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CalmHW12solutions

# CalmHW12solutions - HOMEWORK Week 11 Chapter 12 SOLUTIONS...

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HOMEWORK: Week 11 – Chapter 12 - SOLUTIONS 1. (12.15) Two 6.3-kg bowling balls, each with a radius of 0.11 m, are in contact with one another. What is the gravitational attraction between the bowling balls? SOLUTION A sphere acts like a point mass at the sphere’s center. 2 2 2 11 8 2 2 2 N m (6.3 kg) 6.67 10 5.5 10 N kg (0.22 m) m F G r - - = = × = × 2. (12.22) Consider a spherical asteroid with a radius of 12 km and a mass of 345 10 15 . . × kg (a) What is the acceleration of gravity on the surface of this asteroid? (b) Suppose the asteroid spins about an axis through its center, like the Earth, with an angular speed ϖ What is the greatest value can have before loose rocks on the asteroid’s equator begin to fly off the surface? SOLUTION (a) 2 15 11 3 2 A A 2 2 3 2 A N m (3.45 10 kg) 6.67 10 1.6 10 m/s kg (12 10 m) M g G R - - × = = × = × × (b) A A 2 3 2 4 esc A 3 A A A 2 2(1.6 10 m/s ) 5.2 10 rad/s 12 10 m GM R v g R R R - - × = = = = = × × 3. (12.37) Calculate the gravitational potential energy of a 5.0-kg mass (a) on the surface of the Earth and (b) at an altitude of 1.0 km. (c) Take the difference between the results for parts (b) and (a), and compare with mgh , where h = 10 . . km SOLUTION E M m U G r = - (a) 2 24 11 8 1 2 6 N m (5.97 10 kg)(5.0 kg) 6.67 10 3.12558 10 J kg 6.37 10 m U - × = - × = - × × (b)

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CalmHW12solutions - HOMEWORK Week 11 Chapter 12 SOLUTIONS...

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