121.6 Physics 2007/2008
Assignment 11
This assignment is for practice only. It does not have to be handed in. For Problem type questions write out complete solutions. For Multiple Choice type questions no working needs to be shown, but the letter corresponding to your choice must be clearly shown. 1. Chapter 11, Problem 36. A puck of mass 80.0 g and radius 4.00 cm slides along an air table at a speed of 1.50 m/s as shown in Figure P11.36a. It makes a glancing collision with a second puck of radius 6.00 cm and mass 120 g (initially at rest) such that their rims just touch. Because their rims are coated with instant-acting glue, the pucks stick together and spin after the collision (Fig. P11.36b). (a) What is the angular momentum of the system relative to the center of mass? (b) What is the angular speed about the center of mass? 2. To change the direction of the axis of rotation of a spinning object, one must (A) apply a torque about the axis of rotation. (B) change the moment of inertia about the axis of rotation (C) apply a torque about an axis that is not the axis of rotation. (D) Any of (A), (B) or (C). (E) None of (A), (B) or (C) will work. 3. Chapter 12, Problem 16. Sir Lost-a-Lot dons his armour and sets out from the castle on his trusty steed in his quest to improve communication between damsels and dragons (Fig. P12.16). Unfortunately his squire lowered the drawbridge too far and finally stopped it 20.0 below the horizontal. Lost-a-Lot and his horse stop when their combined center of mass is 1.00 m from the end of the bridge. [i.e. assume his weight acts on the bridge at 1.00 m from the end.] The uniform bridge is 8.00 m long and has mass 2 000 kg. The lift cable is attached to the bridge 5.00 m from the hinge at the castle end, and to a point on the castle wall 12.0 m above the bridge. Lost-a-Lot's mass combined with his armour and steed is 1 000 kg. Determine (a) the tension in the cable and the (b) horizontal and (c) vertical force components acting on the bridge at the hinge.
4. Chapter 12, Problem 8. A mobile is constructed of light rods, light strings, and beach souvenirs as shown in Figure P12.8. Determine the masses of the objects (a) m1, (b) m2, and (c) m3.
5. Chapter 12, Problem 39. A uniform sign of weight Fg and width 2L hangs from a light horizontal beam hinged at the wall and supported by a cable (Fig. P12.39). Determine (a) the tension in the cable and (b) the components of the reaction force exerted by the wall on the beam, in terms of Fg, d, L, and .
6. Chapter 13, Problem 6. During a solar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Moon between the Earth and the Sun. (a) What force is exerted by the Sun on the Moon? (b) What force is exerted by the Earth on the Moon? (c) What force is exerted by the Sun on the Earth? Compare the answers from parts (a) and (b). Why doesn't the Sun capture the Moon away from the Earth? 7. Chapter 13, Problem 11. The free-fall acceleration on the surface of the Moon is about one-sixth that on the surface of the Earth. If the radius of the Moon is about 0.250 RE, find the ratio of their average densities, Moon Earth . 8. The magnitude of the acceleration of a meteor at a height above the Earth's surface equal to the radius of the Earth is (A) about 2.5 m/s2. (B) about 4.9 m/s2. (C) 9.8 m/s2. (D) is greater than 9.8 m/s2. (E) a value that depends on how the meteor is moving.
9. Chapter 13, Problem 18. Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose that the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed it can have so that the matter at the surface of the star on its equator is just held in orbit by the gravitational force. 10. Chapter 13, Problem 22. A spacecraft in the shape of a long cylinder has a length of 100 m and its mass with occupants is 1 000 kg. It has strayed too to close a black hole having a mass 100 times that of the Sun (Fig. P13.22). The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart. 11. Chapter 13, Problem 26. At the Earth's surface a projectile is launched straight up at a speed of 10.0 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth. 12. Chapter 13, Problem 38. A satellite moves around the Earth in a circular orbit of radius r. (a) What is the speed v0 of the satellite? Suddenly, an explosion breaks the satellite into two pieces, with masses m and 4m. Immediately after the explosion the smaller piece of mass m is stationary with respect to the Earth and falls directly toward the Earth. (b) What is the speed vi of the larger piece immediately after the explosion? (c) Because of the increase in its speed, this larger piece now moves in a new elliptical orbit. Find its distance away from the center of the Earth when it reaches the other end of the ellipse. 13. If Martian Orbiter I is sailing around the planet in a circle which has an orbital radius nine times that of Martian Orbiter II, who's speed is v2, what is the speed of Martian Orbiter I? (A) 1 v2 9 (B) 1 v2 3 (C) v2 (D) 3v2 (E) 81v2
14. Chapter 13, Problem 52. The maximum distance from the Earth to the Sun (at aphelion) is 1.521 1011 m, and the distance of closest approach (at perihelion) is 1.471 1011 m. The Earth's orbital speed at perihelion is 3.027 104 m/s. Determine (a) the Earth's orbital speed at aphelion [do not use energy conservation to do this part], (b) the kinetic and potential energies of the EarthSun system at perihelion, and (c) the kinetic and potential energies at aphelion. Is the total energy of the system constant? (Ignore the effect of the Moon and other planets.) 15. Chapter 14, Problem 4. What is the total mass of the Earth's atmosphere? (The radius of the Earth is 6.37 106 m, and atmospheric pressure at the Earth's surface is 1.013 ...