Question

A milk truck carries milk with density 64.6 lb/ft³ in a horizontal cylindrical tank with diameter 14 ft. Find the force exerted by the milk on one end of the tank when the tank is full.

Answer 1

The force exerted by the milk on one end of the tank when the tank is full is approximately (2,332,778) lb.

Step-by-step explanation:

The force exerted by the milk on one end of the tank can be calculated using the formula
`\(F = P \cdot A\)` , where (F) is the force, (P) is the pressure, and A is the area. The pressure (P) is given by the formula
`\(P = \rho \cdot g \cdot h\)` , where
`\(\rho\)` is the density of the milk, (g) is the acceleration due to gravity, and \(h\) is the height of the milk in the tank.

Given that the density
`(\(\rho\)` ) is 64.6 lb/ft³, the acceleration due to gravity (g) is (32) ft/s², and the diameter of the tank (d) is 14 ft, the radius (r) is \(7\) ft. Therefore, the height (\(h\)) is also \(7\) ft, as the tank is full. Substituting these values into the formulas, we get \(P \approx 64.6 \cdot 32 \cdot 7\) lb/ft², and
`\(A \approx \pi \cdot 7^2\) ft².` Finally,
`\(F \approx 64.6 \cdot 32 \cdot 7 \cdot \pi \cdot 7^2\) lb`, yielding the force exerted by the milk on one end of the tank.

In conclusion, the force exerted by the milk on one end of the tank when it is full is approximately (2,332,778) lb, obtained by combining the pressure and area calculations. This force is a result of the weight of the milk pressing against the end of the horizontal cylindrical tank.