ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS JUNE 9 - JUNE 15 (P prefixes) HRW PROBLEM SUPPLEMENT #1 - CHAPTER 6 49. A small coin is placed on a flat, horizontal turntable. The turntable is observed to make three revolutions in 3.14 s. (a) What is the speed of the coin when it rides without slipping at a distance of 5.0 cm from the center of the turntable? (b) What is the acceleration (magnitude and direction) of the coin? (c) What are the magnitude and direction of the frictional force acting on the coin if the coin has a mass of 2.0 g? (d) What is the coefficient of static friction between the coin and the turntable if the coin is observed to slide off the turntable when it is more than 10 cm from the center of the turntable? 61. A 26 kg child on a steadily rotating Ferris wheel moves at a constant speed of 5.5 m/s around a vertical circular path of radius 12 m. What are the magnitude and direction of the force of the seat on the child (a) at the highest point of the path and (b) at the lowest point of the path? 70. A banked circular highway curve is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? SERWAY - CHAPTER 5 46. A ball is suspended from the ceiling of a moving car by a string 25 cm in length. An observer in the car notes that the ball deflects 6 cm from the vertical toward the rear of the car. What is the acceleration of the car? HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 7 31. A force acts on a 3.0 kg particle-like object in such a way that the position of the object as a function of time is given by x = 3.0t - 4.0t^2 + 1.0t^3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 4.0 s. (Hint: What are the speeds at those times?) (P prefixes) HRW PROBLEM SUPPLEMENT #1 - CHAPTER 7 16. A 45 kg block of ice slides down a frictionless incline 1.5 m long and 0.91 m high. A worker pushes up against the ice, parallel to the incline, so that the block slides down at constant speed. (a) Find the magnitude of the worker's force. How much work is done on the block by (b) the worker's force, (c) the gravitational force on the block, (d) the normal force on the block from the surface on the incline, and (e) the net force on the block? 18. A cave rescue team lifts an injured spelunker directly upward and out of sinkhole by means of a motor-driven cable. The lift is performed in three stages, each requiring a vertical distance of 10.0 m: (a) the initially stationaly spelunker is accelerated to a speed of 5.00 m/s; (b) he is then lifted at the constant speed of 5.00 m/s; (c) finally he is decelerated to zero speed. How much work is done on the 80.0 kg rescuee by the force lifting him during each stage? 28. A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of an x axis is applied to the block. The force is given by F(x) = (2.5 - x^2)i N (F and i are vectors), where x is in meters and the initial position of the block is x = 0. (a) What is the kinetic energy of the block as it passes through x = 2.0 m? (b) What is the maximum kinetic energy of the block between x = 0 and x = 2.0 m? 36. A 3.0 kg ladle sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (with k = 500 N/m) whose other end is fixed. The ladle has a kinetic energy of 10 J as it passes through its equilibrium position (the point at which the spring force is zero). (a) At what rate is the spring doing work on the ladle as the ladle passes through its equilibrium position? (b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position? 38. Boxes are transported from one location to another in a warehouse by means of a conveyor belt that moves with a constant speed of 0.50 m/s. At a certain lacation the conveyor belt moves for 2.0 m up an incline that makes an angle of 10 degrees with the horizontal, then for 2.0 m horizontally, and finally for 2.0 m down an incline that makes an angle of 10 degrees with the horizontal. Assume that a 2.0 kg box rides on the belt without slipping. At what rate is the force of the conveyor belt doing work on the box (a) as the box moves up the 10 degree incline, (b) as the box moves horizontally, and (c) as the box moves down the 10 degree incline? SERWAY - CHAPTER 7 22. When a 4-kg mass is hung vertically on a certain light spring that obeys Hooke's law, the spring stretches 2.5 cm. If the 4-kg mass is removed, (a) how far will the spring stretch if a 1.5-kg mass is hung on it, and (b) how much work must an external agent do to stretch the same spring 4.0 cm from its unstretched position? 26. If it takes 4 J of work to stretch a Hooke's-law spring 10 cm beyond its unstressed length, determine the additional work required to stretch it another 10 cm. WOLFSON CHAPTER 8 Q17 This is Question 17 on page 205. SERWAY - CHAPTER 8 56. A 10-g mass is attached to the end of an unstressed, light, vertical spring (k = 49 N/m) and then dropped. Answer the following questions by considering the potential energy due to the spring plus the potential energy due to gravity, i.e. measure distances from the equilibrium position of the spring with no mass attached. (a) What is the maximum speed of the falling mass? (b) How far does the mass drop before coming to rest momentarily? (c) Repeat (a) and (b), but answer the questions by considering the potential energy of the spring with the mass attached, i.e. measure distances from the equilibrium position of the spring with the mass attached. (P prefixes) HRW PROBLEM SUPPLEMENT #1 - CHAPTER 8 42. A worker pushed a 27 kg block 9.2 m along a level floor at constant speed with a force directed 32 degrees below the horizontal. If the coefficient of kinetic friction between block and floor was 0.20, what were (a) the work done by the worker's force, and (b) the increase in thermal energy of the block-floor system?