Page 132 - Fisika Terapan for Engineers and Scientists

332 CHAPTER 10 Systems of Particles

*25. The nucleus of an atom of radioactive copper undergoing beta 10.2 Center of Mass
decay simultaneously emits an electron and a neutrino. The
momentum of the electron is 2.64 10 22 kg m/s, that of the 32. A penny coin lies on a table at a distance of 20 cm from a
neutrino is 1.97 10 22 kg m/s, and the angle between their stack of three penny coins. Where is the center of mass of the
directions of motion is 30.0 . The mass of the residual nucleus system of four coins?
is 63.9 u. What is the recoil velocity of the nucleus? (Hint: 33. A 59-kg woman and a 73-kg man sit on a seesaw, 3.5 m long.
The x and y components of the momentum are conserved Where is their center of mass? Neglect the mass of the seesaw.
separately.)
34. Consider the system Earth–Moon; use the data in the table
*26. The solar wind sweeping past the Earth consists of a stream of printed inside the book cover. How far from the center of the
particles, mainly hydrogen ions of mass 1.7 10 27 kg. There Earth is the center of mass of this system?
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are about 1.0 10 ions per cubic meter, and their speed is 35. Consider the Sun and the planet Jupiter as a two-particle
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4.0 10 m/s. What force does the impact of the solar wind system. How far from the center of the Sun is the center of
exert on an artificial Earth satellite that has an area of 1.0 m 2
mass of this system? Express your result as a multiple of the
facing the wind? Assume that upon impact the ions at first
radius of the Sun. (Use the data inside the cover of this book.)
stick to the surface of the satellite.
36. Two bricks are adjacent, and a third brick is positioned sym-
*27. The record for the heaviest rainfall is held by Unionville,
metrically above them, as shown in Fig. 10.28. Where is the
Maryland, where 3.12 cm of rain (1.23 in.) fell in an interval of
center of mass of the three bricks?
1.0 min. Assuming that the impact velocity of the raindrops on
the ground was 10 m/s, what must have been the average impact
force on each square meter of ground during this rainfall?
*28. An automobile is traveling at a speed of 80 km/h through heavy
rain.The raindrops are falling vertically at 10 m/s, and there are
7.0 10 4 kg of raindrops in each cubic meter of air. For the
following calculation assume that the automobile has the shape FIGURE 10.28 Three bricks.
of a rectangular box 2.0 m wide, 1.5 m high, and 4.0 m long.
(a) At what rate (in kg/s) do the raindrops strike the front *37. Where is the center of mass of a uniform sheet in the shape of
and top of the automobile? an isosceles triangle? Assume that the height of the triangle is
(b) Assume that when a raindrop hits, it initially sticks to the h when the unequal side is the base.
automobile, although it falls off later. At what rate does *38. Consider a pyramid with height h and a triangular base.
the automobile give momentum to the raindrops? What is Where is its center of mass?
the horizontal drag force that the impact of the raindrops
*39. In order to balance the wheel of an automobile, a mechanic
exerts on the automobile?
attaches a piece of lead alloy to the rim of the wheel.The
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*29. A spaceship of frontal area 25 m passes through a cloud of mechanic finds that if he attaches a piece of 40 g at a distance of
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interstellar dust at a speed of 1.0 10 m/s. The density of 20 cm from the center of the wheel of 30 kg, the wheel is per-
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dust is 2.0 10 18 kg/m . If all the particles of dust that fectly balanced; that is, the center of the wheel coincides with
impact on the spaceship stick to it, find the average decelerat- the center of mass. How far from the center of the wheel was
ing force that the impact of the dust exerts on the spaceship. the center of mass before the mechanic balanced the wheel?
**30. A basketball player jumps straight up to launch a long jump *40. The distance between the oxygen and each of the hydrogen
shot at an angle of 45 with the horizontal and a speed of 15 atoms in a water (H O) molecule is 0.0958 nm; the angle
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m/s. The 75-kg player is momentarily at rest at the top of his between the two oxygen–hydrogen bonds is 105 (Fig. 10.29).
jump just before the shot is released, with his feet 0.80 m Treating the atoms as particles, find the center of mass.
above the floor. (a) What is the player’s velocity immediately
after the shot is released? (b) How far from his original posi- y
tion does he land? Treat the player as a point particle. The
mass of a basketball is 0.62 kg.
H
**31. A gun mounted on a cart fires bullets of mass m in the back-
ward direction with a horizontal muzzle velocity u. The initial
mass of the cart, including the mass of the gun and the mass 0.0958 nm 105°
of the ammunition, is M, and the initial velocity of the cart is
zero. What is the velocity of the cart after firing n bullets? O H x
Assume that the cart moves without friction, and ignore the
0.0958 nm
mass of the gunpowder.
FIGURE 10.29 Atoms in a water molecule.