A satellite has a mass of 298 kg and is located at 1.97 ✕ 106 m above the surface of Earth. (a) What is the potential energy associated with the satellite at this location?  J (b) What is the magnitude of the gravitational force on the satellite?  N

13.39 • CALC Consider the ring- shaped object in Fig. E13.39 D. A particle with mass m is placed a distance x from the center of the ring, along the line through the center of the ring and perpendicular to its plane. (a) Calculate the gravitational potential energy U of this system. Take the potential energy to be zero when the two objects are far apart. (b) Show that your answer to part (a) reduces to the expected result when x is much larger than the radius a of the ring. (c) Use F. = -dU/dx to find the magnitude and direction of the force on the particle (see Section 7.4 9). (d) Show that your answer to part (c) reduces to the expected result when x is much larger than a. (e) What are the values of U and F, when x = 0? Explain why these results make sense. Figure E13.39 т M

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A 500 kg communication satellite is to be placed in geostationary orbit around the Earth. a)How high does it have to go to have the same period as the Earth? b)What is the gravitational potential energy of the satellite before going into orbit? c)What is the total energy of the satellite in geostationary orbit? d)What is the work that the rocket must do to place the satellite in geostationary orbit?

please answer all the subparts

A planet with a radius of 6.00 × 107 m has a gravitational field of magnitude 41.7 m/s2 at the surface. What is the escape speed from the planet?

A 260 g particle in a semi-spherical bowl of radius 0.6 m is released from rest at point A at the level of the center of the bowl, and the surface of the bowl is rough. The speed of the particle at B is 2 m/s. The acceleration of gravity is 9.8 m/s2 . a)What is its kinetic energy at B? b)What is the magnitude of the energy lost due to friction as the particle moves from A to B?

A 800 kg roller coaster goes over the first hill with a speed of 17.0 m/s.  If h = 58 m, determine the change in gravitational potential between A and B.  Use g = 10 N/kg.

A spherically symmetric ball of mass m and radius R is centered at the origin. A thin rod has a mass M uniformly distributed along its length L and lies along the x-axis as shown in the figure below. Determine the gravitational potential energy of the system if U = 0 at x = ∞. y L M т

In deep space, sphere A of mass 30 kg is located at the origin of an x axis and sphere B of mass 10 kg is located on the axis at x = 0.85 m. Sphere B is released from rest while sphere A is held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as B is released? (b) What is the kinetic energy of B when it has moved 0.25 m toward A? Additional Materials eBook Powers of Ten