Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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the potential energy function U(r) of a projectile, plotted outward from the surface of a planet of radius Rs. If the projectile is launched radially outward from the surface with a mechanical energy of2.0 * 10^9 J, what are (a) its kinetic energy at radius r = 1.25Rs and (b) its turning point (see Module 8-3) in terms of Rs?
Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?
Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?
Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?
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- Calculate the gravitational potential V for a hemisphere of radius R with uniform mass distribution.arrow_forwardHalf ring with internal radius a and external b, with surface mass distribution σ = σ0/r, where σ0 is a constant. Let a point P be at a height h from the plane of the half ring. The escape velocity at P isarrow_forwardUsing Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass,m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan(+)=gg2REtan , where is the angular velocity of Earth.arrow_forward
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