Centripetal Acceleration and Centripetal Force Problems



Circular Motion

Centripetal Acceleration and Centripetal Force

1. What is the centripetal acceleration of a point on the perimeter of a bicycle wheel of diameter 70. cm when a bike is moving at 8.0 m/s?

5. A race car makes one lap around a track of radius 50. m in 9.0 s.

a) What is the average velocity? b) What was the car’s centripetal acceleration?

6. Norman Neutron swings a rubber ball attached to a string over his head in a horizontal, circular path. The piece of string is 1.5 m long and the ball makes 120 complete turns each minute.

a) What is the average velocity of the ball? b) What is the ball’s centripetal acceleration?

7. A car goes around a curve at 20. m/s. If the radius of the curve is 50. m, what is the centripetal acceleration of the car?

8. Professor Brown holds on to the end of the minute hand of a clock atop city hall. If the minute hand is 4.0 m long, what is the professor’s centripetal acceleration?

9. A flea gets its thrills by riding on the outer edge of a golden oldies record album of radius 15 cm as it is being played with a rotational period of 1.8 seconds.

a) What is the flea’s average speed?

b) What is the flea’s centripetal acceleration?

c) What is the flea’s new speed and acceleration if it moved 6.0 cm in towards the center of the album?

10. A 0.100 kg mass is attached to a string 75 cm long and swings in a horizontal circle, revolving once every 0.80 s. Calculate:

a) the centripetal acceleration of the mass. b) the tension in the string.

12. It takes a 900. kg racing car 12.3 s to travel at a uniform speed around a circular racetrack of radius 90.0 m. What is the centripetal force acting on the car, and which force provides it?

15. Compute the centripetal acceleration of an object on the equator. Use an equatorial radius of 6400 km. The Earth makes one revolution in a day. (1 km = 1000 m)

16. A steel beam is rotated in a horizontal plane to provide the centripetal acceleration for training pilots. If the pilot sits 2.0 m from the center of rotation, at what speed must he rotate to experience a horizontal centripetal acceleration of 78 m/s2?

17. A 0.30 kg mass is attached to a long string and revolves clockwise (looking down from the top) in a horizontal circle of radius 0.10 m with a speed of 0.50 m/s and a period of 1.3 s.

a) Determine the centripetal acceleration of the mass. b) What force is acting through the string?

19. A 900.-kg car moving at 10.0 m/s takes a turn around a circle with a radius of 25.0 m. Determine the acceleration and the net force acting upon the car.

20. A 95-kg halfback makes a turn on the football field. The halfback sweeps out a path which is a portion of a circle with a radius of 12-meters. The halfback makes a quarter of a turn around the circle in 2.1 seconds. Determine the speed, acceleration and net force acting upon the halfback.

24. A 60.-kg merry-go-round worker stands on the ride’s platform 4.0 m from the center. If her speed as she goes around the circle is 5.0 m/s, what is the force of friction needed to keep her from falling off the platform?

Answers

1) 180 m/s2 5a) 35 m/s 5b) 25 m/s2 6a) 19 m/s 6b) 240 m/s2

7) 8.0 m/s2 8) 1.2 x 10-5 m/s2 9a) 0.52 m/s 9b) 1.8 m/s2

9c) 0.31 m/s, 1.1 m/s2 10a) 46 m/s2 10b) 4.6 N

12) 2.11 x 104 N, friction 15) 0.034 m/s2 16) 12 m/s

17a) 2.5 m/s2 17b) 0.75 N 19) 4.00 m/s2, 3.60 x 103 N

20) 9.0 m/s, 6.8 m/s2, 650 N

21) 16.0 m/s2, 24.0 N, 9.30 N 24) 380 N

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