4. A 1.45-kg stone is tied to a 1.18-m long string and whirled in a vertical circle at a constant speed of 5.60 m/s. What is the tension in the string when the stone passes by the highest point? N

In a race like the Indianapolis 500, a driver circles the track counterclockwise and feels his head pulled toward one shoulder. To relieve his neck muscles from having to hold his head erect, the driver fastens a strap to one wall of the car and the other to his helmet. The length of the strap is adjusted to keep his head vertical. (a) Which shoulder does his head tend to lean toward? (b) What force or forces produce the centripetal acceleration when there is no strap? (c) What force or forces do so when there is a strap?

A car is driving around a flat, circularly curved road with a radius of 5.00 102 m. The mass of the car is 1500 kg, and the coefficient of static friction between its tires and the road is 0.30. a. Using the work of Example 6.7 (pages 202203), what is the maximum speed the car can have without slipping? b. What is the magnitude of the centripetal force on the car if it were to travel at the maximum speed around the track?

A pail of water is rotated in a vertical circle of radius 1.00 m. (a) What two external forces act on the water in the pail? (b) Which of the two forces is most important in causing the water to move in a circle? (c) What is the pails minimum speed at the top of the circle if no water is to spill out? (d) Assume the pail with the speed found in part (c) were to suddenly disappear at the top of the circle. Describe the subsequent motion of the water. Would it differ from the motion of a projectile?

A small disk of mass m is attached by a rope to a block with a larger mass M through a hole in a table as shown in Figure P6.53. The disk moves in circle of radius R at constant speed, and the block is at rest. Assume friction between the disk and the table is negligible. Find an expression for its speed vucm in terms of the parameters given and the tension FT in the rope. FIGURE P6.53 Problems 53 and 54.

Harry Potter decides to take Pottery 101 as an elective to satisfy his arts requirement at Hog warts. He sets some clay (m = 3.25 kg) on the edge of a pottery wheel (r = 0.600 m), which is initially motionless. He then begins to rotate the wheel with a uniform acceleration, reaching a final angular speed of 2.400 rev/s in 3.00 s. a. What is the speed of the clay when the initial 3.00 s has passed? b. What is the centripetal acceleration of the clay initially and when the initial 3.00 s has passed? c. What is the magnitude of the constant tangential acceleration responsible for starting the clay in circular motion?

A model airplane of mass 0.750 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 60.0-m-long control wire as shown in Figure P6.44a. The forces exerted on the airplane are shown in Figure P6.44b: the tension in the control wire, the gravitational force, and aerodynamic lift that acts at = 20.0 inward from the vertical. Compute the tension in the wire, assuming it makes a constant angle of = 20.0 with the horizontal. Figure P6.44

You are working during your summer break as an amusement park ride operator. The ride you are controlling consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away (Fig. P6.7). The coefficient of static friction between a person of mass m and the wall is s, and the radius of the cylinder is R. You are rotating the ride with an angular speed suggested by your supervisor. (a) Suppose a very heavy person enters the ride. Do you need to increase the angular speed so that this person will not slide down the wall? (b) Suppose someone enters the ride wearing a very slippery satin workout outfit. In this case, do you need to increase the angular speed so that this person will not slide down the wall? Figure P6.7

(a) A 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force must she exert to stay on if she is 1.25 m from its center? (b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 8.00 m from its center? (c) Compare each force with her weight.

Planetary orbits are often approximated as uniform circular motion. Figure P7.9 is a scaled representation of a planets orbit with a semimajor axis of 1.524 AU. a. Use Figure P7.9 to find the ratio of the Suns maximum gravitational field to its minimum gravitational field on the planets orbit. b. What is the ratio of the planets maximum speed to its minimum speed? c. Comment on the validity of approximating this orbit as uniform circular motion.