FIND: The buoyant force on the house. 

 SOLUTION : The buoyant force is given by 



F s = Pg V 



F R = 1,026 kilograms per cubic meter 



(9.81 meters per second squared) (225 square 

 meters) (2 meters) 



F D = 4.53 x 10 6 kilogram-meters per second squared 



D 



F D = 4.53 x io 6 newtons (1.02 x 10 6 pounds) 



D 

 ************************************* 



************** EXAMPLE PROBLEM 22 ************* 



GIVEN: An empty oil storage tank is 3 meters high and 6.1 meters in 

 diameter. Assume that the tank has a mass of 3,180 kilograms (7,000 

 pound-mass), and that it is filled to a depth of 2.5 meters (8.2 feet) 

 with oil having a specific gravity of 0.88 (density p = 880 kilograms 

 per cubic meter). The tsunami water depth is 1.8 meters. 



FIND : 



(a) The buoyant force on the tank, and 



(b) the force holding the tank in place. 

 SOLUTION : 



(a) The buoyant force is given by 



F g = pg V 



F B = 1, 026(9. 81)(J)(6. 1) 2 (1. 8) 



= 5.29 x io 5 kilogram-meters per second squared 

 F = 5.29 x io 5 newtons (1.19 x IO 5 pounds) 



D 



(b) The force holding the tank in place is the mass, M, of the 

 empty tank multiplied by g plus the volume of oil multiplied by its 

 density and g, so that 



F = 3,180(9.81) + 880(9. 81)(j)(6. 1) 2 (2.5) 



F = 6.62 x IO 5 newtons (1.49 x IO 5 pounds) 



173 



