ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS JUNE 16 - JUNE 22 (P prefixes) HRW PROBLEM SUPPLEMENT #1 - CHAPTER 9 14. A 1000 kg automobile is at rest at a traffic signal. At the instant the light turns green, the automobile starts to move with a constant acceleration of 4.0 m/s^2. At the same instant a 2000 kg truck, traveling at a constant speed of 8.0 m/s, overtakes and passes the automobile. (a) How far is the center of mass of the automobile-truck system from the traffic light at t = 3.0 s? (b) What is the speed of the center of mass of the automobile-truck system then? HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 10 26. A billiard ball moving at a speed of 2.2 m/s strikes an identical stationary ball a glancing blow. After the collision, one ball is found to be moving at a speed of 1.1 m/s in a direction making a 60 degree angle with the original line of motion. (a) Find the velocity of the other ball. (b) Is the collision elastic? (P prefixes) HRW PROBLEM SUPPLEMENT #1 - CHAPTER 10 54. Two 30 kg children, each with a speed of 4.0 m/s, are sliding on a frictionless frozen pond when they collide and stick together because they have Velcro straps on their jackets. The two children then collide and stick to a 75 kg man who was sliding at 2.0 m/s. After this collision, the three-person composite is stationary. What is the angle between the initial velocity vectors of the two children? WOLFSON - CHAPTER 11 30. Hint: At the moment of maximum compression, the two cars must be traveling at the same speed. HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 11 2. The angular position of a point on the rim of a rotating wheel is given by theta = 4.0t - 3.0t^2 + t^3, where theta is in radians and t is in seconds. What are the angular velocities at (a) t = 2.0 s and (b) t = 4.0 s? (c) What is the average angular acceleration for the time interval that begins at t = 2.0 s and ends at t = 4.0 s? What are the instantaneous angular accelerations at (d) the beginning and (e) the end of this time interval? 17. A wheel, starting from rest, rotates with a constant angular accleration of 2.00 rad/s^2. During a certain 3.00 s interval, it turns through 90.0 rad. (a) How long is the wheel turning before the start of the 3.00 s interval? (b) What is the angular velocity of the wheel at the start of the 3.00 s interval? 30. A record turntable is rotating at 33.333 rev/min. A watermelon seed is on the turntable 6.0 cm from the axis of rotation. (a) Calculate the acceleration of the seed, assuming that it does not slip. (b) What is the minimum value of the coefficient of static friction between the seed and the turntable if the seed is not to slip? (c) Suppose that the turntable achieves its angular speed by starting from rest and undergoing a constant angular acceleration for 0.25 s. Calculate the minimum coefficient of static friction required for the seed not to slip during the acceleration period. Fishbane - CHAPTER 9 45. A wheel of radius 24.6 cm whose axis is fixed starts from rest and reaches an angular velocity of 4.15 rad/s in 2.68 s due to a force of 13.4 N acting tangentially on the rim. (a) What is the rotational inertia of the wheel? (b) What is the change in the angular momentum during the 2.68 s? (c) How many revolutions does the wheel make? (d) How much rotational kinetic energy does the wheel have after 2.68 s? Fishbane - CHAPTER 10 13. A square, 20 cm on the side, is made of very light sticks. Four identical masses of m = 0.1 kg form the corners of the square. The square rotates with an angular velocity of 8 rad/s about an axis perpendicular to its plane through the center of the square. (a) Calculate the rotational inertia of the system about the rotation axis and use it to find the angular momentum about this axis. (b) Use the general definition of angular momentum to calculate the angular momentum of each mass with respect to the center of the square, and add these up. Compare the results of (a) and (b). WOLFSON - CHAPTER 12 44. Hint: Consider the flywheel to be a solid disk. Taking into account the hole at the center of the wheel will only change I by 0.7%. (P prefixes) HRW PROBLEM SUPPLEMENT #1 - CHAPTER 12 2. Consider a 66 cm diameter tire on a car traveling at 80 km/h on a level road in the positive direction of the x axis. Relative to a woman in the car, what are (a) the linear velocity v (a vector) and (b) the magnitude a of the linear acceleration of the center of the wheel? What are (c) v (a vector) and (d) a for a point at the top of the tire? What are (e) v (a vector) and (f) a for a point at the bottom of the tire? Now repeat the questions relative to a hitchhiker sitting near the road: What are (g) v (a vector) at the wheel's center, (h) a at the wheel's center, (i) v (a vector) at the tire top, (j) a at the tire top, (k) v (a vector) at the tire bottom, and (l) a at the tire bottom? 15. A yo-yo has a rotational inertia of 950 g cm^2 and a mass of 120 g. Its axle radius is 3.2 mm, and its string is 120 cm long. The yo-yo is released from rest with the string wound around the axle; the end of the string is being held fixed. The yo-yo rolls down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) angular speed, and (f) rotational kinetic energy? HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 12 23. A small sphere, with radius r and mass m, rolls without slipping on the inside of a large fixed hemisphere with radius R and a vertical axis of symmetry. It starts at the top from rest. (a) What is its kinetic energy at the bottom? (b) What fraction of its kinetic energy at the bottom is associated with rotation about an axis through its center of mass? (c) Assuming r<