CALC Neutron Stars and Supernova Remnants. The Crab Nebula is a cloud of glowing gas about 10 light-years across, located about 6500 light-years from the earth ( Fig. P9.86 ). It is the remnant of a star that underwent a supernova explosion , seen on earth in 1054 A.D. Energy is released by the Crab Nebula at a rate of about 5 × 10 31 W. about 10 5 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once every 0.0331 s. and this period is increasing by 4.22 × 10 −13 s for each second of time that elapses, (a) If the rate at which energy is lost by the neutron star is equal to the rate at which energy is released by the nebula, find the moment of inertia of the neutron star . (b) Theories of supernovae predict that the neutron star in the Crab Nebula has a mass about 1.4 times that of the sun. Modeling the neutron star as a solid uniform sphere, calculate its radius in kilometers, (c) What is the linear speed of a point on the equator of the neutron star? Compare to the speed of light , (d) Assume that the neutron star is uniform and calculate its density. Compare to the density of ordinary rock (3000 kg/m 3 ) and to the density of an atomic nucleus (about 10 17 kg/m 3 ). Justify the statement that a neutron star is essentially a large atomic nucleus. Figure P9.86
CALC Neutron Stars and Supernova Remnants. The Crab Nebula is a cloud of glowing gas about 10 light-years across, located about 6500 light-years from the earth ( Fig. P9.86 ). It is the remnant of a star that underwent a supernova explosion , seen on earth in 1054 A.D. Energy is released by the Crab Nebula at a rate of about 5 × 10 31 W. about 10 5 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once every 0.0331 s. and this period is increasing by 4.22 × 10 −13 s for each second of time that elapses, (a) If the rate at which energy is lost by the neutron star is equal to the rate at which energy is released by the nebula, find the moment of inertia of the neutron star . (b) Theories of supernovae predict that the neutron star in the Crab Nebula has a mass about 1.4 times that of the sun. Modeling the neutron star as a solid uniform sphere, calculate its radius in kilometers, (c) What is the linear speed of a point on the equator of the neutron star? Compare to the speed of light , (d) Assume that the neutron star is uniform and calculate its density. Compare to the density of ordinary rock (3000 kg/m 3 ) and to the density of an atomic nucleus (about 10 17 kg/m 3 ). Justify the statement that a neutron star is essentially a large atomic nucleus. Figure P9.86
The Crab Nebula is a cloud of glowing gas about 10 light-years across, located about 6500 light-years from the earth (Fig. P9.86). It is the remnant of a star that underwent a supernova explosion, seen on earth in 1054 A.D. Energy is released by the Crab Nebula at a rate of about 5 × 1031 W. about 105 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once every 0.0331 s. and this period is increasing by 4.22 × 10−13 s for each second of time that elapses, (a) If the rate at which energy is lost by the neutron star is equal to the rate at which energy is released by the nebula, find the moment of inertia of the neutron star. (b) Theories of supernovae predict that the neutron star in the Crab Nebula has a mass about 1.4 times that of the sun. Modeling the neutron star as a solid uniform sphere, calculate its radius in kilometers, (c) What is the linear speed of a point on the equator of the neutron star? Compare to the speed of light, (d) Assume that the neutron star is uniform and calculate its density. Compare to the density of ordinary rock (3000 kg/m3) and to the density of an atomic nucleus (about 1017 kg/m3). Justify the statement that a neutron star is essentially a large atomic nucleus.
Figure P9.86
Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.
While playing a game of billards, your 0.50kg cue ball, travelling at 1.9 m/s glances off a stationary 0.30 kg billard ball so that the billard ball moves off at 1.3 m/s at an angle of 32 degrees clockwise from the cue ball's original path. What is the final speed of the cue ball?
Consider the two pucks shown in the figure. As they move towards each other, the momentum of each puck is equal in magnitude and opposite in direction. Given that v;
= 12.0 m/s, and mhue is 25.0%
green
1
the kinetic energy of the system is converted to internal energy?
2
greater than mareen, what are the final speeds of each puck (in m/s), if
I30.0"
30.0
V green
m/s
Vplue
m/s
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A 20 gg ball of clay traveling east at 2.0 m/sm/s collides with a 20 gg ball of clay traveling north at 2.0 m/sm/s.
What is the speed of the resulting 40 gg ball of clay?
Express your answer with the appropriate units.
Chapter 9 Solutions
University Physics with Modern Physics, Volume 1 (Chs. 1-20) (14th Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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