EPChap13-Solution

EPChap13-Solution - Chap. 13 HW 15. At what altitude above...

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1 Chap. 13 HW 15. At what altitude above Earth's surface would the gravitational acceleration be 4.9 m/s 2 ? a g = GM/r 2 M = mass of Earth a r = distance from Earth’s center. Substituting r = R + h , where R is the radius of Earth and h is the altitude, a g = GM / ( R + h ) 2 . Therefore / g hG M a R =− . Using R = 6.37 × 10 6 m, M = 5.98 × 10 24 kg, () ( ) 11 3 2 24 66 2 6.67 10 m /s kg 5.98 10 kg 6.37 10 m 2.6 10 m. 4.9m /s h ×⋅ × × = × 17. One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R , outer radius 2 R , and mass 4 M . If M = 4.1 × 10 24 kg and R = 6.0 × 10 6 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3 R from the center of the planet? a) Since only the mass M of the core is within the radius R of the center, 2 2 == 7 . 6 m / s . g GM a R b) Total mass is 5 M . Therefore 2 2 5 4 . 2 m / s . 3 g GM a R 19. Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation? The gravitational force must provide the centripetal force to keep the mass at the surface of the Neutron star in circular motion without flying off the surface. Imagine a small mass m sitting on the surface of the neutron star. Applying Newton’s second law (radius of the circular motion is the radius of the star): kg second) ( Using 24 2 3 2 2 2 2 10 7 . 4 2 1 2 × = = = = = = = = GT r G r v m T r T r v r v m r m Gm ma F n N c π ω (Used R = 20 km = 20,000 m and Τ = 1 s).

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2 33. (a) What is the escape speed on a spherical asteroid whose radius is 500 km and whose gravitational acceleration at the surface is 3.0 m/s
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This note was uploaded on 04/07/2008 for the course PHYS 213 taught by Professor Oshea during the Spring '08 term at Kansas State University.

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EPChap13-Solution - Chap. 13 HW 15. At what altitude above...

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