14 ANSWERS TO PRACTICAL QUESTIONS 



How long would it take for a pendulum one mile in length 

 to make, a vibration ? 



How long would it take for a pendulum reac king from 

 the earth to the moon to make a vibration ? 



Required the length of a pendulum that would vibrate 

 centuries. ( 70 be solved like problem 20. ) 



38. Two meteoric bodies in space are 12 miles apart. They 

 weigh 100 and 200 Ibs. respectively. If they should fall 

 together by force of their mutual attraction, what portion of 

 the distance would be passed over by each body ? 



The distance passed over by the two bodies is inversely as 

 their mass; hence one moves 8 miles and the other 4 miles. 



39. If a body weighs 2,000 Ibs. upon the surface of the earth, 

 what would it weigh 2,000 miles above ? 



(6000 mi.) 2 : (4000 mi.) 3 : : 2000 Ibs. : x = 888*/ Ibs. 

 How much 500 miles above? 



(4500 mi.)2 : (4000 mi.) 3 : : 2000 Ibs. : x = 1580+ Ibs. 

 The weight of bodies below the surface of the earth de- 

 creases as the distance increases. Ex. : What would the above 

 body weigh if carried 2 , ooo miles below the surface ? I , ooo Ibs. 

 i , ooo m iles below ? i , 5 oo Ibs. 



40. At what distance above the surface of the earth will a 

 body fall, the first second, 2 1 \ inches ? 



A body falls 16 ft.* (192 inches) at the surface of the earth. 21 1 / 3 inches are 

 : /9 of 192 inches : Now as the attraction is inversely as the square of the dis- 

 tance, the distance must be v/9, or 3 times that at the surface. Hence the body 

 must be 12,000 miles from the centre, or 8,000 miles from the surface of the 

 earth. The problem may be solved directly by proportion, thus : 



a 2 : 4000 2 : : 192 inches : 21 Vs inches. 



* = 12000 miles (distance from the centre) 



12000 miles 4000 miles =8000 miles. 



41. How far will a body fall in 8 seconds? 1,024 ft. In 

 the %th second? 240 ft. In 10 seconds? 1,600 ft. In th* 

 30^ second? 944 ft. 



* According to the best authorities the distance is more exactly 16 l /ir ft. 



