ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS JUNE 24 - JUNE 30 HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 12 25. Two skaters, each of mass 50 kg, approach each other along parallel paths separated by 3.0 m. They have opposite velocities of 1.4 m/s each. One skater carries one end of a long pole with negligible mass, and the other skater grabs the other end of it as she passes. Assume frictionless ice. (a) Describe quantitatively the motion of the skaters after they have become connected by the pole. (b) What is the kinetic energy of the two-skater system? Next, the skaters each pull along the pole so as to reduce their separation to 1.0 m. What then are (c) their angular speed and (d) the kinetic energy of the system? (e) Explain the source of the increased kinetic energy. FISHBANE - CHAPTER 8 6. (The figure for this problem is similar to Fig. 9-35 on page 235 of Wolfson, except that the two objects are of different mass; therefore, the more massive object is closer to the center of mass, i.e in a smaller orbit.) Two objects, of masses m1 and m2 (m2 > m1), respectively, move in circular orbits that have the same center. If the force that gives rise to this motion is a force of attraction between the two objects acting along a line joining them, using momentum conservation and Newton's Second Law, (a) show that they move with the same angular speed, and (b) calculate the ratio of the radii of the two circular orbits. FISHBANE - CHAPTER 9 50. A child of mass 25 kg stands at the edge of a rotating platform of mass 150 kg and radius 4.0 m. The platform with the child on it rotates with an angular speed of 6.2 rad/s. The child jumps off in a radial direction. (a) What happens to the angular speed of the platform? (b) What happens to the platform if, a little later, the child, starting at rest, jumps back onto the platform? (Treat the platform as a uniform disk.) FISHBANE - CHAPTER 12 35. A small package is fired off Earth's surface with a speed v at a 45 degree angle with the local horizontal. It reaches a maximum height h above the surface at h = 6370 km, a value equal to Earth's radius itself. What is its speed when it reaches this height? Ignore any effects that might come from Earth's rotation or from air resistance. (Hint: You will need to use two conservation equations and solve two equations in two unknowns.) 55. The Little Prince (a character in a book by Antoine de Saint- Exupery) lives on the spherically symmetric asteroid B-612. The density of B-612 is 5200 kg/cubic meter. Assume that the asteroid does not rotate. The Little Prince noticed that he felt lighter whenever he walked quickly around the asteroid. In fact, he found that he became weightless and started to orbit the asteroid like a satellite whenever he speeded up to 2 m/s. (a) Estimate the radius of the asteroid from these data. (b) What is the escape speed for the asteroid? (c) Suppose that B-612 does rotate about an axis such that the length of the day there is 12 h. Can the Little Prince take advantage of this rotation when he wants to orbit the asteroid? What is his minimum ground speed for orbit in this case? SERWAY - CHAPTER 12 41. Two hypothetical planets of masses m1 and m2 and radii r1 and r2, respectively, are at rest when they are an infinite distance apart. Because of their gravitational attraction, they head toward each other on a collision course. (Hint: Note that both energy and momentum are conserved.) (a) When their center-to-center separation is d, find the speed of each planet and their RELATIVE speed. (b) Find the kinetic energy of each planet just before they collide if m1 = 2 x 10^24 kg, m2 = 8 x 10^24 kg, r1 = 3 x 10^6 m, and r2 = 5 x 10^6 m. 49. (The picture for this problem is the same as for Fishbane CH 8, problem 6. You may use your result for that problem in solving this one.) Two stars of masses m1 and m2, separated by a distance of d, revolve in circular orbits about their center of mass. Show that each star has a period given by T^2 = (4pi^2)d^3/G(m1+m2) (Hint: Write Newton's 2nd Law for each star, and use r2+r1 = d) PROBLEM G2 You weigh 530 N at sidewalk level outside the Petronas Towers in Kuala Lumpur, Malaysia. Supose that you ride from this level to the top of one of its 420 m towers. Ignoring Earth's rotation, how much less would you weigh there (because you are slightly farther from the center of Earth)? HALLIDAY AND RESNICK - 2ND Ed. - CHAPTER 14 3. The scale of a spring balance that reads from 0 to 15.0 kg is 12.0 cm long. A package suspended from the balance is found to oscillate vertically with a frequency of 2.00 Hz. (a) What is the spring constant? (b) How much does the package weigh? 14. A 10 g particle is undergoing simple harmonic motion with an amplitude of 2.0 mm and a maximum acceleration of magnitude 8000 m/s^2. The phase constant is -pi/3 rad. (a) Write an equation for the force on the particle as a function of time. (b) What is the period of the motion? (c) What is the maximum speed of the particle? (d) What is the total mechanical energy of this simple harmonic oscillator? 15. An oscillating block-spring system has a mechanical energy of 1.00 J, an amplitude of 10.0 cm, and a maximum speed of 1.20 m/s. Find (a) the spring constant, (b) the mass of the block, and (c) the frequency of oscillation. 40. A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has period 1.0 s, at what amplitude of motion will the block and piston separate? (b) If the piston has an amplitude of 5.0 cm, what is the maximum frequency for which the block and piston will be in contact continuously? 55. A simple harmonic oscillator consists of a block of mass 2.00 kg attached to a spring of spring constant 100 N/m. When t = 1.00 s, the position and velocity of the block are x = 0.129 m and v = 3.415 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? (P prefixes) HRW PROBLEM SUPPLEMENT #1 - CHAPTER 16 34. A (hypothetical) large slingshot is stretched 1.50 m to launch a 130 g projectile with speed sufficient to escape from Earth (11.2 km/s). Assume the elastic bands of the slingshot obey Hooke's Law. (a) What is the spring constant of the device? (b) Assume that an average person can exert a force of 220 N. How many people are required to stretch the elastic bands?