Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 5, Problem 5.6P
Compute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere of matter.
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Chapter 5 Solutions
Classical Dynamics of Particles and Systems
Ch. 5 - Prob. 5.3PCh. 5 - Compute directly the gravitational force on a unit...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - A planet of density 1 (spherical core, radius R1)...Ch. 5 - Prob. 5.16PCh. 5 - A thin disk of mass M and radius R lies in the (x,...Ch. 5 - A point mass m is located a distance D from the...
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- What happens to the density of an object as its speed increases, as measured by an Earth observer?arrow_forwardAfter our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now but a radius equal to roughly the size of the Earth's radius. (a) Calculate the average density of this white dwarf if the Sun were to collapse to a radius of 6.31 × 10°m. 1.84e+9 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake i your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg/m- (b) Calculate the free-fall acceleration at its surface. 3.27e+6 m/s² (c) Calculate the gravitational potential energy of a 4.00 kg object at its surface. (Take U, = 0 at infinity.) -8.33e+13 Need Help? Read Itarrow_forwardA solid copper sphere of mass M and radius R has a cavity of radius ½ R. Inside the cavity a particle of mass m placed a distance d > R from the center of the sphere along the line connecting the centers of the sphere and the cavity. Find the gravitational force on m.arrow_forward
- Consider a system of N particles in a uniform gravitational field. Prove that the total gravitational torque about the CM is zero.arrow_forwardYou are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an approximated density of 1 hydrogen atom/m3. Calculate the time it takes your spaceship to reach Sirius. Determine the mass of interstellar gas that collides with your spaceship during the mission. Note: Use 1.673 × 10−27 kg as proton massarrow_forwardYou are standing on the surface of a planet that has sphericalsymmetry and a radius of 5.00 * 10^6 m. The gravitational potential energyU of the system composed of you and the planet is -1.20 * 10+9 Jif we choose U to be zero when you are very far from the planet. Whatis the magnitude of the gravity force that the planet exerts on you whenyou are standing on its surface?arrow_forward
- You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an approximated density of 1 hydrogen atom/m^3 . (a) Calculate the time it takes your spaceship to reach Sirius. (b) Determine the mass of interstellar gas that collides with your spaceship during the mission. Note: Use 1.673 × 10^−27 kg as proton mass.arrow_forwardAfter the Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of Earth. Calculate (a) the average density of the white dwarf, (b) the surface free-fall acceleration, and (c) the gravitational potential energy associated with a 1.00-kg object at the surface of the white dwarf.arrow_forwardIn introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres with masses of 1.90 kg and 19.0 g whose centers are separated by about 2.60 cm. Calculate the gravitational force between these spheres, treating each as a particle located at the center of the sphere.arrow_forward
- Show that the escape velocity of a body from the surface of a planet of radius R and mean density g is R 3arrow_forwardAssuming that the gravitational acceleration inside a homogeneous spherical shell is zero, show that the gravitational acceleration inside a homogenous uniform solid sphere is proportional to the distance from its center.arrow_forwardThe gravitational acceleration on the surface of earth of radius (R) mean density (p) is (a) (4n / 3) GR? p (b) (4т? / 3) GR? p (c) (2n / 3) GR? p (d) (4π / 3) GR ρarrow_forward
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