MathProdigy From: US Posts: 11 Votes: 33 |
A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying horizontally on its side. (In other words, the tank is not standing vertically on one of its flat ends.) If the radius of the cylinder is 1 meters, its length is 3 meters, and its top is 4 meters under the ground, find the total amount of work needed to pump the gasoline out of the tank. (The density of gasoline is 673 kilograms per cubic meter; use g= 9.8m/s2 work = (include units) |

Anonymous From: - Posts: - Votes: - |
The volume of the tank is: V = pi * r^2 * h V = pi * 1.5^2 * 2 V = 4.5*pi m^3 If the tank is full, the mass of the gasoline is: 673 * 4.5*pi = 3028.5*pi kg The weight of the gasoline is: 3028.5*pi * 9.8 = 29679.3*pi Newtons The average (underground) depth of the gasoline is 5 + 1.5 = 6.5 Work = Force * Displacement W = 29679.3 * 6.5 W = 192,915.45 Joules |

MythBrainy From: US Posts: 23 Votes: 92 |
Radius of the cylinder is 1.5 meters, its length is 2 meters, and its top is 5 meters under the ground I assume the tank is initially full and you need the work to empty it and get the fuel toground level. The centre of gravity (useful concept that!) of the fuel in the full tank is the tank centre line. Its distance below ground is 5 + 1.5 = 6.5m Mass of fuel = π x (1.5)² x 2 x 673 = 9514 kg Work required = weight x height = mass x g x height = 9514 x 9.81 x 6.5 = 600.3 k.Joules |

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