EXERCISES AND PROBLEMS
ssm Solution is in the Student Solutions Manual.
~ Solution is available on the World Wide Web at:
Itw Solution is available on the Interactive Leaming Ware.
1a) How far is the center of mass of the Earth-Moon system from the center of Earth? (Appendix C gives the masses of Earth and the Moon and the distance between the two.) (b) Express the answer to (a) as a fraction of Earth’s radius .
2E. A distance of 1.131 X 10 -10 m lies between the centers of the carbon and oxygen atoms in a carbon monoxide (CO) gas molecule. Locate the center of mass of a CO molecule relative to the carbon atom. (Find the masses of C and 0 in Appendix F.)
3E. What are (a) the x coordinate . and (b) the y coordinate of the center of mass of the three-particle .system shown in? (c) What happens to the center of mass as the mass of the topmost particle is gradually increased?
4E. Three thin rods, each of length L, are arranged in an inverted U, as shown. The two rods on the arms of the U each have mass M; the third rod has mass 3M. Where is the center of mass of the assembly?
5E. A uniform square plate 6 m on a side has had a square piece 2 m on a side cut out of it . The center of that piece is at x = 2 rn, y = O. The center of the square plate is at x = y = O. Find (a) the x coordinate and (b) the)’ coordinate of the center of mass of the remaining piece.
6P. Shows the dimensions of a composite slab; half the slab is made of aluminum.
7P. In the ammonia (NH) molecule , the three hydrogen (H) atoms an equilateral triangle; the center of the triangle is 9.40 X 10-11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms fomenting the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is 10.14 x 10-11 m. Locate the center of mass of the molecule relative to the nitrogen atom.
8P. Shows a cubical box that has been constructed from metal plate of uniform density
and negligible thickness. The box is open at the top and has edge length 40 cm. Find (a) the x coordinate, (b) the y coordinate. and (c) the z coordinate of the center of mass of the box. W. A right cylindrical can with mass M. height H, and uniform density is initially filled with soda of mass m . We punch small holes in the top and bottom to drain the soda; we then consider the height h of the center of mass of the can and any soda within it. What is h (a) initially and (b) when all the soda has drained? (c) What happens to h during the draining of the soda? (d) If x is the height of the remaining soda at any given instant, find x (in terms of M, H, and m) when the center of mass reaches its lowest.
Newton’s Second Law for a System of Particles
10E. Two skaters. one with mass 65 kg and the other with mass 40 kg, stand on an ice rink holding a pole of length 10 m and negligible mass. Starting from the ends of the pole. the skaters pull themselves along the pole until they meet. How far does the 40 kg skater move?
l1E. An old Chrysler with mass 2400 kg is moving along a straight stretch of road at 80 km/h. It is followed by a Ford with mass 1600 kg moving at 60 km/h. How fast is the center of mass of the two cars moving? sam
12E. A man of mass m clings to a rope ladder suspended below a balloon of mass M; see Fig. 9-29. The balloon is stationary with respect to the ground. (a) If the man begins to climb the ladder at speed v (with respect to the ladder). in what direction and with what speed (with ‘respect to the ground) will the balloon move.
13P. A stone is dropped at t = O. A second stone, with twice the mass of the first, is dropped from the same point at t = 100 ms. (a) How far below the release point is the center of mass of the two stones at t = 300 ms? (Neither stone has yet reached the ground.) (b) How fast is the center of mass.
14P. A stone is dropped at t = O. A second stone, with twice the mass of the first, is dropped from the same point at t = 100 ms. (a) How far below the release point is the center of mass of the two stones at t = 300 ms? (Neither stone has yet reached the ground.) (b) How fast is the center of mass.
15P. A shell is shot with an initial velocity, at an angle of 60 with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and that air drag is negligible.
16P. A big olive (m = 0.50 kg) lies at the origin and a big Brazil nut (M = 1.5 ~) lies ~t the point (1.0, 2.0) m in an to act on the olive. and a force begins to act on the nut. In unit-vector notation, what is the displacement of the center of mass of the olive-nut system at t = 4.0 s, with respect to its position at t = O?
17P. Two identical containers of sugar are connected by a mass less cord that passes over a mass less, friction less pulley with. a diameter f50 mm (Fig. 9-31). The two containers are at the same level. Each originally has a mass of 500 g. (a) What is the horizontal position of their center of mass? (b) Now 20 g of sugar is transferred from one container to the other, but the containers are prevented from moving.
18P. Ricardo, of mass 80 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and symmetrically located with respect to the canoe’s center.
Ricardo notices that the canoe moves 40 em relative to a submerged log during the exchange and calculates Carmelita’s mass, which she has not told him.
The linear Momentum System Particles
20E. How fast’ must an 816 kg Beetle travel (a) to have the linear momentum as a 2650 kg Cadillac going 16 km/h and (b) to have the same kinetic energy?
21E. Suppose that your mass is 80 kg. How fast would have to run to have the same linear momentum as a 1600 kg car moving.
22E. A 0.70 kg ball is moving horizontally with a speed of 5.0 mls when it strikes a vertical wall. The ball rebounds with a speed of 2.0 m/s. What is the magnitude of the change in linear. momentum of the ball?
23P. A 2100 kg truck traveling north at 4) km/h turns east and accelerates to 5) km/h. (a) What is the change in the kinetic energy of the truck? What are (b) the magnitude and (c) the direction of change in the linear momentum of the truck?
25P. An object is tracked by a radar station and found to have a position vector.
26P. A 0.30 kg softball has a velocity of 15 mls at an angle of 35° below the horizontal just before making contact with the bat. What is the magnitude of the change in momentum of the ball while it is in contact.
Conservation linear Momentum
27E. A 91 kg man lying on a surface of negligible friction shovesa 68 g stone away from him, giving it a speed of 4.0 m/s. What velocity does the man acquire as a result?
28E. Two blocks of masses 1.0 kg and 3.0 kg are connected by a spring and rest on a friction less surface. They are given velocities toward each other such that the 1.0 kg block travels initially at I. 7 mls toward the center of mass, which remains at rest. What is the initial velocity of the other block?
29E. A 75 kg man is riding on a 39 kg cart traveling at a speed of 2.3 mls. He jumps off with zero horizontal speed relative to the ground. What is the resulting change in the speed of the cart?
30E. A mechanical toy slides along an x axis on a friction less surface with a velocity of (0.40 mls)i when two internal springs separate the toy into three parts, as given in the table. What is the velocity of part A?
24P. A 0.) 65 kg cue ball with an initial speed of 2.00 mls bounces
off the rail in a game dr pool, ‘as
shown from an overhead view in ‘
Fig. 9-33. For x and )’ axes located
as shown, the bounce reverses
the y component