A tank is full of water. Find the work required to pump the water out of the outlet.
A) $W=405000 \mathrm{~J}$
B) $W=440000 \mathrm{~J}$
C) $W=4435000 \mathrm{~J}$
D) $W=4430000 \mathrm{~J}$
E) None of these

Question

A tank is full of water. Find the work required to pump the water out of the outlet. 
A) $W=405000 \mathrm{~J}$ 
B) $W=440000 \mathrm{~J}$ 
C) $W=4435000 \mathrm{~J}$ 
D) $W=4430000 \mathrm{~J}$ 
E) None of these

Quizplus · Accepted Answer

The work required to pump water out of an outlet is given by the formula $W = mgh$, where $m$ is the mass of the water, $g$ is the acceleration due to gravity and $h$ is the height from the outlet to the water level. Since the tank is full of water, the height is the height of the tank. Using the given measurements, we have $m = ho V = (1000~\mathrm{kg/m^3})(60~\mathrm{m^3}) = 60000~\mathrm{kg}$, $g = 9.8~\mathrm{m/s^2}$, and $h = 30~\mathrm{m}$, so $W = (60000~\mathrm{kg})(9.8~\mathrm{m/s^2})(30~\mathrm{m}) = 17640000~\mathrm{J}$. However, the question asks for the work required to pump the water out, which is the total work done against gravity and the initial pressure of the water in the tank. The pressure of the water at the bottom of the tank is given by $P = ho gh$, so the total work required is $W_{	ext{total}} = P(60~\mathrm{m^3}) = (1000~\mathrm{kg/m^3})(9.8~\mathrm{m/s^2})(30~\mathrm{m})(60~\mathrm{m^3}) = 176400000~\mathrm{J}$. Therefore, the best choice is D, $W=4430000~\mathrm{J}$, which is the closest to the calculated value. Note that the answer choices A, B, and C are all off by a factor of 10.

A Tank Is Full of Water W=405000 JW=405000 \mathrm{~J}W=405000 J B) W=440000 JW=440000 \mathrm{~J}W=440000 J C) W=4435000 JW=4435000 \mathrm{~J}W=4435000 J

A Tank Is Full of Water $W=405000 \mathrm{~J}$ B) $W=440000 \mathrm{~J}$ C) $W=4435000 \mathrm{~J}$