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.
Batman is driving his 1000kg Batmobile straight north
at 150km/h, while talking on the batphone with Batgirl. The Joker is driving his
1200kg Jokercar straight east at 180km/h while talking on the phone with
Catwoman. Neither Batman nor the Joker realize they are about to hit each
other. Assuming the collision is perfectly inelastic, what is the speed and
direction of the mangled wreck after the cars hit each other? How much energy
went into crumpling the cars?
Two metal spheres are suspended by vertical cords as
shown below. Sphere 1, m, = 25g, is pulled to a height h, = 8.0cm and then
released from rest. After swinging down, it undergoes an elastic collision with
sphere 2, m2 = 80g. What is the velocity of sphere 1 right after the collision? To
what height will sphere 2 rise?
Given that the force vector is 2î + 4j – 1k and that the
position vector is 3î – 1j + 2k, determine:
a) The cross product i x F
b) The angle between the vectors
Batman is driving his 1000kg Batmobile straight north
at 150km/h, while talking on the batphone with Batgirl. The Joker is driving his
1200kg Jokercar straight east at 180km/h while talking on the phone with
Catwoman. Neither Batman nor the Joker realize they are about to hit each
other. Assuming the collision is perfectly inelastic, what is the speed and
direction of the mangled wreck after the cars hit each other? How much energy
went into crumpling the cars?
15
75
Vb+w
だ
h
A block of mass m,-1.28 kg slides to the right at a speed of 2.46 m/s on a frictionless horizontal
surface, as shown in the figure. It "collides" with a wedge of mass mw, which moves to the left at a
speed of 1.13 m/s. The wedge is shaped so that the block slides seamlessly up the Teflon
(frictionless!) surface, as the two come together. Relative to the horizontal surface, block and
wedge are moving with a common velocity Vb+w at the instant the block stops sliding up the wedge.
a) If the block's center of mass rises by a distance h = 0.38 m, what is the mass of the wedge? The
gravitational acceleration is g = 9.8 m/s².
Express your answer in kg.
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