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Unformatted text preview: homework 07 BROWNING, ADAM Due: Oct 19 2007, 1:00 am 1 Question 1, chap 9, sect 1. part 1 of 1 10 points According to some nineteenth-century geo- logical theories (now largely discredited), the Earth has been shrinking as it gradually cools. If so, how would g have changed over geo- logical time? 1. It would decrease; the Earths radius is decreasing. 2. It would increase; g is inversely propor- tional to the square of the radius of the Earth. correct 3. It would not change; the mass of the Earth remained the same. Explanation: The acceleration g of gravity would increase if the Earth shrank, but its mass stayed the same, since g 1 r 2 . Question 2, chap 9, sect 1. part 1 of 2 10 points Given: G = 6 . 67259 10- 11 Nm 2 / kg 2 In Larry Nivens science fiction novel Ring- world , a ring of material rotates about a star. n Star F g The rotational speed of the ring is 1 . 34 10 6 m / s, and its radius is 6 . 57 10 10 m. The inhabitants of this ring world experience a normal contact force vector n . Acting alone, this normal force would produce an inward accel- eration of 9 . 78 m / s 2 . Additionally, the star at the center of the ring exerts a gravitational force on the ring and its inhabitants. What is the total centripetal acceleration of the inhabitants? Correct answer: 27 . 3303 m / s 2 (tolerance 1 %). Explanation: The centripetal acceleration of the inhabi- tants is a c = v 2 r = (1 . 34 10 6 m / s) 2 6 . 57 10 10 m = 27 . 3303 m / s 2 . Question 3, chap 9, sect 1. part 2 of 2 10 points The difference between the total acceler- ation and the acceleration provided by the normal force is due to the gravitational at- traction of the central star. Calculate the approximate mass of the star. Correct answer: 1 . 13533 10 33 kg (tolerance 1 %). Explanation: The difference a between the total accel- eration and the acceleration provided by the normal force is due to the gravitational at- traction of the central star and is equal to a = a c- a i . On the other hand, this difference can be expressed from Newtons law of gravity a = GM r 2 , where M is the mass of the central star. Using the values for a c and a i , the mass of the star is M = r 2 a G = r 2 ( a c- a i ) G = (6 .....
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