Passage
Black holes have played an important part in astrophysics for the last half-century. A black hole is a region of space where the force of gravity is especially strong and gravitational potential energy U is very large. Analogous to the electrostatic potential energy associated with electrical charges, U is defined as the work required to move an object of mass m from an infinite distance to a point at radial distance r within the gravitational field of a second mass M as given by
Equation 1where G is the gravitational constant. Near a black hole, the gravitational potential energy can become so negative that not even light has enough energy to escape the black hole's gravity.Escape velocity can be determined by launching an object of mass m with velocity v to an infinite radial distance from the surface of a central mass M (eg, a star or a planet) with radius R. For a black hole to exist, the escape velocity must be equal to the speed of light.Scientists have thoroughly studied the physics of black holes. Stars near the center of our galaxy have been observed to orbit an extremely massive, invisible object (millions of times more massive than our Sun) that is almost certainly a black hole. The orbital angular velocity ω of a star is defined as
ω=360°⋅fEquation 2where f is the frequency of rotation in hertz (Hz) . Likewise, black holes are not merely static masses but are often observed to rotate about their own axis. The interaction between the rotation of a black hole and matter falling into the hole is suspected to form powerful beams (jets) of ionized matter that project away from the black hole along its axis of rotation. Nevertheless, many aspects of how these jets are formed remains a mystery. Black holes will remain a fruitful area for research far into the future.
-A black hole emits a jet with a power of 10⁴⁴ W. If the black hole has a rotational period of 0.1 ms, what is the energy emitted by the jet during one rotation of the black hole?

Question

Passage
Black holes have played an important part in astrophysics for the last half-century. A black hole is a region of space where the force of gravity is especially strong and gravitational potential energy U is very large. Analogous to the electrostatic potential energy associated with electrical charges, U is defined as the work required to move an object of mass m from an infinite distance to a point at radial distance r within the gravitational field of a second mass M as given by

Equation 1where G is the gravitational constant. Near a black hole, the gravitational potential energy can become so negative that not even light has enough energy to escape the black hole's gravity.Escape velocity can be determined by launching an object of mass m with velocity v to an infinite radial distance from the surface of a central mass M (eg, a star or a planet) with radius R. For a black hole to exist, the escape velocity must be equal to the speed of light.Scientists have thoroughly studied the physics of black holes. Stars near the center of our galaxy have been observed to orbit an extremely massive, invisible object (millions of times more massive than our Sun) that is almost certainly a black hole. The orbital angular velocity ω of a star is defined as

ω=360°⋅fEquation 2where f is the frequency of rotation in hertz (Hz) . Likewise, black holes are not merely static masses but are often observed to rotate about their own axis. The interaction between the rotation of a black hole and matter falling into the hole is suspected to form powerful beams (jets) of ionized matter that project away from the black hole along its axis of rotation. Nevertheless, many aspects of how these jets are formed remains a mystery. Black holes will remain a fruitful area for research far into the future.
-A black hole emits a jet with a power of 10⁴⁴ W. If the black hole has a rotational period of 0.1 ms, what is the energy emitted by the jet during one rotation of the black hole?

Quizplus · Accepted Answer

11ecba2d_132f_d849_a3bf_f55360448b41_MD0008_00 Power (P) measures the rate at which energy (E) is expended by a physical process over a period of time (t): 11ecba2d_132f_ff5a_a3bf_8df8d3090c88_MD0008_00 In mechanics, power is the amount work done by a force acting on a system per unit time. Power can also reflect a rate of energy transfer or conversion between systems. For example, electric power in a circuit is the rate at which energy is dissipated as heat and light by an electric current passing through a resistor. In the case of a black hole, the immense rotational and magnetic forces acting on nearby charged matter cause a mechanical acceleration of the matter, which forms high-energy jets that travel away from the black hole along its axis of rotation. The power associated with these jets is: 11ecba2d_132f_ff5b_a3bf_fb29fe58ac06_MD0008_00 The energy emitted by the jet during one rotation of the black hole is related to the power of the jets and the rotational period of the black hole: 11ecba2d_132f_ff5c_a3bf_27988a7f74b2_MD0008_00 11ecba2d_132f_ff5d_a3bf_63a98909f329_MD0008_00 11ecba2d_132f_ff5e_a3bf_efa8b02d14d3_MD0008_00 Therefore, the amount of energy released by the jet during one rotation of the black hole is 10⁴⁰ J (Choice A). Educational objective: Power describes the rate at which energy is expended within a system per unit time. Power also quantifies the transfer of energy or the total work done on a system over a period of time.

Passage Black Holes Have Played an Important Part in Astrophysics for for the Last