Page 136 - Fisika Terapan for Engineers and Scientists

336 CHAPTER 10 Systems of Particles

84. A tugboat of mass 400 metric tons and a ship of 28000 metric
tons are joined by a long towrope of 400 m. Both vessels are ini-
tially at rest in the water. If the tugboat reels in 200 m of towrope,
how far does the ship move relative to the water? The tugboat?
4.0 m Ignore the resistance that the water offers to the motion.
85. A cat stands on a plank of balsa wood floating in water. The
mass of the cat is 3.5 kg, and the mass of the balsa is 5.0 kg. If
the cat walks 1.0 m along the plank, how far does she move in
relation to the water?
86. Three firefighters of equal masses are climbing a long ladder.
When the first firefighter is 20 m up the ladder, the second is
15 m up, and the third is 5 m up. Where is the center of mass
FIGURE 10.37 Grain from a chute of the three firefighters?
falls into a railroad car.
87. Four identical books are arranged on the vertices of an equilat-
eral triangle of side 1.0 m. Two of the books are together at
79. A boy and a girl are engaged in a tug-of-war on smooth, fric- one vertex of the triangle, and the other two are at the other
tionless ice. The mass of the boy is 40 kg, and that of the girl is two vertices. Where is the center of mass of this arrangement?
30 kg; their separation is initially 4.0 m. Each pulls with a 88. Three identical metersticks are arranged to form the letter U.
force of 200 N on the rope. What is the acceleration of each? Where is the center of mass of this system?
If they keep pulling, where will they meet?
89. Two uniform squares of sheet metal of dimensions L L are
80. An automobile of 1200 kg and an automobile of 1500 kg are joined at right angles along one edge (see Fig. 10.39). One of
traveling in the same direction on a straight road.The speeds of the squares has twice the mass of the other. Find the center of
the two automobiles are 60 km/h and 80 km/h, respectively. mass of the combined squares.
What is the velocity of the center of mass of the two-automobile
system? L
81. An automobile traveling 40 km/h collides head-on with a truck
which has 5 times the mass of the automobile.The wreck remains
at rest after the collision. Deduce the speed of the truck.
82. The nozzle of a fire hose ejects 800 liters of water per minute
L
at a speed of 26 m/s. Estimate the recoil force on the nozzle.
By yourself, can you hold this nozzle steady in your hands?
83. The distance between the centers of the atoms of potassium
and bromine in the potassium bromide (KBr) molecule is
0.282 nm (Fig. 10.38). Treating the atoms as particles, find
the center of mass.
y

FIGURE 10.39 Two square pieces of sheet metal joined along
0.282 nm
one edge.

m 1 m 2 *90. Find the center of mass of a uniform solid hemisphere of
Br K x
CM radius R.

FIGURE 10.38 Atoms in a potassium bromide molecule.