A cylindrical tank of radius 8 m and height 18 m is filled with a liquid whose density is 3.16 kg/m³. How much work is needed to lift the liquid out of the tank? A) 102,927.623 J B) 5,738.201 J C) 1,008,690.707 J D) 126,086.338 J E) 321,076.224 J

Question

Quizplus · Accepted Answer

The work done in lifting the liquid out of the tank is equal to the gravitational potential energy gained by the liquid. The gravitational potential energy is given by the formula:

Potential Energy = mgh

Where m is the mass of the liquid, g is the acceleration due to gravity, and h is the height to which the liquid is lifted.

We can find the mass of the liquid by multiplying its density by its volume. The volume of the liquid is the same as the volume of the cylinder:

Volume = πr²h = π(8m)²(18m) = 3,628.32 m³

Mass = Density x Volume = 3.16 kg/m³ x 3,628.32 m³ = 11,483.64 kg

The height to which the liquid is lifted is equal to the height of the cylinder, which is 18 m.

Therefore, potential energy = mgh = 11,483.64 kg x 9.81 m/s² x 18 m = 2,038,935.843 J

However, we need to subtract the work done to lift the empty tank from the ground to its initial position on the ground. The work done in lifting the empty tank is given by:

Work = mgh = density x volume x g x h = 3.16 kg/m³ x π(8 m)² x 18 m x 9.81 m/s² = 1,030,245.136 J

Therefore, the work needed to lift the liquid out of the tank is:

Potential Energy - Work done to lift empty tank = 2,038,935.843 J - 1,030,245.136 J = 1,008,690.707 J

Hence, the answer is (C) 1,008,690.707 J.

A Cylindrical Tank of Radius 8 M and Height 18