4. The equation mgy for gravitational potential energy is valid only for objects near the surface...
4. The equation mgy for gravitational potential energy is valid only for objects near the surface of a planet. Consider two very large objects of mass m1 and m2, such as stars or planets, whose centers are separated by the large distance r. These two large objects exert gravitational forces on each other.The gravitational potential energy is U = − Gm1m2 r where G = 6.67 × 10−11Nm2/kg2 is the gravitational constant.
(a) Sketch a graph of U versus r. The mathematical difficulty at r = 0 is not a physically significant difficulty because the masses will collide before they get that close together.
(b) What separation r has been chosen as the point of zero potential energy? Does this make sense? Explain.
(c) Two stars are at rest 1.0 × 1014 m apart. This is about 10 times the diameter of the solar system. The first star is the size of our sun, with a mass of 2.0 × 1030 kg and a radius of 7.0 × 108 m. The second star has mass 8.0 × 1030 kg and radius of 11.0 × 108 m. Gravitational forces pull the two stars together. What is the speed of each star at the moment of impact?
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4. The equation mgy for gravitational potential energy is valid
only for objects near the surface...
Only A and B please :) The equation mgy for gravitational potential energy is valid only...
Only A and B please :)
The equation mgy for gravitational potential energy is valid only for objects near the surface of a planet. Consider two very large objects of mass m_1 and m_2, such as stars or planets, whose centers are separated by the large distance r. These two large objects exert gravitational forces on each other. The gravitational potential energy is U = -Gm_1 m_2/r where G = 6.67 times 10^-11 Nm^2/kg^2 is the gravitational constant. (a) Sketch...
Stars form from the gravitational collapse of clouds of interstellar ("between the stars") gas. To simplify...
Stars form from the gravitational collapse of clouds of interstellar ("between the stars") gas. To simplify the situation, assume that a single star forms from a uniform, spherical cloud of gas of mass 2.0 x 1030 kg and radius 1.0 x 1013 m. 2. Before it begins to collapse, the cloud is rotating with a period of 1.4 million years. What is the angular speed of the cloud? (2.26 × 10-14 rev/s) The cloud eventually collapses to form a star...
Problem 1. The form of the gravitational potential energy of objects of mass mi and m2...
Problem 1. The form of the gravitational potential energy of objects of mass mi and m2 located at positions r,-z1x + yı у + zł z and r,-z2z + угу + z2z can be written as G mim2 G mim2 A) Find the gravitational force that particle 2 exerts on particle 1. Use Fon-VU B) Find the gravitational force that particle 1 exerts on particle 2. Use Fon2=-▽2U C) Do the forces found above satisfy Newton's third law of motion?
2) Densities We discussed White Dwarfs and Neutron stars, very dense objects compared to stars like...
2) Densities We discussed White Dwarfs and Neutron stars, very dense objects compared to stars like our sun. On the other hand, we also discussed Red Giants which are much less dense than our sun. To realize just how dense, please compute the average densities (in kg/m) for a) the sun (Rsun=7 x 10 km, Msun= 2 x 1030 kg) b) when the sun becomes a red giant (R= 1AU, M=Msun). By what factor is a Red Giant less dense...
The gravitational potential energy of a small satellite with mass m orbiting the Earth, mass M,...
The gravitational potential energy of a small satellite with mass m orbiting the Earth, mass M, is U(r) = −(GMm)/r, where r is the radial distance from the center of Earth to the satellite. Derive the gravitational force F(r) acting on the satellite by evaluating the gradient of the potential energy.
3 GM2 (5) The gravitational potential of a uniform-density sphere of mass M and radius R is E,-- Consider a white dwarf...
3 GM2 (5) The gravitational potential of a uniform-density sphere of mass M and radius R is E,-- Consider a white dwarf star which contains N electrons whose Fermi energy is Es. Since kaT <<Ef, the average electron energy is 3/5Er (derived in assignment 1) and the total electron energy is Ed-3/5NEs. The energies of the nuclei can be neglected. OE (a) Derive an expression for the gravitational pressure: P- OE (b) Derive an expression for the degeneracy pressure: Pa-...
3. A simple model of a Neutron star is an ideal gas of neutrons (each with spin 1/2 in units of h...
3. A simple model of a Neutron star is an ideal gas of neutrons (each with spin 1/2 in units of h). Aside from the kinetic energy of the neutrons, one must consider the gravitational energy, which for a homogeneous star of mass M and radius R, is 3GM2 5R where G 6.67 x 10-11m3kg-'s-2 is the universal gravitational constant (i) We suppose in this problem that the Fermi temperature is large enough for T0 What general condition determines the...
