39. A ball of mass 4.0 kg is attached to the end of a 1.2 m long string and whirled around in a circle that describes a vertical plane. (APP) (a) What is the minimum speed that the ball can be moving at and still maintain a circular path? Provide a free-body diagram(3) (b) At this speed, what is the maximum tension in the string? Provide another free-body diagram.(2) (c) If the ball is rotated in a horizontal circle at the same speed with the end of the string held above the head, what angle does the string make with the horizontall?(2) 40. An Earth satellite has an orbital period of 3.2 h. What is its orbital radius? (APP)(2) (ME=5.98 × 1024 kg) 8 of 13

A man whirls a 0.20-kg piece of lead attached to the end of a string of length 0.500 m in a circular path and in a vertical plane. If the man maintains a constant speed of 4.00 m/s, what is the tension in the string when the lead is (a) at the top of the circular path? (b) at the bottom of the circular path? (Sec Section 7.4.)

The following objects are moving in uniform circular motion. Draw a free-body diagram for each object and identify the force responsible for the centripetal acceleration. Object 1. A person riding on the barrel-of-fun ride (Fig. 6.27, top) Object 2. The lead object in the laboratory set-up (Fig. 6.27, center) Object 3. A jogger running on a circular track (Fig. 6.27, bottom)

Modem roller coasters have vertical loops like the one shown here. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. (a) What is the speed of the roller coaster at the top of the loop if the radius of curvature there is 15.0 m and the downward acceleration of the car is 1.50 g ? (b) How high above the top of the loop must the roller coaster start from rest, assuming negligible friction? (c) If it actually starts 5.00 m higher than your answer to (b), how much energy did it lose to friction? Its mass is 1.50103kg .