EXAMPLES. 81 



4. If a piece of wood whose vertical height is 2 ft. be 

 placed in the Dead Sea, how many inches will it become 

 submerged, the densities of the wood and Dead Sea water 

 being .53 and 1.24 respectively ? Ans. 10.26 ins. 



5. Find the depth to which a rectangular block will sink 

 in water, the depth of the block being a feet, and the weight 



of each cubic foot of it being w Ibs. aw 



Ans. -> 

 62.5 



6. A barge of a rectangular shape is I ft. long, b ft. broad, 

 and a ft. deep, outside measure. The thickness of the 

 planking is e ft., and the weight of a cubic foot of the tim- 

 ber is w Ibs. To what depth will the barge sink when 

 loaded with W Ibs. ? 



w[abl-(a-e)(b-2e)(l-2e)} + W 

 62. 5W. 



7. A cylindrical piece of wood, weight W, floats in water 

 with its axis vertical and immersed to a depth li. Find 

 how much it will be depressed by placing a weight w on the 



to P ofiL Ans li 



.!/(>. ^JJ- H* 



w 



8. An isosceles triangle floats in water with its base hori- 

 zontal. .Find the position of equilibrium when the base is 

 above the surface, its height being k and its density being 



4 that of water. h /= 



Ans. -y6. 



o 



9. A rectangular barge, I ft. long, b ft. broad, and a ft. 

 deep, outside measure, sinks to \ its whole depth when un- 

 loaded. Required its weight in Ibs. Ans. 12.5abL 



10. If a rectangular barge sinks to -J of its whole depth 

 when unloaded, and to of its whole depth when loaded, 

 find the load, the weight of the barge being w. Ans. $w. 



11. The diameter of the base of a right cone is 2r, its 

 altitude is Ji, and its density is f that of water. To what 