3. Potential energy of rings. You know that the gravitational potential energy of two interacting spherical...
3. Potential energy of rings. You know that the gravitational potential energy of two interacting spherical masses (e g. Earth and Sun) s u--GMm, where r distance between their centers. If the masses are not spherical, this expression is not valid. However, we can still find the total potential energy by dividing the non-spherical mass into bits, treating each tiny bit as a point mass (which gravitates like a sphere), and adding their effects. That is, U-J -GMdm. This integral...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses is Ug-GMm Use this fact to show that the virial theorem holds for a mass m, executing uniform circular motion about a much larger mass M (b) (3 marks) The potential energy of a collection of N particles each of mass m in a region with radius R can be written as Use this expression to derive a mass estimate for the virialized system...
i got to the end but couldnt find the right value for R. and explanation would...
i got to the end but couldnt find the right value for R. and
explanation would be appreciated.
26. A satellite with mass 10 kg has a circular orbit 106 m above the Earth's surface (the radius of the Earth is 6.4 x 106 m). What is the total (kinetic +potential) energy of the satellite? Take the potential energy to be zero when the Earth and satellite are infinitely far apart. It might help to know that the mass of...
Only A and B please :)
The equation mgy for gravitational potential energy is valid only for objects near the surface of a planet. Consider two very large objects of mass m_1 and m_2, such as stars or planets, whose centers are separated by the large distance r. These two large objects exert gravitational forces on each other. The gravitational potential energy is U = -Gm_1 m_2/r where G = 6.67 times 10^-11 Nm^2/kg^2 is the gravitational constant. (a) Sketch...
Stars form from the gravitational collapse of clouds of interstellar ("between the stars") gas. To simplify the situation, assume that a single star forms from a uniform, spherical cloud of gas of mass 2.0 x 1030 kg and radius 1.0 x 1013 m. 2. Before it begins to collapse, the cloud is rotating with a period of 1.4 million years. What is the angular speed of the cloud? (2.26 × 10-14 rev/s) The cloud eventually collapses to form a star...
Problem 1. The form of the gravitational potential energy of objects of mass mi and m2 located at positions r,-z1x + yı у + zł z and r,-z2z + угу + z2z can be written as G mim2 G mim2 A) Find the gravitational force that particle 2 exerts on particle 1. Use Fon-VU B) Find the gravitational force that particle 1 exerts on particle 2. Use Fon2=-▽2U C) Do the forces found above satisfy Newton's third law of motion?
2) Densities We discussed White Dwarfs and Neutron stars, very dense objects compared to stars like our sun. On the other hand, we also discussed Red Giants which are much less dense than our sun. To realize just how dense, please compute the average densities (in kg/m) for a) the sun (Rsun=7 x 10 km, Msun= 2 x 1030 kg) b) when the sun becomes a red giant (R= 1AU, M=Msun). By what factor is a Red Giant less dense...
3 GM2 (5) The gravitational potential of a uniform-density sphere of mass M and radius R is E,-- Consider a white dwarf star which contains N electrons whose Fermi energy is Es. Since kaT <<Ef, the average electron energy is 3/5Er (derived in assignment 1) and the total electron energy is Ed-3/5NEs. The energies of the nuclei can be neglected. OE (a) Derive an expression for the gravitational pressure: P- OE (b) Derive an expression for the degeneracy pressure: Pa-...
3. A simple model of a Neutron star is an ideal gas of neutrons (each with spin 1/2 in units of h). Aside from the kinetic energy of the neutrons, one must consider the gravitational energy, which for a homogeneous star of mass M and radius R, is 3GM2 5R where G 6.67 x 10-11m3kg-'s-2 is the universal gravitational constant (i) We suppose in this problem that the Fermi temperature is large enough for T0 What general condition determines the...
3. Potential energy of rings. You know that the gravitational potential energy of two interacting spherical masses (e g. Earth and Sun) s u--GMm, where r distance between their centers. If the masses are not spherical, this expression is not valid. However, we can still find the total potential energy by dividing the non-spherical mass into bits, treating each tiny bit as a point mass (which gravitates like a sphere), and adding their effects. That is, U-J -GMdm. This integral...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses is Ug-GMm Use this fact to show that the virial theorem holds for a mass m, executing uniform circular motion about a much larger mass M (b) (3 marks) The potential energy of a collection of N particles each of mass m in a region with radius R can be written as Use this expression to derive a mass estimate for the virialized system...
i got to the end but couldnt find the right value for R. and
explanation would be appreciated.
26. A satellite with mass 10 kg has a circular orbit 106 m above the Earth's surface (the radius of the Earth is 6.4 x 106 m). What is the total (kinetic +potential) energy of the satellite? Take the potential energy to be zero when the Earth and satellite are infinitely far apart. It might help to know that the mass of...
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