Page 135 - Fisika Terapan for Engineers and Scientists

Review Problems 335

two fragments of equal mass which fall freely. One of the frag- 70. A projectile of 45 kg fired from a gun has a speed of 640 m/s.
ments has zero speed immediately after the explosion and lands The projectile explodes in flight, breaking apart into a frag-
on the ground directly below the point of the explosion. Where ment of 32 kg and a fragment of 13 kg (we assume that no
does the other fragment land? Ignore the friction of air. mass is dispersed in the explosion). Both fragments move
63. A 15-g bullet moving at 260 m/s is fired at a 2.5-kg block of along the original direction of motion. The speed of the first
wood. What is the velocity of the center of mass of the fragment is 450 m/s and that of the second is 1050 m/s.
bullet–block system? (a) Calculate the translational kinetic energy of the center of
64. A 60-kg woman and a 90-kg man walk toward each other, mass motion before the explosion.
each moving with speed v relative to the ground. What is the (b) Calculate the translational kinetic energy of the center of
velocity of their center of mass? mass motion after the explosion. Calculate the total
65. A projectile of mass M reaches the peak of its motion a hori- kinetic energy. Where does the extra kinetic energy come
zontal distance D from the launch point. At its peak, it from?
explodes into three equal fragments. One fragment returns 71. Consider the automobile collision described in Problem 16.
directly to the launch point, and one lands a distance 2D from What is the translational kinetic energy of the center of mass
the launch point, at a point in the same plane as the initial motion before the collision? What is the total kinetic energy
motion. Where does the third fragment land? before and after the collision?
*66. A projectile is launched with speed v at an angle of with 72. Two isolated point masses m and m are connected by a
2
0
1
respect to the horizontal. At the peak of its motion, it explodes spring. The masses attain their maximum speeds at the same
into two pieces of equal mass, which continue to move in the instant. A short time later both masses are stationary. The
original plane of motion. One piece strikes the ground a hori- maximum speed of the first mass is v . What is the maximum
1
zontal distance D further from the launch point than the point speed of the second mass? When the masses are stationary,
directly below the explosion at a time t v sin /g after the what is the energy stored in the spring?
0
explosion. How high does the other piece go? Where does the 73. The typical speed of a helium atom in helium gas at room
other piece land? Answer in terms of v , ,D, and t. temperature is 1.4 km/s; that of an oxygen molecule (O ) in
0
2
**67. Figure 9.13a shows the positions of the three inner planets oxygen gas is close to 500 m/s. Find the total kinetic energy of
(Mercury, Venus, Earth) on January 1, 2000. Measuring angles one mole of helium atoms and that of one mole of oxygen
off this figure and using the data on masses, orbital radii, and molecules.
periods given in Table 9.1, find the velocity of the center of *74. Two automobiles, each of mass M/2 and speed v, drive
mass of this system of three planets. around a one-lane traffic circle. What is the total kinetic
1
energy of the two-car system? What is the quantity Mv 2 CM
2
if the automobiles are (a) on opposite sides of the traffic
10.4 Energy of a System of Par ticles
circle, (b) one-quarter of the circle apart, and (c) locked
68. Two automobiles, each of mass 1500 kg, travel in the same together?
direction along a straight road. The speed of one automobile is *75. Consider the Sun and Jupiter to be a two-particle system,
25 m/s, and the speed of the other automobile is 15 m/s. If we orbiting around the center of mass. Find the ratio of the
regard these automobiles as a system of two particles, what is kinetic energy of the Sun to that of Jupiter. (Use the data
the translational kinetic energy of the center of mass? What is inside the book cover.)
the total kinetic energy? *76. The typical speed of the vibrational motion of the iron atoms
69. Repeat the calculation of Problem 68 if the two automobiles in a piece of iron at room temperature is 360 m/s. What is the
travel in opposite directions. total kinetic energy of a 1.0-kg chunk of iron?

REVIEW PROBLEMS

77. A hunter on skates on a smooth sheet of ice shoots 10 bullets 78. Grain is being loaded into an almost full railroad car from an
at a target at the shore. Each bullet has a mass of 15 g and a overhead chute (see Fig. 10.37). If 500 kg per second falls
speed of 600 m/s. The hunter has a mass of 80 kg. What recoil freely from a height of 4.0 m to the top of the car, what down-
speed does he acquire? ward push does the impact of the grain exert on the car?