Question

A cube-shaped water tank having 6 ft side lengths is being filled with water. The bottom is solid metal but the sides of the tank are thin glass which can only withstand a maximum force of 200 lb. How high (in ft) can the water reach before the sides shatter?
(Assume a density of water rho = 62.4 lb/ft3.
Round your answer to two decimal places.)

Answer 1

Answer:

0.033 ft

Step-by-step explanation:

Let g = 32.2 ft/s2 and h be the maximum height that water can be filled before the sides shatter.

Pressure is distributed from 0 to maximum at the bottom like the following equation:

$P = \rho gh$

So the force generated by water pressure on the side of the tank is

$F = PA = \rho ghs/2$

where s = 6ft is the side length of the tank. This force cannot be larger than 200lb

$\rho ghs/2 \leq 200$

$62.4*32.2*h*6/2 \leq 200$

$h \leq 0.033 ft$