pic]; ac = 95.9 m/s2
[pic]; v = 1.70 m/s
10-4. An object revolves in a circle of diameter 3 m at a frequency of 6 rev/s.What is the period of revolution, the linear speed, and the centripetal acceleration? [ R = (3 m/2) = 1.5 m ]
[pic]; T = 0.167 s ;
[pic]; v = 56.5 m/s
[pic]; ac = 2130 m/s2
10-5. A car moves around a curve 50 m in radius and undergoes a centripetal acceleration of 2 m/s2. What is its constant speed?
[pic]; v = 10.0 m/s
10-6. A 1500-kg car moves at a constantspeed of 22 m/s along a circular track. The centripetal acceleration is 6 m/s2. What is the radius of the track and the centripetal force on the car?
[pic]; R = 80.7 m
[pic]; Fc = 9000 N
10-7. An airplane dives along a curved path of radius R and velocity v. The centripetal acceleration is 20 m/s2. If both the velocity and the radius are doubled, what will be the new acceleration?[pic];
a2 = 2a1 = 2(20 m/s2; a = 40 m/s2
10-8. A 20-kg child riding a loop-the-loop at the Fair moves at 16 m/s through a track of radius 16 m. What is the resultant force on the child?
[pic]; Fc = 320 N
10-9. A 3-kg rock, attached to a 2-m cord, swings in a horizontal circle so that it makes one revolution in 0.3 s. What is the centripetal force on the rock?Is there an outward force on the rock?
[pic]; Fc = 2630 N, No
10-10. An 8-lb object swings in horizontal circle with a speed of 95 ft/s. What is the radius of the path, if the centripetal force is 2000 lb?
[pic]; R = 1.13 ft
*10-11. Two 8-kg masses are attached to the end of a tin rod 400 mm long. The rod is supported in the middle and whirled in a circle. The rod cansupport a maximum tension of only 800 N. What is the maximum frequency of revolution? [ R = (400 mm/2) = 200 mm ]
[pic]; v = 4.47 m/s
[pic]; f = 3.56 rev/s
*10-12. A 500-g damp shirt rotates against the wall of a washer at 300 rpm. The diameter of the rotating drum is 70 cm. What is the magnitude and direction of the resultant force on the shirt? [ R = (70 cm/2) = 35 cm; f =300 rpm(60 s/min) = 1800 rev/s ]
Fc = 2.24 x 107 N, toward the center
*10-13. A 70-kg runner rounds a track of radius 25 m at a speed of 8.8 m/s. What is the central force causing the runner to turn and what exerts the force?
[pic]; Fc = 217 N, friction
*10-14. In Olympic bobsled competition, a team takes a turn of radius 24 ft at a speed of 60 mi/h. What is the acceleration?How many g’s do passengers experience? (60 mi/h = 88 ft/s)
[pic]; ac = 323 ft/s2 or 10.1 g’s
Flat Curves and Banked Curves
10-15. On a rainy day the coefficient of static friction between tires and the roadway is only 0.4. What is the maximum speed at which a car can negotiate a turn of radius 80 m?
vc = 17.7 m/s or 63.8 km/h
10-16. A bus negotiates a turn ofradius 400 ft while traveling at a speed of 60 mi/h. If slipping just begins at this speed, what is the coefficient of static friction between the tires and the road? (60 mi/h = 88 ft/s)
[pic]; (s = 0.605
10-17. Find the coefficient of static friction necessary to sustain motion at 20 m/s around a turn of radius 84 m.
[pic]; (s = 0.486
*10-18. A 20-kg child sits 3 m from the...