Question

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 0.5 meters, its length is 5 meters, and its top is 2 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=9.8 m/s2.)

Answer 1

The total amount of work needed to pump the gasoline out of the tank is 41343.04 J.

Step-by-step explanation:

To find the total amount of work needed to pump the gasoline out of the tank, we need to calculate the gravitational potential energy of the gasoline.

The volume of the tank is given by the formula V = πr^2h, where r is the radius of the cylinder and h is its length. Substituting the given values, we have V = π(0.5)^2(5) = 3.14 m^3.

The mass of the gasoline is given by the formula m = ρV, where ρ is the density of gasoline. Substituting the given density, we have m = (673 kg/m^3)(3.14 m^3) = 2110.22 kg.

The work done in pumping the gasoline out of the tank is given by the formula W = mgh, where g is the acceleration due to gravity and h is the height of the gasoline above the ground. Substituting the given values, we have W = (2110.22 kg)(9.8 m/s^2)(2 m) = 41343.04 J.

Therefore, the total amount of work needed to pump the gasoline out of the tank is 41343.04 J.