Chapter 10. Uniform Circular Motion
10-1. A ball is attached to the end of a 1.5 m string and it swings in a circle witha 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. A drive 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 wouldbe 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 revolvesin 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 constant speed 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 onthe 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 velocityand the radius are doubled, what will be the new acceleration?
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 16m/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...