Chapter 4 Circular Motion and Gravitation 4.1 Centripetal Acceleration Homework # 27 01. A car traveling at 80.0 km/h rounds a circular curve of radius 95.0 m. What is the car's centripetal acceleration? II 02. A ball in a roulette wheel makes 85 revolutions in 45.0 s before falling. If the radius of the wheel is 57.5 cm. what is the average centripetal acceleration of the ball? 03. If a coin is placed 5.00 cm from the center of a 45 rpm record, what is the centripetal acceleration of the coin when the record reaches its rated speed? 04. A bicycle tire is making 12.5 revolutions per minute. If the diameter of the tire is 68.0 cm, what centripetal acceleration would a point on the outer edge of the tire experience? 05. A car tachometer indicates the flywheel is spinning at 2200 rpm. The flywheel is 35.0 cm in diameter. a.) what is the centripetal acceleration of a point on the edge of the wheel? b.) what is the centripetal acceleration of a point on the wheel that is halfway between the center and the edge of the wheel? 06. A jet plane traveling at 1800 km/h pulls out of a dive by moving in an arc of radius 4.00 km. What is the plane's acceleration in g's? 07. A child on a merry-go-round experiences a centripetal acceleration of 5.25 m/s'. The wooden horse on which the child sits is 6.25 m from the center of the rotating disk. a.) What is the linear speed of the child? b.) What is the frequency (in rpm's) of the child? 08. Calculate the centripetal acceleration of the earth in its orbit around the sun. Assume the earth's orbit is a circle with a radius of 1.50 x 10" m. 09. The hammer throw is an Olympic sport in which the contestant twirls a steel cord attached to a "weight" (mass) called the hammer and releases the cord so the hammer is "thrown" across a field. The length of the hammer is 1. 195-1.215 m and the mass is 7.256 kg while the diameter of the head is 1 1 cm. The throwing circle is 2.135 m in diameter. If the cord is swung in a radius of 2.65 m and the hammer experiences a final centripetal acceleration of 211 m/s , what is the frequency (rpm's) of the contestant as he releases the hammer? 10. One aspect of training for an astronaut involves experiencing and enduring extreme accelerations. To achieve this a device that rotates in a circle was designed. The astronaut is strapped into a chair in a spherical chamber. This chamber is attached to a motor in the center of the room by a metallic, multiple-poled structure I will call the arm. If the arm is 4.50 m long and the astronaut is to experience an acceleration of 5g's, calculate the following. a. ) What is the lincar speed of the spherical chamber? b. ) What frequency (in rpm's) must the motor generate to achieve this acceleration? ANSWERS: 01. 5.21 m/s' 02. 81.0 m/s2 03. 1.11 m/s 04. 0.582 m/s' 05. a.) 9.29 x 10 m/s' b.) 4.64 x 10 m/s 06. 6.39g's 07. a.) 5.73 m/s b.) 8.75 rpm 08. 5.95 x 10" m/s- 09. 85.2 rpm's 10. a.) 14.8 m/s b.) 31.5 rpm's