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Chapter 12: Q. 31 (page 331)
The 3.0-m-long, 100 kg rigid beam of FIGURE EX12.31 is supported at each end. An 80 kg student stands 2.0 m from support 1. How much upward force does each support exert on the beam?
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During most of its lifetime, a star maintains an equilibrium size in which the inward force of gravity on each atom is balanced by an outward pressure force due to the heat of the nuclear reactions in the core. But after all the hydrogen “fuel” is consumed by nuclear fusion, the pressure force drops and the star undergoes a gravitational collapse
until it becomes a neutron star. In a neutron star, the electrons and protons of the atoms are squeezed together by gravity until they fuse into neutrons. Neutron stars spin very rapidly and emit intense pulses of radio and light waves, one pulse per rotation. These “pulsing
stars” were discovered in the 1960s and are called pulsars.
a. A star with the mass M = 2.0 x 1030 kg and size R =7.0 x 108 m of our sun rotates once every 30 days. After undergoing gravitational collapse, the star forms a pulsar that is observed by astronomers to emit radio pulses every 0.10 s. By treating the neutron star as a solid sphere, deduce its radius.
b. What is the speed of a point on the equator of the neutron star? Your answers will be somewhat too large because a star cannot be accurately modeled as a solid sphere. Even so, you will be able to show that a star, whose mass is 106larger than the earth’s, can be compressed by gravitational forces to a size smaller than a typical state in the United States!
A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 250 kg is spinning at 20 rpm. John runs tangent to the merry-go-round
at 5.0 m/s, in the same direction that it is turning, and jumps onto the outer edge. John’s mass is 30 kg. What is the merry-goround’s angular velocity, in rpm, after John jumps on?
A 750 g disk and a 760 g ring, both 15 cm in diameter, are rolling along a horizontal surface at 1.5 m/s when they encounter a 15° slope. How far up the slope does each travel before rolling back down?
Determine the moment of inertia about the axis of the object shown in FIGURE P12.51.
A skater holds her arms outstretched as she spins at . What is the speed of her hands if they are apart?
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