Answer to Question #272772 in Classical Mechanics for joseph

Question

1. A 3-m-diameter, 7-m-long cylindrical tank is completely filled with water. The tank is pulled by a truck on a level road with the 7-m-long axis being horizontal. Determine the pressure difference between the front and back ends of the tank along a horizontal line when the truck (a) accelerates at 3 m/s² and (b) decelerates at 4 m/s².

2. A 30-cm-diameter, the 90-cm-high vertical cylindrical container is partially filled with 60-cm-high water. Now the cylinder is rotated at a constant angular speed of 180 rpm. Determine how much the liquid level at the center of the cylinder will drop as a result of this rotational motion.

3. A 4-m-diameter vertical cylindrical milk tank rotates at a constant rate of 15 rpm. If the pressure at the center of the bottom surface is 130 kPa, determine the pressure at the edge of the bottom surface of the tank. Take the density of the milk to be 1030 kg/m³.

Answer 1

$\omega=\frac{2\pi \nu}{60}=18.85~\frac{rad}s,$

$h'=h\frac{\omega^2d^2}{16g}=0.4~m,$

$\Delta h=h-h'=0.2~m.$