Pascal's Principle Archives • Nerd Notes

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What we found:

The \( 70 \) \( \text{kg} \) student in the figure balances a \( 1200 \) \( \text{kg} \) elephant on a hydraulic lift. Assume that it is filled with oil, which is incompressible and has a density \( \rho = 900 \) \( \text{kg/m}^3 \). What is the diameter of the piston the student is standing on? Assume each piston has a cylindrical shape, i.e., a circular cross-sectional area. Note: The two pistons are at the same height. Also, the diameter of the wider piston is given in the figure to be \( 2.0 \) \( \text{m} \). \textit{Hint: Refer to your notes on Pascal’s Law and hydraulic lifts which says that the forces are related by:} \[ \frac{F_1}{A_1} = \frac{F_2}{A_2} + \rho gh \]

A diver descends from a salvage ship to the ocean floor at a depth of \(35 \text{ m}\) below the surface. The density of ocean water is \(1.025 \times 10^3 \text{ kg/m}^3\). Calculate the gauge pressure on the diver on the ocean floor. Calculate the absolute pressure on the diver on the ocean floor. The diver finds a rectangular aluminum plate having dimensions \(1.0 \text{ m} \times 2.0 \text{ m} \times 0.03 \text{ m}\). A hoisting cable is lowered from the ship and the diver connects it to the plate. The density of aluminum is \(2.7 \times 10^3 \text{ kg/m}^3\). Ignore the effects of viscosity.

A \(2\)-N force is used to push a small piston \(10\) \(\text{cm}\) downward in a simple hydraulic machine. If the opposite large piston rises by \(0.5\) \(\text{cm}\), what is the maximum weight the large piston can lift?

The figure shows a horizontal pipe with sections with different cross-sectional areas. Small tubes extend from the top of each section. The cross-sectional area of the pipe at location C is half that at A, and the areas at A and D are the same. Water flows in the pipe from left to right. Which of the following correctly ranks the height \( h \) of the water in the tubes above the labeled locations?